{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[16, -21, 25, -15, -12, -33, -14, 17, -34, -6, 2, -34],\n [0, 24, -15, -3, 22, -14, 13, 23, 6, 24, -21, 26],\n [0, 0, 26, 15, 19, 28, -33, 15, -29, -15, 3, -18],\n [0, 0, 0, -27, 17, -34, 24, 35, 8, -28, 11, -1],\n [0, 0, 0, 0, -30, 18, -32, 18, 27, -18, 8, -2],\n [0, 0, 0, 0, 0, 4, 17, -12, -10, 24, 5, -7],\n [0, 0, 0, 0, 0, 0, -28, 27, -25, -28, -1, -1],\n [0, 0, 0, 0, 0, 0, 0, -3, 12, -13, 26, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, -9, -27, -21, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -23, -4, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4811", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -12, 23, -4, 16, 26, 22, 16, -24, 3, -34, -33],\n [0, 23, -34, -34, 18, -35, -17, -34, 17, 8, -4, 34],\n [0, 0, 19, 20, -19, 2, -12, 33, 34, -25, -20, 23],\n [0, 0, 0, 23, 0, -17, 31, -17, -16, 35, 16, -3],\n [0, 0, 0, 0, 21, 14, -13, -5, 6, -29, -20, 24],\n [0, 0, 0, 0, 0, 1, -4, -27, -17, 12, -33, -16],\n [0, 0, 0, 0, 0, 0, -11, -18, 30, 18, -1, 25],\n [0, 0, 0, 0, 0, 0, 0, -16, -28, -29, 31, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, -28, -9, -9, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 13, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "791", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, -34, -19, -3, -27, 7, 12, 3, 6, -10, 14, -11],\n [-12, -23, 24, -29, 21, 0, 9, -16, 29, -28, -20, -22],\n [-21, 30, -4, 27, 15, -11, 22, 27, 26, -14, 22, 22],\n [13, 16, 6, 34, -21, 18, 24, -28, 17, 24, -31, 32],\n [-30, 11, 19, 4, 16, -20, -23, -6, -17, -19, 27, -17],\n [22, 19, 26, -13, -27, -24, -35, 22, -35, -2, 12, -35],\n [-20, 25, 28, 27, 33, -14, 31, -10, -20, 15, 21, -7],\n [33, 11, 26, 33, -20, 12, 3, -3, -13, -26, 33, -2],\n [16, -26, -17, 22, -35, 33, -32, -20, -12, -34, -4, -12],\n [-24, 14, -1, -3, -3, 25, 15, 7, -24, 31, 29, -3],\n [4, 7, 8, -7, -23, -24, 10, -34, -1, -28, -10, -2],\n [-29, 32, 22, -7, 0, -15, 0, -26, -12, 28, 13, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1645", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (2, 10) rounded to the nearest integer?\n[[-12, -13, 26, 1, -24, 19, -23, -13, -6, -19, 26, -23],\n [0, -17, 13, -24, 25, -17, -27, 35, -8, 16, -20, 33],\n [0, 0, 16, 17, -13, -20, 21, 3, 17, 6, 22, 3],\n [0, 0, 0, -18, -27, 22, -19, -29, 10, -23, 4, 6],\n [0, 0, 0, 0, -31, -7, 1, 2, -28, 29, -19, 35],\n [0, 0, 0, 0, 0, -17, 25, 18, 3, -17, 3, 31],\n [0, 0, 0, 0, 0, 0, -35, -33, 26, 27, -11, 20],\n [0, 0, 0, 0, 0, 0, 0, 9, 25, 11, -15, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, -5, -35, 18, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 24, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8679", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-25, -10, 27, 23, -9, 13, -3, -35, -15, 19, -30, 33],\n [-31, -33, 17, -13, 17, 1, -19, -35, 15, 9, -32, 26],\n [29, -4, -2, 3, -10, -2, 18, -33, 14, -24, 29, 18],\n [-31, 21, -19, 11, -13, -22, 30, 15, 2, 28, 2, 14],\n [-6, 15, 27, 16, 2, -6, 15, -31, -7, -32, -26, 20],\n [-19, -19, 33, -2, -30, 17, 30, 7, -13, 19, -20, -28],\n [-32, -32, 20, -11, 31, 31, -9, -4, 14, 25, 15, -17],\n [-15, -31, 6, 25, -14, -15, 34, -35, -31, -24, 10, -2],\n [13, 9, -9, -10, 11, 20, 27, 12, 25, -10, 0, -35],\n [-28, 16, 11, 20, -22, -8, -34, -10, -22, 23, 20, -29],\n [-33, -13, -18, 2, -21, 28, -8, 3, 21, -19, 8, -11],\n [-19, -23, -11, 32, -26, 31, -18, -2, -28, 4, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5779", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-30, 16, -10, 28, 23, 20, 23, 34, -3, 17, -14, -15],\n [34, 34, -32, 26, 26, -12, 19, -27, -33, -5, 4, 0],\n [-12, -30, 30, -32, -30, 15, 26, 21, 30, -28, -10, 15],\n [9, 8, -31, 34, -10, 32, -17, -16, -24, 11, -35, -22],\n [28, 2, 1, -25, -33, -3, -30, 14, -26, -31, -13, -26],\n [8, -34, -23, 4, -34, 29, 27, -19, -27, -21, -12, 2],\n [-1, 13, 33, 26, 24, 14, -27, -2, -1, -35, 4, 28],\n [-14, 24, 28, -25, -22, 24, -6, -1, 1, -31, -10, 26],\n [-32, 6, -18, 4, 3, -22, -4, 15, 2, -13, 27, -21],\n [-11, -19, 30, 17, 15, 3, 15, 34, -30, 31, -29, 15],\n [6, 28, -21, -7, -3, -9, 0, -7, 2, 21, -9, 19],\n [-3, 32, 30, -26, -31, 2, -23, -5, 11, 16, 20, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1324", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-7, -28, -31, -7, 11, 32, 9, -34, -9, 0, 0, -10],\n [0, -9, 33, -16, -25, 2, -30, -13, 11, 10, -24, -23],\n [0, 0, 7, 32, -31, 1, -5, -27, 15, -7, 4, 5],\n [0, 0, 0, 10, -15, 0, 18, 21, -35, 27, 18, 19],\n [0, 0, 0, 0, 17, -27, 16, 21, -10, 5, -1, 27],\n [0, 0, 0, 0, 0, -19, 7, 23, 15, 18, -12, -11],\n [0, 0, 0, 0, 0, 0, 27, -14, -10, -8, 13, 35],\n [0, 0, 0, 0, 0, 0, 0, -23, 15, 20, 26, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, -18, -35, 11, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -26, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "683589", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-29, -29, -3, -13, -17, -17, 0, -7, 24, -34, -35, 11],\n [33, -16, -25, -34, 31, -24, -16, -31, 1, 2, -27, 17],\n [8, -12, -6, 23, -22, -27, 4, 30, -11, -14, -32, -10],\n [22, -7, 1, 34, -18, 6, 5, 2, -2, -19, 1, -11],\n [-9, 21, -5, -30, 4, -24, 17, 35, -26, 9, -19, -10],\n [26, 10, 28, -34, 18, 29, 15, 17, 0, -10, -7, -15],\n [-25, 4, -25, 0, 23, 3, 18, 19, -12, -14, 33, 20],\n [-3, 0, -16, 26, -10, 30, 4, -19, -35, 25, 7, 6],\n [-11, 3, -1, -33, 8, 15, -24, -17, 8, 23, 13, 25],\n [-19, 21, 19, 11, -24, 26, -28, -15, 34, -11, -24, -21],\n [23, -10, -10, 11, -4, -26, -20, 35, -19, -13, -10, -29],\n [-22, -29, -27, 12, 23, 3, -18, 23, -19, -22, -5, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1733", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[24, 9, -33, 1, 7, 4, 19, 3, -21, -32, -11, -23],\n [-3, -20, 6, 30, 19, 6, -2, -6, -23, -23, -18, -4],\n [3, 10, -7, 26, 26, 21, -20, 20, -26, -6, -11, -31],\n [29, 13, -33, 9, -22, -6, 32, -18, 26, 1, -11, 12],\n [29, 17, -21, 13, 32, -24, 23, 1, 25, 7, 34, 3],\n [20, 27, 10, -25, 26, -11, 35, 16, -32, 23, -16, 27],\n [18, 21, 5, -33, -30, -31, -31, 18, 11, 13, -27, -16],\n [25, -1, 14, 26, -19, -33, -4, -23, 32, -22, -25, 20],\n [31, -7, -27, 31, -11, 6, -27, 4, -11, -31, -25, 23],\n [2, -31, 12, -18, 34, 1, 24, 12, -8, 33, 4, 9],\n [26, 22, 31, 20, 4, 4, -3, -30, -17, 4, 23, 23],\n [12, 5, -23, 9, 17, 6, 27, -9, 2, 24, -29, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2050", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -1, 15, -14, -12, -24, -10, 8, -12, 14, 11, -14],\n [-1, 3, 28, -21, 2, -3, -4, 24, 22, -17, 0, -17],\n [15, 28, -8, -1, -12, -18, 28, -8, 2, 6, -22, -24],\n [-14, -21, -1, 29, -8, 4, -26, 28, 1, 2, 14, 16],\n [-12, 2, -12, -8, -30, -6, -1, 6, 0, -6, -11, -14],\n [-24, -3, -18, 4, -6, -4, -6, 0, 0, -10, 6, 0],\n [-10, -4, 28, -26, -1, -6, 33, -28, 0, 28, 15, -6],\n [8, 24, -8, 28, 6, 0, -28, -18, -27, -14, 13, 3],\n [-12, 22, 2, 1, 0, 0, 0, -27, 28, -10, 6, 3],\n [14, -17, 6, 2, -6, -10, 28, -14, -10, 2, -6, 4],\n [11, 0, -22, 14, -11, 6, 15, 13, 6, -6, 9, -3],\n [-14, -17, -24, 16, -14, 0, -6, 3, 3, 4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-112", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, -34, -3, -6, -3, -10, -14, 30, 2, 10, -21, 8],\n [13, 25, 31, -30, -27, -30, -4, 5, -28, 14, 26, 26],\n [-29, -32, -30, 22, -14, -10, -33, 5, 24, -22, -24, -24],\n [-23, -11, 9, -17, 19, 9, -28, 17, 19, -4, 15, 8],\n [34, -18, -14, 1, 20, 23, -33, -8, -1, 25, 18, 27],\n [-29, 13, -5, 22, 25, -12, -16, 1, -32, -16, 24, -12],\n [14, 13, 15, 0, 30, -2, 0, -30, 3, 6, 22, -24],\n [-33, -18, 4, -15, -21, -10, -28, 6, 8, -22, -34, 1],\n [33, 2, 5, 26, 24, -22, -34, 34, -19, -8, 30, -1],\n [-31, 29, 4, 20, 0, 9, -13, 11, -5, -25, -26, 31],\n [-22, -26, -35, -31, -16, -28, 7, -35, 21, 28, -8, 1],\n [11, 1, 13, 8, 20, -8, -30, 25, -16, -34, 1, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-109", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-10, -7, -35, -1, 34, 23, 33, -3, 15, -24, -16, 17],\n [7, 14, -7, 21, 3, 20, 7, 14, -13, 8, 2, -13],\n [9, 16, 14, -28, -35, -28, -7, -31, 11, -2, 29, 19],\n [7, -6, -19, -10, -28, 11, 10, 32, -3, -35, -17, -5],\n [-22, 17, 12, 33, 26, 30, 28, 34, 27, -3, 5, 12],\n [-23, -5, 32, -32, -17, 34, -23, -13, -35, 18, 35, -21],\n [29, 35, -21, -15, -17, 24, -3, 13, -1, 8, -25, 30],\n [10, -27, -33, -10, 12, 30, 34, -8, -10, -11, -24, -31],\n [12, 1, 8, -21, 7, 12, 34, 10, 7, -15, -13, 11],\n [-21, -11, 0, 15, -21, 32, -15, -23, -17, -2, 32, 16],\n [-9, -7, -8, -1, -28, -20, 0, -6, -18, -34, 13, -32],\n [-29, 3, -23, -5, 35, 27, 20, 6, 25, 6, 20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-134", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[32, -28, 21, -12, 4, 8, 18, 0, -7, -20, -16, 8],\n [-28, -21, -12, 4, -20, 4, -22, -16, 32, -7, -8, -15],\n [21, -12, -18, -19, -9, 11, 28, 22, 4, -18, -18, -12],\n [-12, 4, -19, -1, 33, -2, -28, -30, 16, -16, -16, 30],\n [4, -20, -9, 33, 6, 2, 6, -2, 22, 2, -20, 26],\n [8, 4, 11, -2, 2, -33, -18, 0, 16, 10, -12, -8],\n [18, -22, 28, -28, 6, -18, -4, -8, -17, -8, 9, 4],\n [0, -16, 22, -30, -2, 0, -8, -6, -4, 8, 19, 4],\n [-7, 32, 4, 16, 22, 16, -17, -4, -20, -15, -26, -6],\n [-20, -7, -18, -16, 2, 10, -8, 8, -15, -15, 32, -18],\n [-16, -8, -18, -16, -20, -12, 9, 19, -26, 32, 31, 20],\n [8, -15, -12, 30, 26, -8, 4, 4, -6, -18, 20, -24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "580", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[13, 6, 2, 9, -1, -6, -6, -30, 31, -29, 16, -22],\n [-21, -15, -1, 30, -34, -1, -16, -26, -11, 30, -11, 18],\n [-3, 0, -22, 29, 18, 16, -33, 5, -30, -11, -23, -28],\n [-15, 32, -11, 32, 9, 24, -24, -4, -23, -5, -16, -18],\n [24, 27, -30, -4, 7, -34, 24, -13, -5, -31, -2, -26],\n [-34, -25, 14, -5, 20, -27, -15, -8, 26, -29, -20, -32],\n [-32, 4, -19, 16, 16, 0, 2, 14, 27, 27, 26, -29],\n [-9, -22, 35, -31, 19, -34, 26, -15, -15, -26, 22, 3],\n [-31, 29, -23, 17, 9, -4, 0, 24, -25, 27, -15, 16],\n [19, -10, 32, -2, 16, 16, -7, 2, 6, -15, 6, -23],\n [28, -19, -27, 5, -35, -34, 24, 12, -7, -26, 22, 24],\n [-15, -8, -2, -28, 23, 13, -19, 24, 9, 33, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-59", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[29, -16, -10, -30, -6, 2, -1, -16, -18, -21, -18, 5],\n [-16, -25, 9, -18, -25, 1, -7, 15, -14, -23, -15, 9],\n [-10, 9, -28, -6, 6, 0, 9, 0, -6, 21, 11, 14],\n [-30, -18, -6, -24, -15, -14, 2, 2, -24, -6, -10, -4],\n [-6, -25, 6, -15, -18, 11, -12, 12, 4, 12, -6, -10],\n [2, 1, 0, -14, 11, -24, 2, 4, -18, -9, 10, -13],\n [-1, -7, 9, 2, -12, 2, -23, -7, -21, -4, 6, 12],\n [-16, 15, 0, 2, 12, 4, -7, -33, -2, -22, 4, -20],\n [-18, -14, -6, -24, 4, -18, -21, -2, -33, 14, -32, 26],\n [-21, -23, 21, -6, 12, -9, -4, -22, 14, 22, -7, -2],\n [-18, -15, 11, -10, -6, 10, 6, 4, -32, -7, -16, -8],\n [5, 9, 14, -4, -10, -13, 12, -20, 26, -2, -8, -16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (6, 10) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-19, 35, -32, -22, -33, 22, 19, -32, -12, -2, -6, -17],\n [0, 24, 24, -17, 13, 27, -14, -12, -6, 22, -5, 28],\n [0, 0, 9, 19, 19, -18, 27, 11, 21, 9, -3, -19],\n [0, 0, 0, 11, -21, 34, 11, -27, -20, 33, 25, -26],\n [0, 0, 0, 0, -17, 6, -1, 10, -10, 33, 28, 1],\n [0, 0, 0, 0, 0, -32, 3, -1, -35, -12, 21, 34],\n [0, 0, 0, 0, 0, 0, -5, -12, 0, -6, -12, -6],\n [0, 0, 0, 0, 0, 0, 0, 34, 8, 9, 20, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, -16, -21, 12, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -33, 1, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-14, 21, 30, -20, 15, 3, 4, 2, 24, 23, -26, 28],\n [0, 13, 28, -4, -29, -15, -16, -10, 32, -21, -22, -9],\n [0, 0, -8, -10, 27, 30, -11, -33, 8, 6, -30, 3],\n [0, 0, 0, 7, -17, 33, 15, -25, -24, -28, -12, 5],\n [0, 0, 0, 0, -21, 12, 6, 24, 34, -24, -34, -29],\n [0, 0, 0, 0, 0, -35, -28, -4, 12, -32, 34, -17],\n [0, 0, 0, 0, 0, 0, -35, 27, -15, -6, -23, -2],\n [0, 0, 0, 0, 0, 0, 0, 32, -11, -16, -2, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 30, 11, -33, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 22, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104347", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[11, 2, -21, 27, -15, 21, 17, 10, -22, -19, 3, -27],\n [0, -13, 23, 10, 2, -22, 26, -1, -17, -6, -11, 4],\n [0, 0, -14, 12, 15, -33, 6, -17, -8, 9, 35, 27],\n [0, 0, 0, 2, 17, 25, 0, 4, -6, -27, 28, -3],\n [0, 0, 0, 0, 5, 32, 32, -28, -34, 5, 19, -20],\n [0, 0, 0, 0, 0, -25, 28, 14, -15, 33, 12, -16],\n [0, 0, 0, 0, 0, 0, -1, 29, -28, 9, 11, 4],\n [0, 0, 0, 0, 0, 0, 0, -14, -15, 15, 2, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 9, 31, 30, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -9, -28, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248736411", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-19, -15, 15, 23, 3, 19, 5, 3, -23, 28, -25, -17],\n [-25, 10, 9, -35, 4, -17, 25, -24, 25, -3, 9, 33],\n [-28, -11, 10, -6, 11, 13, 11, -18, 30, 32, -3, 0],\n [-17, -8, 4, -21, 5, 3, -34, 27, -7, 30, 15, -26],\n [-22, 15, 3, -8, -33, 34, -9, -34, 2, -33, -20, 4],\n [-34, 5, -24, -1, 29, 19, 9, 26, 13, -11, -13, -12],\n [2, -8, -15, 18, -18, 0, 9, 17, -6, 24, -4, 31],\n [31, -8, 8, 5, 27, -13, 12, -4, 21, -3, -12, 3],\n [-2, 20, -8, 1, -29, 32, 1, 20, 29, 29, 11, -16],\n [-17, -7, 24, -18, -1, 7, -25, 13, 2, 28, 33, -28],\n [-2, 12, 20, 29, -5, -32, 14, 33, -6, 23, 31, 9],\n [-32, -10, -9, 10, 28, 15, 14, -30, 23, -21, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6203", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[1, 20, -8, -24, 22, -18, 4, 27, 8, -18, -18, 2],\n [20, 1, 10, -11, -13, 4, 16, -5, 17, -16, 8, 4],\n [-8, 10, -25, 2, -25, 20, 2, 5, -20, 2, -21, -1],\n [-24, -11, 2, -8, -28, -2, 6, -20, 29, 5, -5, -12],\n [22, -13, -25, -28, -31, 27, -24, 8, 8, -15, 2, -12],\n [-18, 4, 20, -2, 27, 19, -16, 26, -12, -25, 8, -2],\n [4, 16, 2, 6, -24, -16, -1, 4, 4, 7, -4, -10],\n [27, -5, 5, -20, 8, 26, 4, -14, 14, 30, 9, -1],\n [8, 17, -20, 29, 8, -12, 4, 14, -6, 10, 5, 4],\n [-18, -16, 2, 5, -15, -25, 7, 30, 10, -11, 16, -18],\n [-18, 8, -21, -5, 2, 8, -4, 9, 5, 16, 27, -2],\n [2, 4, -1, -12, -12, -2, -10, -1, 4, -18, -2, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, 30, 4, -19, -2, -20, 24, 30, 30, -23, 20, -5],\n [0, 3, 31, -28, 19, -9, 17, 3, 29, -19, -6, 17],\n [0, 0, -17, 17, -17, 21, -11, -5, 19, -13, -4, 26],\n [0, 0, 0, -16, -4, -22, 14, -8, 17, -12, -14, -6],\n [0, 0, 0, 0, -24, -5, -2, 13, 21, -10, -18, 2],\n [0, 0, 0, 0, 0, 8, 28, -7, -8, -25, 29, -17],\n [0, 0, 0, 0, 0, 0, 15, -23, 13, 34, 20, 15],\n [0, 0, 0, 0, 0, 0, 0, -26, 11, -13, -15, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, -24, 1, 6, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -34, -20, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-26, 8, 0, -9, 6, -10, -17, 12, -10, -34, -5, -16],\n [8, -11, -26, -15, -26, 19, -19, 7, -7, -20, 22, 26],\n [0, -26, 11, 10, 0, 16, 8, 17, 18, -15, 14, -24],\n [-9, -15, 10, 19, 22, -25, -2, -14, -18, 8, -3, 11],\n [6, -26, 0, 22, -32, 14, 5, 2, 1, 2, -3, 2],\n [-10, 19, 16, -25, 14, -8, 9, -14, 28, 24, -2, -6],\n [-17, -19, 8, -2, 5, 9, -8, -1, -8, -7, -1, -5],\n [12, 7, 17, -14, 2, -14, -1, 16, 10, -6, -2, -10],\n [-10, -7, 18, -18, 1, 28, -8, 10, 26, 30, 14, -26],\n [-34, -20, -15, 8, 2, 24, -7, -6, 30, 5, -15, 30],\n [-5, 22, 14, -3, -3, -2, -1, -2, 14, -15, -30, -12],\n [-16, 26, -24, 11, 2, -6, -5, -10, -26, 30, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2134", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[23, 8, -27, 1, 0, -8, 6, 7, 6, 30, 19, 12],\n [0, -9, 31, -23, 9, -26, -27, 18, -9, -2, -35, -4],\n [0, 0, -16, -1, -19, -18, 9, 17, 32, 29, -35, 22],\n [0, 0, 0, 23, 5, -31, 29, -19, -14, 5, 32, 33],\n [0, 0, 0, 0, -10, -17, 24, 35, 11, 35, -10, 4],\n [0, 0, 0, 0, 0, -28, 5, -17, 10, -8, 32, -21],\n [0, 0, 0, 0, 0, 0, 27, 25, 0, -12, -12, -32],\n [0, 0, 0, 0, 0, 0, 0, 17, 26, 5, 21, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, -33, 15, 11, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -11, -9, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[27, 15, 0, 30, -21, 3, 34, -35, -13, 3, 21, -2],\n [0, -23, 34, -30, 16, -33, 27, 13, 11, 19, 28, 29],\n [0, 0, -4, 32, -18, 7, -1, 22, -3, -22, -2, 25],\n [0, 0, 0, -30, 13, 4, 29, 33, -9, -30, -23, 28],\n [0, 0, 0, 0, 32, 8, -13, -34, -14, 21, -29, 20],\n [0, 0, 0, 0, 0, -31, -9, -24, -19, -30, -31, 21],\n [0, 0, 0, 0, 0, 0, -17, 33, 30, 11, 3, 32],\n [0, 0, 0, 0, 0, 0, 0, -16, -7, -12, 27, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, -8, 26, 5, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -14, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "563456", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[32, 29, -10, -26, 17, 23, -14, 15, 12, -15, -14, -6],\n [-11, -8, 29, 9, 32, -29, 13, -27, 0, -35, -26, 0],\n [10, -4, -4, -30, 12, 2, -19, -9, 18, 14, -1, -11],\n [-8, -21, -32, -9, -10, -17, -19, 7, 5, 6, 14, 4],\n [3, -13, 16, 11, 27, 33, 7, 12, -2, 4, 25, 14],\n [31, 26, 22, -3, -20, 12, -26, 2, -17, 0, 23, 27],\n [10, -33, 29, -28, 15, -30, 3, 24, -8, 18, 1, -27],\n [20, 23, -34, 25, 22, 24, 4, 0, 1, -18, 27, -14],\n [-25, 22, 21, -32, -29, 25, 18, 32, -35, 19, -33, 2],\n [-35, 2, -7, -31, -15, 35, 31, 11, -1, 32, 33, -35],\n [32, -24, 24, -9, 20, -13, -11, -15, 25, 27, 16, -11],\n [19, 10, -4, 19, -31, 0, 13, 22, 3, 25, -27, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-627", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 11) of the inverse of matrix 1/839 * A where A =\n[[-1, 0, -4, -11, -33, -8, 19, 0, 16, 7, 12, -6],\n [0, 10, -20, 10, -10, 32, -20, -2, -10, 5, 6, -8],\n [-4, -20, 0, -2, 2, -18, -15, 23, 2, -6, 9, -6],\n [-11, 10, -2, 26, -2, 22, -2, 2, 6, 12, -9, -26],\n [-33, -10, 2, -2, 13, 30, 10, -12, 9, 0, 2, 28],\n [-8, 32, -18, 22, 30, -29, 6, 22, 14, 6, 10, -5],\n [19, -20, -15, -2, 10, 6, -20, -3, 24, 10, -7, 28],\n [0, -2, 23, 2, -12, 22, -3, 9, -24, -1, 0, 10],\n [16, -10, 2, 6, 9, 14, 24, -24, -14, -32, 17, 11],\n [7, 5, -6, 12, 0, 6, 10, -1, -32, 18, 0, 16],\n [12, 6, 9, -9, 2, 10, -7, 0, 17, 0, -5, 16],\n [-6, -8, -6, -26, 28, -5, 28, 10, 11, 16, 16, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "723", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[23, 35, -27, -30, -7, 22, -19, -20, -33, -15, 28, 0],\n [26, 6, 6, 25, -23, -25, 18, -20, -28, 23, 21, 4],\n [23, -34, -26, 8, -25, -34, 14, -24, -13, -18, 26, 26],\n [2, 31, 2, 31, 25, -35, 9, -8, -15, -23, -9, -29],\n [-14, 17, -32, -13, 34, -3, -8, -28, -35, 1, 27, -14],\n [34, -15, -1, -31, 24, 10, 14, 12, -30, 20, 23, -7],\n [35, -18, -34, -28, 18, 2, 12, -9, -16, -24, 7, 25],\n [-5, 25, 31, -1, -21, -20, -23, -1, 23, -15, 18, -6],\n [12, -1, 2, -5, -12, 13, -4, 19, 22, -33, 33, -26],\n [-11, 32, 25, -7, -17, 7, 30, 25, 7, -11, -16, 12],\n [-12, -25, 19, -8, 33, 27, 23, -31, 15, -15, -24, 14],\n [-32, 6, 2, -11, -22, -4, -25, 25, -18, -9, 19, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1399", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-15, -6, -14, 12, 16, 20, 0, 16, 20, 22, -6, 4],\n [-6, -14, -2, 0, 2, -7, 10, 9, -2, 24, 13, 2],\n [-14, -2, 2, -14, -18, 2, 0, 25, -11, 23, 24, 2],\n [12, 0, -14, 7, -2, 0, -15, -10, 2, 11, 20, -22],\n [16, 2, -18, -2, 23, -2, -2, -17, 4, -14, -6, -2],\n [20, -7, 2, 0, -2, 13, -2, 28, -13, -2, -16, -26],\n [0, 10, 0, -15, -2, -2, -26, -16, 22, -16, -28, 2],\n [16, 9, 25, -10, -17, 28, -16, 20, 13, -9, 8, -12],\n [20, -2, -11, 2, 4, -13, 22, 13, -14, -5, -12, 1],\n [22, 24, 23, 11, -14, -2, -16, -9, -5, 26, -8, 18],\n [-6, 13, 24, 20, -6, -16, -28, 8, -12, -8, -19, -10],\n [4, 2, 2, -22, -2, -26, 2, -12, 1, 18, -10, 24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-271", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[35, 12, -18, -20, 19, 3, 32, 23, 26, -23, -30, 24],\n [-22, 18, -32, 3, -11, -4, 23, 27, 2, 17, 31, -8],\n [-33, -14, 2, 26, 21, -30, -4, -26, -33, 23, 13, 23],\n [-5, 33, 26, 16, 5, -5, -14, -32, -23, 9, 6, 13],\n [-16, 18, 0, -35, -21, -19, -12, 22, -13, 10, -28, 23],\n [23, -23, 3, -8, 25, -20, -34, -19, -6, -23, -23, 7],\n [-15, 19, 4, -21, 16, 17, 16, -6, -3, 21, 16, -27],\n [18, -35, 8, -27, -4, -21, -24, 21, -28, -9, 26, -24],\n [29, 6, 26, -25, 7, -19, -4, 4, -13, 20, -30, 14],\n [1, 28, 18, 13, -25, 13, -15, 30, 27, -8, -19, -30],\n [-17, 20, -8, 30, 2, 1, 32, 13, 7, 0, 22, -23],\n [16, 22, -4, 24, 22, 20, -8, -35, 6, 12, 4, 27]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3074", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-32, 2, -9, -27, -20, 20, -5, -22, -11, -2, 31, -12],\n [-10, -16, 28, -26, 31, -12, -31, 31, 22, -9, -21, -1],\n [17, 8, -10, 11, -2, 14, -24, -32, 12, 19, -35, 30],\n [-6, -33, -15, 13, 26, 2, -21, 16, 10, -11, -15, -31],\n [34, 11, 32, -18, -15, -13, 28, 31, 4, -26, 16, 25],\n [28, -31, 17, 19, 1, 20, 23, 33, 23, -34, 29, 24],\n [15, -6, -25, 3, 27, 28, 25, 18, 22, 20, -2, -5],\n [16, -35, 19, -14, 4, -35, 29, 27, 18, 6, -15, -14],\n [2, -28, 26, 11, -19, -19, -23, -19, 2, 9, -30, -1],\n [-22, 25, -21, 18, -9, -23, -5, -1, 24, -30, 33, 22],\n [13, -13, -2, -10, 11, -31, -16, -30, 34, 23, 28, -18],\n [-32, -19, -22, -23, -29, 8, -21, -17, 27, -1, -1, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-331", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, -1, -4, 12, 8, -12, 25, -19, 35, 14, 29, -4],\n [0, -23, 34, 22, -22, 1, 32, 4, 23, -20, 26, -32],\n [0, 0, 30, -5, -33, -28, -12, -21, 7, -5, 9, 30],\n [0, 0, 0, -6, -18, 33, 3, 24, 7, 9, -13, 33],\n [0, 0, 0, 0, -30, -4, -18, -21, 4, -30, 27, 31],\n [0, 0, 0, 0, 0, 32, 5, -31, -4, 34, -1, -14],\n [0, 0, 0, 0, 0, 0, -22, -18, -13, 11, 33, 11],\n [0, 0, 0, 0, 0, 0, 0, 12, -26, -25, -15, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, -20, -30, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -29, 27, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11138", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, -8, -4, 12, -13, 7, -3, -20, -2, -4, 19, -4],\n [-8, -34, 6, -26, -24, 4, -7, -12, -6, -6, -14, -14],\n [-4, 6, -14, 15, 24, -17, 9, -4, 0, 16, -2, -3],\n [12, -26, 15, -31, -16, 16, -12, 13, 28, 4, -9, 18],\n [-13, -24, 24, -16, -5, 12, 18, 20, 6, 2, 0, 12],\n [7, 4, -17, 16, 12, -19, -22, -6, 2, 12, 10, -28],\n [-3, -7, 9, -12, 18, -22, 29, 21, 10, 13, -2, -18],\n [-20, -12, -4, 13, 20, -6, 21, -24, 12, -2, 24, 11],\n [-2, -6, 0, 28, 6, 2, 10, 12, -11, -14, 20, -3],\n [-4, -6, 16, 4, 2, 12, 13, -2, -14, -4, 15, -20],\n [19, -14, -2, -9, 0, 10, -2, 24, 20, 15, -12, -18],\n [-4, -14, -3, 18, 12, -28, -18, 11, -3, -20, -18, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2431", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (9, 5) rounded to the nearest integer?\n[[9, -13, -8, 21, -10, -11, 18, -7, 0, -22, -1, -6],\n [0, 31, -6, 9, 15, 11, 17, 28, 2, 28, -29, -14],\n [0, 0, 21, -29, 14, 16, -3, -35, 17, 24, -2, -32],\n [0, 0, 0, -32, -35, 35, 14, 25, -1, -28, -12, 0],\n [0, 0, 0, 0, -18, -8, -7, -20, 11, 23, -5, -32],\n [0, 0, 0, 0, 0, 12, 3, -32, -6, -6, -14, 30],\n [0, 0, 0, 0, 0, 0, 22, -30, 34, 8, -12, -17],\n [0, 0, 0, 0, 0, 0, 0, -27, -15, -7, -3, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 7, 2, 1, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -11, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-1, -30, -24, 2, -17, 31, -28, -28, 11, -32, 15, 31],\n [0, -28, -20, 31, -27, 24, 35, -21, 35, 5, -14, -12],\n [0, 0, -26, 20, 14, -24, 24, -10, 5, 0, -13, 7],\n [0, 0, 0, -11, -18, 26, -23, 7, -8, -18, 23, 24],\n [0, 0, 0, 0, -9, -4, -27, 32, 10, 31, -10, -28],\n [0, 0, 0, 0, 0, 33, -11, -16, 30, 9, 11, 27],\n [0, 0, 0, 0, 0, 0, 9, 8, 29, 15, 7, -13],\n [0, 0, 0, 0, 0, 0, 0, -8, 16, 13, 1, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 19, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -15, 21, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149744", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[5, -30, 2, -30, 9, -22, 30, 4, -33, -12, -17, -18],\n [28, -1, 26, -35, -11, 9, 13, -20, -17, -13, -11, -20],\n [18, -35, 6, -17, -2, 19, -18, -2, 9, -30, -15, 34],\n [12, 3, -5, -26, -6, -18, 24, -21, -32, 27, 4, -27],\n [-27, -10, -32, -20, -21, 16, 33, -31, -16, -18, -34, -23],\n [-32, 6, 25, -28, 31, 27, -27, -25, 6, -23, 0, -23],\n [-24, 1, 16, 35, -34, 20, 24, -13, 4, 28, -13, -7],\n [15, 33, -5, 14, -16, 19, -34, -11, -23, 34, 31, 22],\n [28, 33, 23, 24, 26, -20, 32, -21, 19, -1, 19, -22],\n [13, -29, -6, 13, -20, 15, 6, -19, 27, 9, -29, -9],\n [-26, -2, 0, -11, -30, -12, -18, -30, -7, -11, 19, 10],\n [-12, -10, -8, -33, 2, 25, 15, 12, -15, 18, 20, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1594", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[15, -16, 23, 35, -27, -35, -7, 27, 20, 32, -1, -33],\n [-29, -9, -35, 35, 8, 5, 6, -3, 14, 27, 1, 23],\n [12, -31, 12, -33, 11, 26, -22, 27, 25, -5, -19, -12],\n [-13, 14, 34, -9, -21, 14, 0, -28, -33, 26, 11, 25],\n [-4, -23, -35, -2, 26, 35, -5, 28, -11, 2, -22, -28],\n [18, -34, 20, 25, -14, -1, -20, 14, 7, -19, 22, -34],\n [-32, 3, -30, 33, 33, -16, 28, -20, 15, 1, 33, 6],\n [21, 30, -27, 28, -14, -2, 19, -7, 2, -18, 35, 29],\n [-35, -32, -32, -9, 7, 23, -4, -3, -8, 19, 24, 34],\n [26, -2, 20, -23, 20, -18, 18, 7, 3, 25, 6, -18],\n [-13, 18, -6, 22, 32, 31, 35, -18, -29, 4, 34, 29],\n [32, 13, 16, -7, -15, -27, 11, 6, 15, 20, 15, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-16, -9, 2, 29, 18, -12, 11, 35, 27, 21, 19, 24],\n [26, -6, -14, -7, 5, 6, 29, -5, -6, -18, -19, 2],\n [-22, 20, -14, 31, 20, -17, 21, 8, -1, -35, 16, 34],\n [1, 29, 15, -35, -15, 17, -20, 25, 18, 4, -10, 29],\n [28, 7, -19, 23, -13, -29, 8, 17, 35, -2, 10, 32],\n [-20, 35, -17, -34, -26, 14, -24, 34, -14, -4, -35, 18],\n [22, 34, -18, -30, 9, -13, -13, -10, -29, 8, -9, -10],\n [0, 19, 28, 21, 33, 25, -34, 19, 2, -7, -10, -1],\n [31, -7, -2, 5, 5, -13, 35, -33, 22, -4, -5, 7],\n [-29, -35, 25, -22, 16, -30, -26, 35, -6, -15, 24, 27],\n [6, 15, 28, 20, 5, -4, -21, 26, -9, -8, 28, 23],\n [22, -34, 0, 35, -23, -21, 24, -14, 27, -11, 12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7723", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[2, 5, 9, 4, -19, 21, -34, 26, -27, 32, -19, 14],\n [0, 22, -15, -18, 19, -7, -12, -19, -18, 6, 9, -19],\n [0, 0, -7, -32, -16, 11, -27, -9, -21, -17, 16, -10],\n [0, 0, 0, 13, 17, -33, 30, 6, -17, -19, -3, 13],\n [0, 0, 0, 0, 19, -10, 16, -29, 10, 10, -20, -12],\n [0, 0, 0, 0, 0, -11, -26, -20, 22, -7, -30, -20],\n [0, 0, 0, 0, 0, 0, -10, 9, 27, 31, 16, 32],\n [0, 0, 0, 0, 0, 0, 0, -3, -23, -10, -15, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 10, -33, 19, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 16, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-338783", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 9) of the inverse of matrix 1/839 * A where A =\n[[-15, -20, -21, -12, -14, -10, 0, -16, -8, 3, 8, -14],\n [-20, -19, -26, 24, -4, -24, -6, -2, 12, 4, -30, 12],\n [-21, -26, -24, -28, -19, 15, -10, 31, -2, -9, -26, -31],\n [-12, 24, -28, -28, 1, -24, 4, -9, 15, -7, 2, -29],\n [-14, -4, -19, 1, 2, 5, 12, -13, 20, -24, -25, 2],\n [-10, -24, 15, -24, 5, 34, 14, -8, -14, 22, -14, 0],\n [0, -6, -10, 4, 12, 14, -4, 0, 10, -13, 8, 2],\n [-16, -2, 31, -9, -13, -8, 0, -3, 10, 16, 0, -1],\n [-8, 12, -2, 15, 20, -14, 10, 10, 0, 13, -6, 0],\n [3, 4, -9, -7, -24, 22, -13, 16, 13, -24, -10, -3],\n [8, -30, -26, 2, -25, -14, 8, 0, -6, -10, -33, 0],\n [-14, 12, -31, -29, 2, 0, 2, -1, 0, -3, 0, -23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-31, 16, 5, 17, 14, -21, -29, 4, -8, -4, -21, 34],\n [0, -32, -25, -10, 25, 1, -13, 4, -13, -20, 25, 32],\n [0, 0, -11, 8, -24, -27, -24, 33, 18, 18, -8, 20],\n [0, 0, 0, 2, 32, 17, -3, 35, 20, 15, 7, -21],\n [0, 0, 0, 0, 15, -26, -24, -32, -18, 0, -11, 0],\n [0, 0, 0, 0, 0, 7, -1, 27, -32, 5, 9, 14],\n [0, 0, 0, 0, 0, 0, -1, 10, 6, 3, 13, 26],\n [0, 0, 0, 0, 0, 0, 0, 35, -34, 13, -5, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 32, 28, -6, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -13, -8, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-119588", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 11) of the inverse of matrix 1/839 * A where A =\n[[-8, 30, -14, -5, -13, 12, -16, 2, 19, 32, -35, -29],\n [0, -24, -31, 14, 6, -24, -18, 30, -19, 32, 35, 26],\n [0, 0, 34, 9, 22, 15, -2, 8, -21, 34, 14, -4],\n [0, 0, 0, 31, 12, -19, -29, -23, 30, -32, -26, -19],\n [0, 0, 0, 0, -15, -12, -32, -12, 23, -33, 32, 4],\n [0, 0, 0, 0, 0, 32, 10, -23, -9, -30, -19, 0],\n [0, 0, 0, 0, 0, 0, 19, 31, 24, 22, -24, 33],\n [0, 0, 0, 0, 0, 0, 0, 21, 4, 9, -1, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 35, 30, 34, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -19, 9, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-23, 5, 23, 33, 17, 9, -16, -12, 25, 22, -9, -10],\n [-29, 6, 11, 17, 23, 2, 33, 17, -21, -10, 12, -17],\n [-27, 28, 18, 15, 3, -32, -33, 28, -7, -25, 22, -9],\n [-15, 3, 10, 30, 0, 29, 27, -1, -5, -8, -35, -11],\n [7, 31, 27, 15, -34, 28, 33, -27, -34, -2, 24, 25],\n [-5, -26, 0, 13, 34, 13, -33, -31, 25, -10, -31, -21],\n [-20, -35, -20, 1, -33, 16, 11, -23, 19, -15, 30, 18],\n [-9, 2, 22, 26, 10, -25, -28, 35, 28, -15, 27, 28],\n [-16, -28, 22, 10, -5, -27, -21, -10, -26, -7, 0, 1],\n [35, -13, 5, -8, 12, 2, -5, -22, -7, 15, 13, 7],\n [-31, 6, -29, 6, 0, -9, 22, 10, 30, -11, -9, -35],\n [6, 16, -11, 18, 31, -30, 22, 34, 17, 30, 22, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-14, 1, -16, -12, 29, 29, -35, -33, 10, 19, 28, 9],\n [-10, 29, -12, -1, -12, -8, -20, 23, 18, -20, -21, -25],\n [29, 32, 7, 33, -23, -26, 5, 14, 35, 23, 3, -33],\n [-29, 13, -10, -3, 12, -34, 35, -4, -32, -16, 0, -4],\n [-8, -35, 24, 20, -1, -6, 18, 0, 19, 22, 29, 33],\n [15, -14, 17, 0, 32, 0, 16, 17, 14, 5, -18, -14],\n [30, -15, 8, 11, 3, -7, 18, -19, 24, -5, 13, -34],\n [12, -22, 23, 22, 22, 15, -34, 5, -20, -32, -24, -7],\n [-29, -22, -24, -31, -4, 7, 33, 9, -27, 13, -3, -18],\n [-27, 26, 21, -7, -11, -21, -30, 6, -7, -32, 21, 13],\n [8, -22, -33, 26, 28, 9, 22, -16, 22, 21, 32, 16],\n [1, -28, 8, -31, 33, -5, 9, -27, -4, -3, 31, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, -33, 21, -6, -27, -10, -34, 26, -33, 10, 32, -11],\n [0, -23, 8, -1, 19, -27, -34, 25, 5, 8, 28, -5],\n [0, 0, 33, 22, 8, 20, 7, -2, -6, 35, 34, 19],\n [0, 0, 0, -10, 21, -12, 17, 34, 7, 24, 22, 13],\n [0, 0, 0, 0, 16, 10, 8, -14, 17, 23, -6, -28],\n [0, 0, 0, 0, 0, -9, 4, -10, -9, 26, 14, 6],\n [0, 0, 0, 0, 0, 0, -13, -29, -10, -24, -31, 33],\n [0, 0, 0, 0, 0, 0, 0, -13, -18, -6, -10, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 10, 14, 2, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 3, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-386", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-17, 31, -31, 31, -25, 32, 33, -35, 27, -7, -24, 5],\n [0, 1, 9, 12, -12, -14, -25, 22, 10, -7, -1, -21],\n [0, 0, 7, 13, 28, -4, 28, -34, -12, 30, 2, -5],\n [0, 0, 0, -11, 12, 29, 17, 31, -18, -27, 2, -15],\n [0, 0, 0, 0, 8, -8, 9, -19, 4, -33, 30, 10],\n [0, 0, 0, 0, 0, 30, -5, -3, 3, 10, 1, 24],\n [0, 0, 0, 0, 0, 0, 22, -31, 16, 9, -16, 25],\n [0, 0, 0, 0, 0, 0, 0, 5, 31, -35, 15, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, -14, 21, 11, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 8, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "245479", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (10, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, 21, 22, -22, -16, -6, -17, 17, 20, -13, 26, -3],\n [0, -3, -4, 25, 18, -19, -17, 34, -2, -11, 32, -25],\n [0, 0, -29, -20, -20, 4, -24, -1, -15, 14, 7, -19],\n [0, 0, 0, -9, -16, -11, 30, -27, 17, 25, 2, -33],\n [0, 0, 0, 0, 9, 11, -10, -22, 18, 35, 10, -5],\n [0, 0, 0, 0, 0, 22, -12, 27, -11, 23, -4, -18],\n [0, 0, 0, 0, 0, 0, -6, 17, 27, -25, -5, 13],\n [0, 0, 0, 0, 0, 0, 0, -10, -34, -21, -32, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, -18, 19, 14, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -11, -15, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, -12, -4, -16, 20, -16, -10, 0, -24, 5, -5, 11],\n [-12, 11, -3, 25, 6, 10, 6, -21, 4, -2, -15, -20],\n [-4, -3, -8, -6, -22, 11, -18, -6, 17, -9, 22, 16],\n [-16, 25, -6, -29, -10, 8, 0, 20, -13, 0, -14, 12],\n [20, 6, -22, -10, 31, -10, -10, -2, 4, -8, -6, -2],\n [-16, 10, 11, 8, -10, -11, -12, -17, 1, -17, 12, 1],\n [-10, 6, -18, 0, -10, -12, -33, 2, 0, 15, -24, -10],\n [0, -21, -6, 20, -2, -17, 2, -35, 7, -12, -4, 31],\n [-24, 4, 17, -13, 4, 1, 0, 7, 18, -4, 21, 5],\n [5, -2, -9, 0, -8, -17, 15, -12, -4, -1, 14, 16],\n [-5, -15, 22, -14, -6, 12, -24, -4, 21, 14, -27, 4],\n [11, -20, 16, 12, -2, 1, -10, 31, 5, 16, 4, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6725", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-26, 31, -25, -24, -26, -11, 13, 13, -25, 26, 0, 3],\n [0, 20, -35, 20, -32, -6, -24, -1, 16, -5, 32, 16],\n [0, 0, 20, 22, 28, -24, -29, 19, 26, 19, 0, -12],\n [0, 0, 0, -23, -5, -8, 24, -9, -21, -3, -16, 6],\n [0, 0, 0, 0, -5, 18, -31, -23, -8, 7, 11, 35],\n [0, 0, 0, 0, 0, -28, 16, -3, 6, -9, -28, -13],\n [0, 0, 0, 0, 0, 0, 2, 2, 17, -5, 8, 24],\n [0, 0, 0, 0, 0, 0, 0, 7, -1, 18, 26, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, -13, -27, 22, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 14, -2, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "423", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[13, 27, -4, -26, -25, 34, 26, 11, -2, -19, 18, 4],\n [-17, 31, 17, 28, 11, -30, -20, -18, 16, 12, 7, 3],\n [13, -24, -26, 35, 19, -35, 13, 0, -15, 1, -12, 19],\n [-11, -29, 35, 35, -12, -25, -24, -1, 27, 32, 21, -23],\n [-13, 3, -24, -2, 35, -5, 26, -23, -5, -34, -21, 21],\n [-2, 32, -7, 30, -20, 3, 1, -15, 8, -17, 35, -28],\n [30, 5, 34, 25, -10, 35, 34, -7, 30, -17, 32, 22],\n [34, 21, 1, 25, -6, 35, -11, 29, -30, -18, -26, -25],\n [29, 29, 16, 31, -5, -19, 19, 0, -10, 17, -19, -11],\n [-34, -31, -32, 0, -30, -15, -10, 19, 3, -3, -22, 20],\n [-15, 10, -20, -20, -7, -28, -33, -17, 30, -14, 10, -23],\n [-3, -31, -9, -12, 31, 27, 12, 27, -24, -8, 8, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-67", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-19, -13, 6, 9, 4, 21, 4, -14, -12, -2, 14, 7],\n [-13, 29, -4, -4, -24, 2, 22, 3, 32, 10, 10, -12],\n [6, -4, 2, -22, -8, 20, 0, 12, -12, -4, 3, 6],\n [9, -4, -22, 5, 8, 0, -24, -14, 24, -10, -6, -15],\n [4, -24, -8, 8, 34, 6, -7, 14, -3, -30, 11, 10],\n [21, 2, 20, 0, 6, -34, -4, 12, 17, -12, -14, 0],\n [4, 22, 0, -24, -7, -4, 25, -14, 20, 0, -10, -22],\n [-14, 3, 12, -14, 14, 12, -14, 24, 6, -17, 12, 2],\n [-12, 32, -12, 24, -3, 17, 20, 6, 1, 16, 17, -8],\n [-2, 10, -4, -10, -30, -12, 0, -17, 16, 6, -16, 2],\n [14, 10, 3, -6, 11, -14, -10, 12, 17, -16, -14, 0],\n [7, -12, 6, -15, 10, 0, -22, 2, -8, 2, 0, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5989", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[12, -29, 33, -20, -35, 1, 1, 28, 26, 25, -3, 30],\n [-6, -16, 24, -12, -32, 1, -32, -18, 30, 12, -3, 22],\n [-8, -1, -26, 29, 6, -27, 24, -21, 21, 33, -14, 28],\n [5, 35, 20, -13, -11, -30, -2, 27, -27, 24, 13, 15],\n [24, 34, 1, -5, 5, 26, 22, -22, 0, 0, -28, -10],\n [0, 12, -8, 32, 26, 15, 6, -7, -26, 3, -35, 3],\n [-15, 29, -21, -32, 24, 25, -16, -26, -2, 12, -3, 25],\n [-26, 18, 29, -35, -31, -21, -8, -13, -19, -23, -22, -25],\n [-8, 6, 25, 28, -5, -26, -28, -15, 23, 14, 33, 34],\n [-6, -19, -16, 12, -34, 1, -35, -32, 18, -11, -33, -27],\n [-2, 7, -14, 34, -34, 30, -4, -20, -35, 12, 14, -23],\n [-21, 17, 8, -28, 10, 33, -17, 2, -25, 7, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-89", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[-15, 21, 14, -10, -6, -5, 6, 32, 25, 25, 34, 32],\n [-19, -17, 15, 34, 27, -6, -11, 35, -10, 20, -14, -17],\n [-5, -10, 6, 5, -13, 11, -23, 30, 30, -20, -8, -1],\n [5, -5, -4, 18, 23, 5, 30, 18, 4, -8, 1, 29],\n [19, -32, -26, 11, -22, 2, -24, 9, -19, -1, 30, 5],\n [31, -7, -18, -16, -22, -2, 13, 18, -5, 22, 6, 22],\n [-6, -11, 27, -17, -28, -33, 31, -19, -22, -27, 26, -15],\n [1, -25, -16, -1, 17, 11, 16, -28, -32, -9, 8, 4],\n [11, 8, 12, 16, 32, -25, -32, 12, -10, 3, 22, -17],\n [22, -8, 30, -26, 22, -22, -21, -3, -19, -12, -6, 26],\n [-23, 26, 11, -20, 30, 7, -28, -33, -24, -20, 23, 13],\n [27, 26, 13, 15, -3, -6, 23, -21, -13, 9, 26, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-21, 10, 28, 10, 20, 8, -7, 26, 16, 18, 21, 30],\n [0, -16, -3, -11, 10, 21, -31, 19, 25, -28, -20, 12],\n [0, 0, 29, -14, -33, 18, -22, 0, 31, -26, 13, 29],\n [0, 0, 0, 35, 21, -21, -6, -16, 1, -33, 5, 3],\n [0, 0, 0, 0, -20, -27, -23, -8, -9, 15, 28, 16],\n [0, 0, 0, 0, 0, -27, -23, 4, 19, 7, 8, 32],\n [0, 0, 0, 0, 0, 0, 26, -18, 27, -11, -24, -15],\n [0, 0, 0, 0, 0, 0, 0, -35, -11, 23, 33, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, -35, 22, -20, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 32, -22, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3380", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (7, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 34, 17, 8, 18, -16, -5, -29, 22, -26, -26, 3],\n [0, -6, 1, 31, 7, 16, 20, 32, -27, -13, 27, 25],\n [0, 0, -12, 15, 22, -3, -20, -14, 21, 26, 35, 34],\n [0, 0, 0, 21, -27, -5, 35, -27, -23, 22, -33, -1],\n [0, 0, 0, 0, -1, -21, -30, -4, 16, -8, 28, -17],\n [0, 0, 0, 0, 0, 17, 20, 23, 34, 22, -23, 7],\n [0, 0, 0, 0, 0, 0, -8, -7, -19, 32, 8, 25],\n [0, 0, 0, 0, 0, 0, 0, -9, -18, 18, -35, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 20, 11, -26, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 2, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[1, 30, -19, 4, 2, 25, -27, 25, -20, -34, 7, 6],\n [0, 31, -6, -23, -17, -29, -27, 18, 25, -34, 14, -5],\n [0, 0, -3, -29, -5, 12, 11, 17, -17, -30, 13, 14],\n [0, 0, 0, 33, 23, 0, -33, 22, 19, 21, -19, 3],\n [0, 0, 0, 0, -15, -15, 16, 7, 16, 31, 8, -4],\n [0, 0, 0, 0, 0, 17, 15, 17, -32, -19, 31, 11],\n [0, 0, 0, 0, 0, 0, 22, 23, -35, -33, 31, 1],\n [0, 0, 0, 0, 0, 0, 0, 12, -33, -13, 32, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 29, 25, -17, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1093", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-13, -6, 24, -18, 20, 17, -29, 33, 16, -32, -2, 33],\n [0, 33, 2, -10, -35, -32, 3, 18, -3, -3, -16, -20],\n [0, 0, 26, -5, 6, -24, 29, -33, -27, 15, -20, -33],\n [0, 0, 0, 35, -15, -17, 11, -14, -3, -4, 28, 3],\n [0, 0, 0, 0, -17, -16, 34, -19, 32, -33, 15, -10],\n [0, 0, 0, 0, 0, 9, -32, 1, 35, -3, -5, 19],\n [0, 0, 0, 0, 0, 0, -17, 20, -22, -3, -26, 28],\n [0, 0, 0, 0, 0, 0, 0, -15, -14, -27, -27, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 5, 19, -31, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 4, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[7, 24, 21, 35, -19, 14, -4, -14, 19, 21, -23, 11],\n [0, 18, -7, -14, 29, -7, 12, -31, -1, 35, 10, -1],\n [0, 0, -26, 30, 34, -11, 8, 24, 11, 4, -29, 10],\n [0, 0, 0, -15, -35, -17, 24, -3, -32, -33, 16, -8],\n [0, 0, 0, 0, -20, -12, 33, 5, 11, 33, -5, -6],\n [0, 0, 0, 0, 0, -18, 20, -5, 23, -34, 3, 25],\n [0, 0, 0, 0, 0, 0, -1, -25, 25, 8, 32, -11],\n [0, 0, 0, 0, 0, 0, 0, -33, 26, 28, -19, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, -20, -18, -29, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 20, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9388406", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-20, -18, 26, -9, -1, 9, -1, -8, -27, -21, -15, 16],\n [-1, 15, 19, 8, 29, -11, 11, 20, 2, -25, 31, -21],\n [-35, -29, -35, 13, -7, -10, 9, 35, -24, -4, -16, 15],\n [0, 31, -35, -9, 4, -22, 33, -30, -3, 19, -17, -7],\n [25, 34, -12, -13, -26, 18, 5, 13, -19, 20, 9, -6],\n [8, 19, -17, -7, -34, 0, -17, -29, -10, 2, -33, 30],\n [35, 7, 26, 35, -12, 3, 32, 8, -31, 19, -6, -7],\n [-10, -10, 1, 17, -6, -33, 7, -29, 13, 5, 18, 33],\n [-9, -28, -4, 28, -26, -23, 27, -1, 25, 18, -28, -7],\n [5, -6, -15, -25, -34, 14, 5, 30, -33, 15, 32, -11],\n [-6, -25, -19, -10, -13, 20, 16, 12, -16, -34, -5, -9],\n [-34, -32, -23, -1, 30, -30, -5, -26, -15, -13, -33, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4644", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, -16, 8, 21, -16, 2, 10, 34, -21, 8, -23, -32],\n [-16, -9, 2, -30, -3, 18, -1, -18, 4, 12, 24, 22],\n [8, 2, -11, 12, -12, 24, -17, 24, -16, 4, 33, 0],\n [21, -30, 12, -13, 6, -2, -32, 20, -16, 14, 2, 22],\n [-16, -3, -12, 6, -2, 10, 3, 22, 4, 15, 4, -2],\n [2, 18, 24, -2, 10, -27, 12, -11, 15, 15, 12, 30],\n [10, -1, -17, -32, 3, 12, 27, 4, 2, -24, 3, 8],\n [34, -18, 24, 20, 22, -11, 4, 18, -6, -14, 6, 24],\n [-21, 4, -16, -16, 4, 15, 2, -6, -13, -28, 9, 23],\n [8, 12, 4, 14, 15, 15, -24, -14, -28, 26, 4, -8],\n [-23, 24, 33, 2, 4, 12, 3, 6, 9, 4, -30, 19],\n [-32, 22, 0, 22, -2, 30, 8, 24, 23, -8, 19, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[15, 16, -2, 0, 34, 7, -20, 23, 17, -17, 5, 11],\n [0, 19, -17, 26, 23, 29, 32, -8, -18, -10, -17, 19],\n [0, 0, -35, -28, 15, -11, 11, 19, 28, -26, 20, -24],\n [0, 0, 0, 25, -26, -5, 24, 34, -19, 14, 1, 26],\n [0, 0, 0, 0, -1, -3, -18, 1, -23, 28, -35, 27],\n [0, 0, 0, 0, 0, -7, -24, -19, 12, -10, -24, -15],\n [0, 0, 0, 0, 0, 0, -1, -21, 29, -11, 23, -30],\n [0, 0, 0, 0, 0, 0, 0, 26, -32, -18, 20, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, 1, -33, 27, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -19, 4, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3459621", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-29, -20, -17, -30, -25, 25, 6, -23, -24, -16, 14, 0],\n [33, 1, -24, 4, 18, -34, 14, 5, 9, -27, 26, 11],\n [-31, -35, 8, -14, 2, -17, -5, 31, 6, -10, -23, 22],\n [-18, 31, -33, 19, 22, 27, 16, -12, -27, 1, 17, -12],\n [-15, 4, 26, 34, 33, -22, 6, 14, 25, -32, -19, 21],\n [12, 8, 9, -3, -5, 11, -30, 35, -2, 17, -22, -20],\n [7, -24, 34, -17, 5, 17, -7, 34, 23, 28, -12, -20],\n [16, -30, 1, -32, 2, 5, -22, 35, 15, 29, 16, -6],\n [21, -6, 6, -25, -9, -12, 3, -18, 9, -24, 13, -5],\n [-14, 8, 28, -11, 15, -29, -30, -12, -17, -27, 0, 4],\n [-12, 12, 27, 33, 17, 18, 6, 9, -22, -7, -30, -29],\n [1, 17, -18, 2, 23, -35, 32, 8, 11, -1, 24, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-194", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-28, 5, -33, 33, -22, -10, 34, 22, 4, 15, -31, -4],\n [-35, 18, -25, 17, -28, -11, 4, -4, -8, -33, 26, -9],\n [9, -11, 25, 8, 10, -22, -28, 12, -22, 29, -29, 13],\n [19, -23, 20, 20, -21, 21, 22, -1, -20, -28, 9, 4],\n [18, -22, 23, 17, -9, 11, -30, 19, 8, -18, -20, -24],\n [-16, 9, 28, 23, -14, 11, -7, 9, -27, -12, -21, 0],\n [-23, 8, 35, 0, 25, 4, -9, -35, -2, 32, -15, -3],\n [-29, 29, -33, 15, 18, 23, -30, -7, -19, 24, -14, -12],\n [15, 14, -25, 20, 35, 6, 3, 33, 12, 21, -15, -16],\n [-21, 33, 15, 26, 1, -30, 35, -10, -28, -32, -15, -5],\n [-15, -11, -21, -1, 13, 7, 5, 1, 21, 6, 11, 25],\n [-22, 32, 17, -2, -12, -16, 33, -6, -29, 0, 2, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12889", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (4, 5) rounded to the nearest integer?\n[[-21, 10, -13, -24, 8, -21, 13, -15, -21, -22, 6, -21],\n [27, 32, -9, 17, 16, 27, 17, 21, 16, 7, -29, 6],\n [-32, 33, -31, 5, -32, -34, 31, -15, 34, 7, 33, -27],\n [-8, -10, -33, 13, -19, 27, 19, -13, -2, 33, -21, 11],\n [-33, -8, -33, -32, -5, 9, 23, 9, 1, 29, -27, -19],\n [29, -33, -10, 17, -5, -10, -13, -6, -26, 28, -14, -21],\n [20, -16, 11, 17, 17, -35, -34, 22, -17, 26, -24, -10],\n [-9, -7, -21, 10, -35, 24, 21, -33, -18, 16, 24, -2],\n [24, -10, -17, -14, -3, 2, -1, 31, -26, -21, -25, -12],\n [-32, -23, 21, 1, 12, 35, -35, 24, -24, -15, -25, 8],\n [22, 8, -2, -11, -32, 28, -20, -26, 30, -1, -30, -17],\n [23, 17, -28, -26, 31, 2, -7, -21, -13, 10, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (3, 12) rounded to the nearest integer?\n[[-26, 11, -32, 19, 30, 31, -29, 19, -5, -17, -8, -8],\n [-17, -16, -23, 7, -25, 12, -21, -19, 18, 14, -8, -32],\n [-14, 3, -2, 8, 6, 4, -24, -34, -8, 31, 35, -26],\n [21, 1, 28, 4, 24, 12, -17, -3, 8, 1, 0, -15],\n [-34, -5, -6, 8, -24, 15, 13, -12, -12, 24, -25, -23],\n [28, -16, 35, -8, -34, 7, -28, -23, -1, -13, 10, -21],\n [-34, 25, 28, 16, 0, 31, 33, 31, 11, -34, 8, 28],\n [-8, 18, 31, 0, 27, -11, 12, 3, 11, -15, -6, -5],\n [-10, -14, -15, -35, 1, 10, -27, -19, 11, 23, 18, -24],\n [28, -30, 17, -20, -31, 10, -22, 8, 27, 16, -10, 17],\n [-7, -17, 11, -28, -13, -1, 17, 22, -31, -20, -19, -4],\n [16, -16, 30, -35, 22, 8, -30, 14, -16, -22, -31, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[4, -2, 9, 35, 35, -9, 8, -3, -3, 8, -16, 0],\n [-29, -4, 31, 3, -12, 34, 18, 2, -4, 9, 25, 34],\n [17, 15, 20, -9, 2, 26, -18, 28, -6, 13, 5, -23],\n [-2, -11, 30, -18, -31, -17, 6, -18, -4, -15, -26, 1],\n [13, -23, 19, -19, -27, 8, 10, -28, 1, -17, 27, 10],\n [35, -10, 10, 10, -22, 27, -33, -8, -7, -18, -1, 11],\n [-31, 23, 23, 11, -23, -3, 26, -20, 8, 22, -30, -21],\n [-32, 20, 28, 32, -2, 20, -4, -27, 27, -3, -15, 19],\n [21, -34, -23, -32, 14, 12, -6, -7, -28, -24, 5, -10],\n [14, -34, 19, 20, -22, -30, 25, -24, -23, -17, 8, 23],\n [1, -11, -20, 2, 7, -22, -30, -13, 24, -24, -23, -30],\n [27, 2, 14, 16, 4, -28, 25, -28, -2, 24, 21, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-14, 4, 9, 19, 15, -31, -23, -8, 26, -12, -29, 2],\n [1, 32, 6, -31, 28, 14, -21, 17, -11, -27, 2, -14],\n [13, 32, -21, 29, 18, -6, -16, -3, -29, -28, -8, 9],\n [-25, -5, -24, 15, 8, 14, -19, -1, -35, -7, 15, 28],\n [-32, -8, -20, 27, 17, -19, 4, -23, 16, 22, 1, 25],\n [-2, 34, -19, -16, 23, 33, -3, -19, 21, -35, -23, -9],\n [34, 23, -30, -13, -26, 15, -17, 15, 32, 6, 21, 32],\n [2, 26, -29, 35, 14, 16, -10, -10, -17, -27, 25, -16],\n [14, -14, -23, -24, -26, 29, -6, -28, -15, -14, -18, 30],\n [12, 8, -27, 31, 18, -10, -10, -2, -28, -26, 12, 19],\n [18, 4, -21, -18, -13, 26, 10, 3, -21, 17, 28, 27],\n [-20, 34, 30, -23, 11, -27, 27, -2, -7, 1, 7, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "215", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-12, 35, -2, 12, -24, -13, -23, 9, 29, 11, 22, -31],\n [0, 24, -15, -12, -18, -15, 18, -26, -12, 24, 21, -13],\n [0, 0, -2, 34, -8, 3, 6, -13, 34, -34, -12, -19],\n [0, 0, 0, 24, 14, -24, 11, 31, 29, -9, 12, 26],\n [0, 0, 0, 0, 19, 11, -34, 3, 9, -4, 29, 2],\n [0, 0, 0, 0, 0, -19, 32, -31, 24, -13, 10, 16],\n [0, 0, 0, 0, 0, 0, 12, -7, -9, -18, 24, 33],\n [0, 0, 0, 0, 0, 0, 0, -2, 6, -16, 32, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, -17, 4, -19, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -16, -33, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-128542", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-30, -21, 5, 1, 11, -3, 11, 12, -10, 16, -4, -28],\n [-21, 31, -6, -4, 18, -16, -12, -16, 20, -10, 7, -6],\n [5, -6, 18, 21, -2, 28, 10, 26, 6, 20, -14, 6],\n [1, -4, 21, -24, -6, -5, -33, -31, -17, 10, 21, 24],\n [11, 18, -2, -6, -25, -12, -20, -22, 0, 22, -16, -14],\n [-3, -16, 28, -5, -12, -22, 2, 3, -7, 21, -10, 10],\n [11, -12, 10, -33, -20, 2, -25, 16, -32, 22, 4, -1],\n [12, -16, 26, -31, -22, 3, 16, -32, 10, -11, -14, 30],\n [-10, 20, 6, -17, 0, -7, -32, 10, 20, 3, 4, -9],\n [16, -10, 20, 10, 22, 21, 22, -11, 3, -3, -2, 4],\n [-4, 7, -14, 21, -16, -10, 4, -14, 4, -2, 2, -8],\n [-28, -6, 6, 24, -14, 10, -1, 30, -9, 4, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[16, -18, -20, 30, -31, -33, 34, -29, 14, -22, 2, 11],\n [0, 7, -7, 21, -31, 24, 34, -34, 34, 7, -32, 20],\n [0, 0, -33, 12, 7, -35, 21, 17, -20, 15, 19, -35],\n [0, 0, 0, 24, 23, -14, -28, 13, 6, -9, 3, -11],\n [0, 0, 0, 0, 14, 30, -22, 17, -4, 12, 3, 4],\n [0, 0, 0, 0, 0, 15, 27, 13, -9, -27, 3, 29],\n [0, 0, 0, 0, 0, 0, 17, 21, -9, 18, -32, -13],\n [0, 0, 0, 0, 0, 0, 0, -26, 13, -15, 17, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, -34, -20, -30, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 23, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "618422", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[17, -22, 16, 0, -28, 4, -14, -20, 24, 24, -26, -11],\n [-5, -15, -3, -5, -15, 0, 29, -32, 32, -32, -27, -6],\n [9, -32, 33, -13, -20, -14, 12, 26, 24, -31, -29, 15],\n [29, -27, 9, 11, 31, -12, -26, 12, -1, 18, 35, -20],\n [17, 4, -16, 33, 9, -30, 33, 13, 3, -34, 3, -15],\n [4, 18, -24, 1, 2, -21, -29, 14, 29, 31, 8, -5],\n [7, 12, 25, -26, -7, 12, 26, -23, 8, 11, 28, 17],\n [8, -8, -34, 21, 21, -2, 22, 16, -7, -1, 12, -3],\n [-27, 12, 31, 0, 35, 8, 24, 27, -31, 4, -17, 11],\n [29, 31, -18, 14, -6, 30, -31, 6, -31, 14, 22, -28],\n [-5, -24, -15, 26, -3, -10, 4, 29, 23, -21, -35, -25],\n [19, -34, 29, 8, -20, -14, -18, 11, -6, -26, 22, 26]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-30, 31, 5, 7, -18, 22, 24, -9, 32, -14, -12, 4],\n [30, 4, -30, -18, -6, -15, 26, -26, -23, -27, 32, 3],\n [-12, -2, 25, 5, -31, 14, -32, 15, 16, 3, -28, 9],\n [-8, -9, 29, -2, 26, 26, 2, -10, -12, 3, -15, 11],\n [12, -23, -33, -4, -1, -17, -22, 12, 32, 9, -17, 28],\n [30, 30, 9, 31, 33, -33, 2, 6, 4, 14, -1, -12],\n [-19, 4, 30, 8, -13, -30, 30, -15, -1, -7, -29, 17],\n [1, -13, -28, 12, -26, -12, 11, 17, 3, 31, 30, -30],\n [-15, 0, -33, 6, 9, 8, -3, 24, 34, -10, -15, -34],\n [11, -6, -9, 35, -16, 14, -13, -23, -32, -22, -16, -23],\n [-33, 11, -33, -35, -12, -1, -22, 31, -23, 11, 14, -10],\n [-33, 15, 4, 32, 0, 15, -35, -3, -29, 16, -25, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5103", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (8, 3) rounded to the nearest integer?\n[[-22, 10, -26, -12, 25, -18, -27, -19, 22, -23, 14, -30],\n [15, 0, 35, -11, -25, 8, -22, -7, 14, -31, 33, 21],\n [-10, -30, -20, 24, -24, -33, 27, 28, 26, -30, -17, -18],\n [7, -33, 2, 32, 8, 27, 6, 28, 18, 35, 1, -32],\n [-34, 8, 31, 32, 26, -35, -19, -20, -27, 17, 23, -27],\n [-24, 5, -21, 30, -25, -28, 19, -30, 17, -16, 3, -2],\n [21, -17, 35, -5, 4, -22, 1, 8, -27, 22, -16, 14],\n [-16, 0, -9, -4, -35, -19, -27, 9, 30, -4, 9, -27],\n [-6, 2, 24, -35, -31, 27, 0, 29, -12, -32, 32, -11],\n [-29, -23, 32, 7, 21, 0, -22, -9, 1, 35, -11, 31],\n [-32, -20, -17, -7, 15, -18, 22, 8, -20, 29, -34, 20],\n [-8, 29, -31, -14, -23, 29, -20, 28, -4, 15, 22, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[16, 27, 24, 29, 19, 21, 35, -10, -24, 35, 10, 11],\n [2, -15, -22, -34, 34, -3, -30, 1, -22, 1, -28, -23],\n [4, 22, -18, 21, 2, -4, 30, -11, 22, -3, 30, -6],\n [-2, 33, 12, 4, 15, -23, -5, 3, 27, 12, 12, 25],\n [-24, 20, -18, -9, -8, 16, -20, 22, -27, -10, -8, 0],\n [-27, 11, 15, 21, -4, 31, 21, 18, -20, 26, 20, -13],\n [-19, 2, -6, 22, -14, -19, -21, 12, -4, 4, 21, 22],\n [-20, -8, -35, 5, 12, -5, 0, -3, -3, -13, 24, -6],\n [9, 3, 9, -24, -4, 20, -12, -23, -16, 20, 17, 32],\n [18, -2, -8, 14, -34, -10, 15, 11, -10, 25, -13, 1],\n [5, 16, 13, -9, -30, 30, -12, 2, -8, -8, 30, 25],\n [10, 33, 7, 23, -34, -21, 1, 35, -16, -1, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-17, 32, -12, 3, 18, 3, -19, -17, 12, -1, -4, 11],\n [11, 28, 10, -1, -19, 6, -7, 34, -19, -22, -12, 21],\n [14, 21, 25, 3, 19, 0, 1, -22, -9, -5, 8, 32],\n [12, 21, -14, -32, 10, 23, -2, -25, -5, -25, 20, 2],\n [-15, -26, -10, -28, -28, 24, -2, -20, -23, -14, -9, 28],\n [-34, -10, 33, -6, -28, 2, 25, 29, 31, 10, 7, 23],\n [10, -1, 3, 15, -32, 15, -31, 19, -16, -12, 0, -2],\n [18, -2, -19, -31, -18, 19, 17, 14, 9, -23, -20, -23],\n [-16, 30, 11, -17, 9, 1, 18, -30, -22, -32, 19, -2],\n [-9, -29, -33, 11, -34, -11, 24, -12, -21, -22, 18, -30],\n [-18, -16, 26, 4, 3, 16, -4, -9, 16, 27, 27, -19],\n [13, -13, -23, -13, 21, 26, 18, -16, 16, -13, -1, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-2, -3, 10, 9, -17, -21, 30, 3, -18, 34, 23, -4],\n [0, 4, -9, -34, 3, 20, -23, 20, 30, 20, -8, 28],\n [0, 0, 20, 5, 5, -32, 21, -6, 10, 20, -5, -29],\n [0, 0, 0, 33, 8, -23, -16, -4, 24, 14, -9, -11],\n [0, 0, 0, 0, 3, -21, 17, 2, 12, 16, -8, -20],\n [0, 0, 0, 0, 0, 12, -14, 13, 16, -35, 30, 28],\n [0, 0, 0, 0, 0, 0, -21, 14, 35, 2, 4, 30],\n [0, 0, 0, 0, 0, 0, 0, 11, 0, 28, -23, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, -13, 14, 15, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -29, 30, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32384", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (1, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -29, 8, -7, 8, 0, -17, -30, -11, -5, -27, 1],\n [0, -23, 5, 30, -12, 8, 24, -27, -34, 20, -6, -14],\n [0, 0, -20, 9, 29, -25, 34, -16, 27, -24, 26, 6],\n [0, 0, 0, -9, -8, -10, 13, -15, -35, 22, 19, -10],\n [0, 0, 0, 0, -13, -6, 18, -25, -5, -30, -25, -24],\n [0, 0, 0, 0, 0, -14, -29, -21, -25, -12, 31, -6],\n [0, 0, 0, 0, 0, 0, -23, -24, -27, 12, 13, 17],\n [0, 0, 0, 0, 0, 0, 0, 13, 13, 24, 29, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 14, -22, -30, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 30, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-15, -30, 5, -21, -33, 7, 11, -22, 30, -7, -32, -10],\n [-24, -34, -19, -1, -26, 7, -15, -21, -1, 24, 8, -31],\n [-18, -15, 15, 5, -12, -12, 2, 8, 21, 23, -2, -13],\n [7, 4, 11, 5, 11, -16, 29, 32, -12, 0, 9, -34],\n [-8, -10, -13, 0, -30, -1, 2, -1, 17, 2, 23, 7],\n [-32, -31, 32, 9, -11, -25, -7, -2, -22, -12, 23, 3],\n [-10, 7, 0, 3, 25, -20, 23, -30, 20, -28, -9, 35],\n [-9, 10, 5, -11, -18, -24, 15, 3, -26, 18, -7, 5],\n [-27, 27, 1, -22, 3, 4, 18, -33, 19, -3, 35, -17],\n [-2, 14, 11, 10, 20, 21, 15, 18, -8, -17, -9, 12],\n [-17, 15, -29, -7, 7, 33, 22, -28, 6, 6, -23, -10],\n [-18, 6, 15, -20, -33, 9, -14, -13, 23, 26, 32, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "257", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[21, -5, -3, 10, 14, 12, 12, 4, -14, 17, 12, 5],\n [-5, 29, 12, 0, -26, 12, -18, 10, 3, -19, 6, -2],\n [-3, 12, 2, 7, -4, 2, -30, 16, -8, -14, 10, 22],\n [10, 0, 7, 16, 8, 11, 6, -4, -8, 22, 6, 8],\n [14, -26, -4, 8, -33, 12, -14, 0, -10, 6, -20, 13],\n [12, 12, 2, 11, 12, 14, -18, 19, 15, -20, 7, 18],\n [12, -18, -30, 6, -14, -18, -4, 12, -10, 12, -4, -16],\n [4, 10, 16, -4, 0, 19, 12, -3, -11, 18, -18, -18],\n [-14, 3, -8, -8, -10, 15, -10, -11, 32, 12, 5, 27],\n [17, -19, -14, 22, 6, -20, 12, 18, 12, -27, 28, 8],\n [12, 6, 10, 6, -20, 7, -4, -18, 5, 28, -17, -28],\n [5, -2, 22, 8, 13, 18, -16, -18, 27, 8, -28, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3717", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-29, -19, 28, -24, 20, 10, 11, -20, 33, -34, 18, -9],\n [-5, 5, 0, 11, 7, 29, 14, -35, 21, -20, -8, -14],\n [5, -17, 14, 23, 33, -2, 3, -29, 16, 24, 16, -12],\n [-10, -26, -19, -34, -9, 35, 12, -27, -13, 35, -9, 35],\n [7, -29, 27, 8, 3, 4, -29, 34, -11, 23, -23, 26],\n [-28, 9, -18, 24, 24, -34, 30, -22, 12, 20, -24, 19],\n [-8, -32, 0, 14, -33, -35, -19, 35, 26, 12, 26, 33],\n [-17, -2, 13, 11, 14, -10, 20, -22, -11, -32, -4, 29],\n [25, -16, -26, -2, 25, -9, 4, 29, -3, 32, 35, -27],\n [-20, -31, -13, 7, 21, 15, -23, -12, -25, 16, -19, 1],\n [-23, 26, -28, 20, 34, 8, 24, 5, -15, 6, -7, 29],\n [-19, -6, -10, 17, -17, 17, -19, 10, 17, 28, 9, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1964", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-17, 35, 29, 1, 34, -10, -34, 23, -31, 1, -5, 12],\n [-30, -21, -21, 25, -20, -16, 8, 6, 10, -2, 28, -7],\n [-33, -27, -11, 6, 10, 23, -15, -14, -7, 27, 25, 28],\n [33, 4, -35, 29, 26, 18, 24, 10, -31, -14, 17, 34],\n [-4, -25, -26, 3, -5, -24, 2, 31, 30, 16, -31, -25],\n [-11, -1, -1, -14, 1, 19, 28, -16, -32, -18, 15, 32],\n [-16, -27, -10, -11, 32, 5, 23, 9, 5, 2, -17, -22],\n [-15, -21, -33, 1, 10, -20, -22, -27, -29, -22, -30, -21],\n [16, -2, -35, 33, -16, -29, -29, 14, -34, 11, -22, -5],\n [14, 25, 5, -22, -31, -31, 28, -7, -31, 0, -17, 28],\n [-14, -2, 20, -19, 20, -19, -18, 9, 20, 14, 22, -18],\n [-29, -26, 33, -33, 8, 34, -22, -32, -18, 16, 2, -16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-188", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[8, 6, 4, 6, 30, -3, 8, 26, -7, -8, 9, -2],\n [6, -17, 27, 0, -22, -11, -2, 6, -5, -5, -30, 14],\n [4, 27, -23, -28, 14, 1, -14, -2, 18, 2, 14, -4],\n [6, 0, -28, -6, 8, -20, 4, 14, 16, 10, 4, -4],\n [30, -22, 14, 8, -4, 1, 0, -14, -14, 15, 18, -4],\n [-3, -11, 1, -20, 1, -25, 10, 9, -18, -18, 10, -8],\n [8, -2, -14, 4, 0, 10, -2, 11, 5, -30, -21, 2],\n [26, 6, -2, 14, -14, 9, 11, -14, 16, -14, 24, -12],\n [-7, -5, 18, 16, -14, -18, 5, 16, 4, 0, -3, 3],\n [-8, -5, 2, 10, 15, -18, -30, -14, 0, -29, -27, -6],\n [9, -30, 14, 4, 18, 10, -21, 24, -3, -27, -18, 2],\n [-2, 14, -4, -4, -4, -8, 2, -12, 3, -6, 2, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-135", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (11, 12) rounded to the nearest integer?\n[[31, 17, -34, 32, 29, 21, 34, -29, -17, 8, 27, 29],\n [0, -10, 8, -24, -14, -22, -6, 8, 2, 23, 6, 16],\n [0, 0, -2, 3, 5, 1, 29, -4, -28, -18, 9, -3],\n [0, 0, 0, 4, -31, -2, -12, -19, 35, -14, -21, -21],\n [0, 0, 0, 0, -4, -15, 32, 8, 30, -22, -21, -16],\n [0, 0, 0, 0, 0, 27, -1, -23, 10, 20, -27, 0],\n [0, 0, 0, 0, 0, 0, 10, -21, 31, -21, 15, -28],\n [0, 0, 0, 0, 0, 0, 0, -30, 21, -5, -30, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, -24, 21, 8, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -15, -30, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-14, -5, -29, -15, -20, -16, 7, 8, 11, -17, 12, 33],\n [-25, -7, 9, 32, 0, 12, -21, 8, 31, 4, -22, 27],\n [15, 22, -21, 29, 19, -26, 6, -25, -20, -17, -5, 17],\n [-28, -12, -28, 12, -6, 22, 19, 26, 12, -32, 1, -28],\n [-35, 34, 11, -31, 14, -12, 11, -18, -8, -31, -6, -35],\n [10, 33, -5, 34, 20, -8, -20, 18, 17, -24, -16, -2],\n [17, 28, -13, -9, -19, 12, -15, 14, 4, -33, -19, 25],\n [14, -30, -8, 19, 22, 9, -17, -7, -13, -4, -26, 13],\n [29, -7, 23, 9, 31, 15, -25, -30, 31, 26, -31, -27],\n [-8, 2, 7, -15, 26, 10, 34, 2, 13, 3, 35, -6],\n [-15, -35, -4, -28, 33, -6, -28, -17, 23, 19, -6, 0],\n [19, 8, -9, 18, 12, -6, 3, -23, -20, 8, 35, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1535", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[9, -1, -8, -29, 26, 15, 10, -16, 2, 25, -4, -10],\n [22, 3, -16, 14, 16, -14, 17, 30, 7, -13, 28, -27],\n [-29, 5, 18, 29, -34, -32, -4, -34, 28, -22, -16, 13],\n [-28, 27, 10, -15, -4, -28, -20, 4, -9, -18, -1, 16],\n [-21, 27, 17, 30, -5, 25, 28, -2, 19, 23, -33, -19],\n [10, 2, -1, -35, -7, -32, 25, -19, -8, 14, -28, -2],\n [23, -18, 23, -9, -20, -26, -14, -20, -24, 15, -35, -9],\n [31, -24, -6, -27, 17, 25, 18, 1, 29, 6, 13, -32],\n [28, 15, 24, -5, 22, -32, -14, -33, 11, 2, -3, 12],\n [29, -10, -28, 14, 2, -26, 6, 1, -10, -24, 13, -22],\n [10, -1, -7, -24, 8, 30, -34, 23, -19, -26, -18, -14],\n [22, 17, -35, 25, -5, -5, 30, -17, 17, -14, -13, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-130", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[21, 9, -34, 32, 14, -7, -26, -9, -21, 24, -5, -15],\n [0, 22, 5, 10, 9, -10, 15, 0, 16, 15, -33, -22],\n [0, 0, 21, -19, 14, -22, 23, -33, 4, 30, -2, -27],\n [0, 0, 0, -11, -27, 26, -10, 21, 1, -20, 1, -12],\n [0, 0, 0, 0, -5, -17, -16, -9, 8, -1, 35, -14],\n [0, 0, 0, 0, 0, -2, -19, -8, -22, -2, 21, 19],\n [0, 0, 0, 0, 0, 0, 16, -18, 17, 27, 17, -9],\n [0, 0, 0, 0, 0, 0, 0, -18, -15, -17, -32, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 16, -35, 4, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 35, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-562", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (8, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -10, -13, 26, -23, -27, -16, 21, -12, -3, -16, 24],\n [12, 28, -6, -19, -22, -17, 35, 23, 31, 8, -4, -25],\n [-34, 32, -19, 4, 10, -32, 2, 27, -7, -17, -7, -1],\n [34, -13, 10, 8, 12, 16, -28, 19, 30, 4, -5, 12],\n [25, 16, 2, 0, 19, -23, 1, 11, 35, -14, 3, 22],\n [-6, -18, -18, 3, -10, 35, -29, 33, 29, 10, -18, -23],\n [-11, -28, -4, -19, 12, 27, 4, -21, -30, 27, -28, -4],\n [9, 16, -23, -12, 4, -22, 34, 26, 25, -35, 30, -4],\n [-23, -3, -4, 20, -12, -32, -13, -7, -15, -6, -16, -20],\n [31, 13, 22, 8, -11, -13, 23, -35, -21, 16, 22, 5],\n [8, -32, 32, -29, 10, -27, -3, -3, -32, 29, -2, 28],\n [-11, 19, -27, -19, -15, 24, -23, -33, 32, -32, -29, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[-12, -26, -23, 8, 3, -17, 15, -17, 16, 11, -6, 10],\n [-15, 12, 26, 22, -18, 23, 12, 27, -24, -2, 25, 17],\n [-11, 26, -32, -23, 6, 13, 20, 11, -28, 19, -18, -1],\n [-4, -12, -29, -23, 33, 6, -5, -10, -4, 16, -16, 4],\n [23, -22, 8, 12, 7, -20, -1, 17, -2, -33, 32, -31],\n [-26, 16, -7, -5, 30, 33, 1, -9, -3, 32, 23, 28],\n [8, 13, 17, 13, 30, 27, -11, -32, 15, -25, -19, 30],\n [34, 33, -7, -16, -9, -28, 25, -8, 34, -33, 33, -29],\n [24, -32, -31, -25, -21, 28, -23, -29, -30, 20, 28, 14],\n [-6, -14, -11, -8, 3, 31, -31, 29, -21, 31, 4, 33],\n [7, -35, -14, 26, -10, -18, 12, -27, -35, -27, -13, 9],\n [-34, -22, 2, 4, 27, -20, -30, -33, -22, 30, 31, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, -29, -29, -9, -28, -8, 30, 35, 11, -26, -3, -29],\n [0, -22, 8, 10, 25, 0, -23, -20, -31, 2, 14, 2],\n [0, 0, 12, 23, 8, 19, 19, -35, -28, -32, 17, 22],\n [0, 0, 0, -17, -35, -7, -3, 16, 5, -13, -31, 35],\n [0, 0, 0, 0, -32, 28, 1, -5, 1, 9, -28, 4],\n [0, 0, 0, 0, 0, 15, -5, -29, -6, 22, -33, 15],\n [0, 0, 0, 0, 0, 0, 21, 2, 26, 34, 29, 26],\n [0, 0, 0, 0, 0, 0, 0, 5, -24, 18, -25, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, -20, -22, -11, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 29, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5329", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 28, 0, 12, -34, 3, 2, -2, 8, -34, 28, -24],\n [28, -6, 20, -14, -16, -8, -20, 4, 7, 20, 10, -8],\n [0, 20, -9, 4, 18, 8, -28, -6, -14, -11, -26, 10],\n [12, -14, 4, -31, 30, -9, 4, -24, 10, -14, 2, -16],\n [-34, -16, 18, 30, -17, 2, 17, -2, 2, 10, -26, -16],\n [3, -8, 8, -9, 2, 33, 25, -15, 13, 13, -3, 28],\n [2, -20, -28, 4, 17, 25, 6, 7, -4, 16, -11, 9],\n [-2, 4, -6, -24, -2, -15, 7, 27, -18, -12, 12, 4],\n [8, 7, -14, 10, 2, 13, -4, -18, -30, 22, 10, 12],\n [-34, 20, -11, -14, 10, 13, 16, -12, 22, -11, 17, 18],\n [28, 10, -26, 2, -26, -3, -11, 12, 10, 17, 23, 14],\n [-24, -8, 10, -16, -16, 28, 9, 4, 12, 18, 14, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-145", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (1, 10) of the inverse. Round your answer to the nearest integer:\n[[-28, -7, -14, 34, 25, 7, 13, -7, -5, 17, -2, 2],\n [0, -32, -34, -24, -1, 34, -15, 25, -1, 12, -21, 35],\n [0, 0, 32, -14, -4, -14, -9, -21, 8, -27, -2, -21],\n [0, 0, 0, -17, -20, -28, -3, -18, -1, 7, 14, -33],\n [0, 0, 0, 0, 34, 11, -22, -29, -5, 15, -7, -21],\n [0, 0, 0, 0, 0, 21, -5, -33, 31, 14, -19, 24],\n [0, 0, 0, 0, 0, 0, 30, -21, -1, 33, -9, -29],\n [0, 0, 0, 0, 0, 0, 0, 10, 35, 34, 32, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, -7, -28, -35, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -29, -19, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2122", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (10, 9) of the inverse of matrix 1/839 * A where A =\n[[-22, 15, 2, -16, 1, 14, -24, 10, -19, 4, -3, -2],\n [15, -9, 22, -30, 24, 2, -8, 24, 6, -8, -20, 23],\n [2, 22, -5, -6, 24, 7, 22, 12, -5, -4, 16, 14],\n [-16, -30, -6, -19, -2, -8, -14, 12, 10, 18, -5, 4],\n [1, 24, 24, -2, 8, 20, -6, 10, 0, 2, -16, -18],\n [14, 2, 7, -8, 20, -21, -9, 8, -14, -17, 9, -16],\n [-24, -8, 22, -14, -6, -9, 27, -29, -13, 32, -7, 4],\n [10, 24, 12, 12, 10, 8, -29, -15, 18, 6, -30, 10],\n [-19, 6, -5, 10, 0, -14, -13, 18, -19, -19, 3, -24],\n [4, -8, -4, 18, 2, -17, 32, 6, -19, 19, -2, 8],\n [-3, -20, 16, -5, -16, 9, -7, -30, 3, -2, -31, -20],\n [-2, 23, 14, 4, -18, -16, 4, 10, -24, 8, -20, -21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[11, 12, -6, 26, 7, 28, -13, 3, 1, 8, 6, 4],\n [12, -12, -6, -2, 19, -12, 15, 6, 12, 2, 10, -32],\n [-6, -6, 6, -4, -12, -22, 19, -16, 14, 14, 14, -6],\n [26, -2, -4, 20, 20, -14, 4, -8, -6, 4, 10, -22],\n [7, 19, -12, 20, -33, 2, 17, -18, -18, -19, -13, -1],\n [28, -12, -22, -14, 2, -5, 7, 3, 7, 8, -10, -2],\n [-13, 15, 19, 4, 17, 7, -1, -13, -2, -1, -6, -32],\n [3, 6, -16, -8, -18, 3, -13, -27, 31, -10, 30, -4],\n [1, 12, 14, -6, -18, 7, -2, 31, -32, -12, -21, 6],\n [8, 2, 14, 4, -19, 8, -1, -10, -12, -16, -4, -14],\n [6, 10, 14, 10, -13, -10, -6, 30, -21, -4, -18, 3],\n [4, -32, -6, -22, -1, -2, -32, -4, 6, -14, 3, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1865", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[6, 10, 17, -10, 25, 31, 18, -14, -10, 24, 3, 0],\n [-15, 5, 12, -10, 27, 0, -12, -15, -18, -21, -30, 7],\n [-5, -8, -28, -7, -15, 22, 24, 14, -5, 11, -2, -34],\n [31, 16, -29, -17, -21, 12, -22, -33, 14, 18, -30, 13],\n [-13, -16, 24, 9, 25, 20, -34, 9, 4, -12, -7, 31],\n [32, 30, 18, 17, 13, -4, 25, 6, -35, 27, -1, 15],\n [35, 9, 29, -22, -33, -12, 29, 12, -26, -23, -22, -26],\n [4, -13, 19, 27, 35, 6, 30, 11, 16, -18, -18, -12],\n [-13, -24, -13, -15, 28, -2, -34, 33, -5, 32, 34, -17],\n [-23, 29, -30, 35, -9, 16, 12, 32, 8, -19, 2, -26],\n [18, -30, -30, 16, -21, 32, 21, 20, -29, 15, 22, 28],\n [-10, 22, -5, 30, -23, -18, -23, -12, 21, -7, 20, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-70", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-31, -1, -17, 19, 33, 8, 2, 26, -14, 4, -10, -31],\n [18, 13, -33, 2, -22, 11, -22, 2, 28, 8, 34, 29],\n [-11, -20, -21, -33, 31, 1, 19, 2, 27, -35, 35, -17],\n [16, -6, 19, -22, -23, -9, -27, 5, 12, -24, -26, -30],\n [-2, 16, 5, -30, -34, -21, -19, -20, -8, -26, -26, -26],\n [-8, -12, -17, 32, 20, 31, 6, -24, -18, -13, -30, 17],\n [6, 30, -6, -27, 6, -2, 4, -19, -7, 14, 13, 25],\n [10, 10, -19, 30, -31, 18, -20, -29, -28, 2, 18, -21],\n [14, 20, -27, -28, -17, 15, 21, 32, -5, -33, 7, -7],\n [-26, -24, 10, -6, -4, 11, 27, -10, -33, -13, 14, 0],\n [-23, -7, 2, -31, -16, -22, -28, 12, -23, -12, 29, -2],\n [15, -33, 22, 19, 6, -15, -26, 21, -11, 20, 2, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[11, -4, 8, 18, -4, 22, 14, 27, -2, 10, -4, -6],\n [-4, 21, 12, -6, 14, -14, -8, 15, 2, -16, 10, 32],\n [8, 12, 9, 4, 0, 6, 5, 0, -10, 3, -30, 28],\n [18, -6, 4, -28, 2, 5, 9, 0, -17, 21, -2, 2],\n [-4, 14, 0, 2, -21, -2, 0, -26, -22, 16, -12, -16],\n [22, -14, 6, 5, -2, 9, 28, 8, -26, -8, 23, -31],\n [14, -8, 5, 9, 0, 28, -9, 12, 14, 15, 2, -20],\n [27, 15, 0, 0, -26, 8, 12, 6, 16, 19, 6, 22],\n [-2, 2, -10, -17, -22, -26, 14, 16, 5, -6, -6, 0],\n [10, -16, 3, 21, 16, -8, 15, 19, -6, -10, -12, 4],\n [-4, 10, -30, -2, -12, 23, 2, 6, -6, -12, 33, 8],\n [-6, 32, 28, 2, -16, -31, -20, 22, 0, 4, 8, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1391", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (10, 2) of the inverse. Round your answer to the nearest integer:\n[[-15, 10, 2, -8, -11, 2, 6, 16, -4, -2, -5, -14],\n [10, 26, -11, -23, -9, -19, -16, 10, 18, 1, -7, -6],\n [2, -11, 34, -24, -17, 6, 18, -10, 16, 18, 4, -10],\n [-8, -23, -24, -20, -1, 16, 20, -2, 2, -9, 22, 4],\n [-11, -9, -17, -1, 31, 13, 27, 7, 12, -1, 4, 12],\n [2, -19, 6, 16, 13, 27, 18, -10, -26, -25, 12, -3],\n [6, -16, 18, 20, 27, 18, -4, 8, -2, 8, -18, -8],\n [16, 10, -10, -2, 7, -10, 8, -13, -13, -2, -6, -9],\n [-4, 18, 16, 2, 12, -26, -2, -13, 28, -24, 18, -17],\n [-2, 1, 18, -9, -1, -25, 8, -2, -24, 14, 30, -22],\n [-5, -7, 4, 22, 4, 12, -18, -6, 18, 30, -34, 28],\n [-14, -6, -10, 4, 12, -3, -8, -9, -17, -22, 28, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "165", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-29, 20, 28, -16, 2, 22, -20, 15, -9, 15, -20, 24],\n [0, 31, -34, 12, 16, -12, -34, 29, -16, -2, 5, 5],\n [0, 0, 8, 31, 26, -24, -6, 29, 5, -16, -30, -32],\n [0, 0, 0, -35, -28, 27, -3, -21, -5, -15, -33, 30],\n [0, 0, 0, 0, 20, 9, 23, 14, -24, -24, -3, 13],\n [0, 0, 0, 0, 0, 13, 28, -10, 35, -29, 26, -12],\n [0, 0, 0, 0, 0, 0, 18, -15, 12, 11, 32, 27],\n [0, 0, 0, 0, 0, 0, 0, -2, 24, 26, -34, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, -7, 22, 12, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -13, -28, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91065", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-35, -8, 26, 11, 23, -5, 34, 13, -31, -5, 1, -21],\n [16, 33, -25, 7, 34, -13, 4, 27, -34, 11, -6, -20],\n [23, 11, -6, -27, 29, 23, 28, -28, 16, -18, 22, 13],\n [-4, 12, 9, 18, 10, -5, 1, -20, 10, 10, 25, 10],\n [15, 26, -1, 6, 9, 32, 11, -6, -12, 30, 7, -2],\n [-13, 25, 1, -23, 35, -29, 6, 2, 16, 8, 28, -23],\n [-8, -35, 7, 6, 14, 24, -35, 15, -20, 3, -21, -3],\n [17, -19, -30, -5, 33, 4, -6, 33, -29, -23, -32, 14],\n [-33, -24, 29, -9, 14, -19, -4, 15, -19, -2, -1, -12],\n [18, -18, 14, 10, 12, -3, -9, -35, 23, -26, -11, 21],\n [30, -21, -8, -23, -22, 30, -2, -11, 18, -24, -27, -5],\n [17, 7, 2, 6, 12, 31, 30, -20, -20, -5, 22, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "512", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-32, -26, 15, -18, 11, -4, -6, 0, -27, 0, -7, -20],\n [-15, 28, 30, 23, -8, 19, -5, -3, 24, 5, 10, 13],\n [29, 6, -13, -9, -4, -33, 24, -19, -4, -29, 35, 33],\n [22, 4, 12, 15, 21, 35, 1, 19, 5, -16, -3, 4],\n [-2, 26, -17, 7, 33, 27, -26, -23, -31, 22, 23, 23],\n [-21, -35, 2, 17, 16, -35, -25, 22, 4, 24, 8, -30],\n [-8, -5, -28, -31, 18, -19, 2, -27, -22, -10, 26, -11],\n [0, -3, -33, -25, 22, 28, -18, 11, 8, 23, 14, 33],\n [-7, 31, -34, -11, -17, 4, -34, 29, 26, 18, 9, 13],\n [33, 2, -32, -19, 17, 17, -5, -14, -25, -2, -21, -26],\n [17, 12, -5, 1, -8, -5, 34, -22, -20, -11, 3, 30],\n [2, 5, 4, 28, -20, 23, -25, -35, -23, -6, 33, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-23, -4, 35, 14, 35, -5, 15, -9, 24, -3, 17, -3],\n [5, -17, 5, 6, -13, -3, -16, -11, 16, -24, -4, -3],\n [32, -21, 15, -30, 33, 33, -1, -2, 27, 32, -18, -10],\n [25, 12, -5, -2, -29, -29, 11, -28, -35, -33, 17, 2],\n [15, -21, 31, 28, 32, -31, -26, -28, -24, 28, 23, 31],\n [14, -13, 4, -18, -15, -35, 2, 5, 6, -27, -13, -25],\n [35, -5, -10, -6, -2, 10, 33, -31, 25, 2, -8, -10],\n [25, -13, 10, -6, 31, -3, -33, 33, 6, 26, 22, 21],\n [-35, 24, 33, 23, 10, -2, -11, 6, -7, -11, 18, 31],\n [-21, -32, 2, -16, -13, 1, 26, -28, 1, 9, -3, -29],\n [-14, -31, -21, -15, -19, 20, 14, -29, 14, 24, -29, 4],\n [9, 23, 19, 28, 29, 18, 4, 17, 8, 27, -34, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-107", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 11) of the inverse of matrix 1/839 * A where A =\n[[14, 16, -27, -16, -18, -6, 29, -12, 11, 8, -7, 32],\n [0, -31, 14, 4, 10, 15, -25, -24, -23, 28, -28, 29],\n [0, 0, -23, -34, 32, 12, -33, 32, -30, -31, -33, -26],\n [0, 0, 0, -15, 7, -8, -15, 0, -12, 18, 2, -19],\n [0, 0, 0, 0, 25, 2, 30, -3, 7, -5, -1, 1],\n [0, 0, 0, 0, 0, 1, -32, -14, -14, -19, 2, -12],\n [0, 0, 0, 0, 0, 0, 7, 17, -21, 20, 20, -5],\n [0, 0, 0, 0, 0, 0, 0, -21, 27, -17, 27, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 21, -26, 1, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 20, -29, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33772", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[19, 12, 20, -26, 16, 14, -2, 0, 25, -20, -18, 35],\n [0, -4, 7, 4, 29, -1, 33, 14, -24, 22, 27, 13],\n [0, 0, 11, -4, 17, -4, 26, 1, 2, -6, 22, -4],\n [0, 0, 0, 23, -16, 1, 13, -17, 19, 4, -29, -31],\n [0, 0, 0, 0, 13, -6, 5, -33, 4, 15, -4, 12],\n [0, 0, 0, 0, 0, 4, 16, 3, 32, 25, 29, 26],\n [0, 0, 0, 0, 0, 0, 27, 28, -24, 5, -7, -13],\n [0, 0, 0, 0, 0, 0, 0, 25, 25, 15, 2, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 32, 15, -23, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -15, 29, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-83184", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[9, 18, -20, 4, 8, 5, -2, 26, 15, 8, 14, -12],\n [18, -11, 6, 15, 20, 0, -8, 4, 20, -4, -16, 3],\n [-20, 6, -20, 3, 7, -2, -10, -16, -12, 0, -18, -22],\n [4, 15, 3, -29, 2, -21, -7, -18, -8, -16, -7, 28],\n [8, 20, 7, 2, 4, -30, -2, 16, -18, 5, 16, 6],\n [5, 0, -2, -21, -30, -19, 12, -27, 24, 7, 4, -4],\n [-2, -8, -10, -7, -2, 12, -29, -28, 20, -29, 10, 16],\n [26, 4, -16, -18, 16, -27, -28, -2, -4, 27, -28, -22],\n [15, 20, -12, -8, -18, 24, 20, -4, -24, -12, 28, -4],\n [8, -4, 0, -16, 5, 7, -29, 27, -12, -9, -25, -12],\n [14, -16, -18, -7, 16, 4, 10, -28, 28, -25, -25, 2],\n [-12, 3, -22, 28, 6, -4, 16, -22, -4, -12, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 5) of the inverse of matrix 1/839 * A where A =\n[[-13, 34, -6, 19, -29, -24, 24, 16, -9, -24, -23, 26],\n [0, -1, 24, -7, -5, 25, -34, -3, 26, 23, 4, 13],\n [0, 0, -23, 18, -23, 3, -13, -22, -19, -12, 22, 27],\n [0, 0, 0, -15, 1, -29, -23, -6, -5, -31, -4, -20],\n [0, 0, 0, 0, 1, -20, 7, 27, -21, 8, -27, 29],\n [0, 0, 0, 0, 0, -5, 30, -18, -8, 32, 29, 9],\n [0, 0, 0, 0, 0, 0, 3, -35, -22, 35, -13, 7],\n [0, 0, 0, 0, 0, 0, 0, -17, 26, 35, 31, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 29, 29, 21, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -4, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-796", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-20, -15, -26, -32, 8, -28, 19, -17, 28, 4, 15, -27],\n [0, 20, 8, 23, -21, 32, 34, 25, -13, 11, -19, 21],\n [0, 0, -14, 3, -23, 30, 16, -22, 27, 35, -8, 10],\n [0, 0, 0, 23, 16, -32, -33, 1, -12, -1, -34, -3],\n [0, 0, 0, 0, 23, -27, 24, 27, 16, -13, -6, 7],\n [0, 0, 0, 0, 0, -13, 22, -5, 33, -30, 29, 23],\n [0, 0, 0, 0, 0, 0, -20, -22, -25, -2, 24, -23],\n [0, 0, 0, 0, 0, 0, 0, 32, 24, -24, -20, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 13, -34, 17, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -29, -31, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15341", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-17, 19, 24, -15, -10, -8, 3, -3, 4, -7, -16, -16],\n [-24, -11, -11, -32, -32, -27, -21, -10, 35, -4, 16, -4],\n [-27, -23, 20, 8, -6, -20, -24, 30, -18, -23, -12, -24],\n [24, 24, -35, 7, 19, 4, 28, -2, -2, 12, -3, 32],\n [-6, 35, 35, -7, -13, -2, -21, 17, -19, 28, 25, 21],\n [1, -29, -28, 32, -15, 25, -7, -11, 22, -22, 30, 18],\n [31, -6, -18, 18, -15, 17, -20, -8, -32, 19, -21, 28],\n [29, -20, -16, 28, -3, 33, 33, 22, 3, 0, 32, -15],\n [27, -30, -12, 17, 14, -24, 20, -21, 4, 5, 33, 33],\n [-30, 31, -3, 7, -15, 29, -19, -28, 28, -8, -23, -23],\n [2, -11, 26, -13, -15, 18, 27, -6, 32, -4, -12, -29],\n [-35, -33, -8, 7, 10, -35, 2, -1, 18, -12, -8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-20, -12, 28, 20, -12, 8, 22, 10, 11, -8, -6, -10],\n [-12, 34, -20, 6, -2, 14, -24, 7, -12, 5, -10, 13],\n [28, -20, -30, -4, 14, 20, -12, 20, -11, 0, 5, -8],\n [20, 6, -4, 32, -30, 6, 10, 8, 8, -28, -7, -16],\n [-12, -2, 14, -30, -1, 1, -26, -28, -2, 2, -18, 22],\n [8, 14, 20, 6, 1, 32, -12, 4, 34, 2, -2, -8],\n [22, -24, -12, 10, -26, -12, 9, -2, 22, -17, 32, 32],\n [10, 7, 20, 8, -28, 4, -2, -2, -18, 4, -4, -11],\n [11, -12, -11, 8, -2, 34, 22, -18, -18, 28, -6, -14],\n [-8, 5, 0, -28, 2, 2, -17, 4, 28, -9, -10, 16],\n [-6, -10, 5, -7, -18, -2, 32, -4, -6, -10, -25, 12],\n [-10, 13, -8, -16, 22, -8, 32, -11, -14, 16, 12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-90", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-2, -1, -3, -4, 19, -28, 10, -22, -28, 35, 18, -15],\n [0, -34, 25, -19, 12, -28, 20, -19, 33, -24, 2, -18],\n [0, 0, 34, 5, 6, 5, 11, -22, -35, -19, 19, 17],\n [0, 0, 0, -6, 30, 9, -18, 9, -17, 32, 14, -11],\n [0, 0, 0, 0, 3, 27, -29, 22, 23, 12, -31, 0],\n [0, 0, 0, 0, 0, 30, 3, -18, -35, 27, -33, -15],\n [0, 0, 0, 0, 0, 0, 9, 0, 28, 18, 32, 14],\n [0, 0, 0, 0, 0, 0, 0, -10, 17, -22, 28, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 35, -12, -24, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 34, -20, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32443", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[26, -31, -26, 27, -11, 8, -11, -6, -22, 7, -8, -17],\n [6, -16, -25, 18, -12, 34, -19, -8, 14, 19, -26, -15],\n [22, -2, 7, -25, -3, 22, 10, 25, 26, -35, -15, 26],\n [28, 20, -35, -15, -14, 18, -32, 29, 15, 27, -21, 0],\n [-7, 16, 10, 33, -7, 11, -11, -20, 5, 29, 33, -16],\n [33, 0, 22, 12, -34, -7, -20, -1, 26, -32, 32, 15],\n [-3, -12, -11, -8, -29, 0, -26, 0, -18, -30, -29, -24],\n [5, 27, -11, 17, -3, -30, 26, 30, -27, 31, -20, 19],\n [4, -10, 2, -1, 32, 23, -22, 11, 35, 6, 15, -17],\n [30, 11, 29, 6, 2, -23, 8, -12, -6, 34, 2, -13],\n [21, -13, 0, 21, -35, -33, -22, -2, 34, 33, 15, -7],\n [12, -20, 21, -26, -17, 31, 0, -32, -3, -8, -27, -30]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[13, -14, 12, -15, -3, 20, -7, 17, 4, -18, 11, -23],\n [-9, 26, 9, -33, -14, -9, 19, 31, -3, -34, 10, -3],\n [22, -29, -21, -10, -25, 2, -9, -29, -35, -15, -6, -28],\n [-33, 19, -21, 0, -30, 6, 14, -18, 14, -6, 3, -24],\n [23, 8, -32, 0, 12, -22, 13, 31, -27, -15, -20, -20],\n [-8, 15, 20, 21, 16, 10, 2, 12, 5, 23, 31, 30],\n [-9, -4, 20, -26, 4, -19, 22, -30, 3, -18, 6, -32],\n [-16, -8, 4, 29, 8, -13, 21, 11, -23, -20, 19, 29],\n [-20, 1, 16, -26, 2, 8, 18, 15, 16, 34, 23, -23],\n [5, -24, 14, 21, 14, 21, 18, 30, -28, 27, -27, 24],\n [27, -33, -23, -27, 16, 26, -28, 9, 17, 27, 21, 18],\n [-17, 31, 10, -26, -18, -24, 13, -13, 26, -25, 20, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-11, -27, -24, -25, 2, -8, -28, 11, 0, 14, -27, 24],\n [0, 17, -19, 17, -8, 27, -21, -17, 34, 11, 35, 12],\n [0, 0, -34, 28, 0, -31, 28, -29, 34, -14, 10, 4],\n [0, 0, 0, -1, -35, -7, -27, -27, -14, 27, 30, 22],\n [0, 0, 0, 0, -3, 29, 24, -24, 7, -19, 32, -7],\n [0, 0, 0, 0, 0, -30, -29, 10, 21, 18, 10, -26],\n [0, 0, 0, 0, 0, 0, -13, 1, -33, -23, -2, 29],\n [0, 0, 0, 0, 0, 0, 0, -3, 18, 0, 20, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, -34, -9, -34, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -15, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149368", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[1, 1, -22, 8, 6, -35, -13, 28, -8, -32, 5, 24],\n [0, 27, 25, 13, 11, 3, -30, 17, -11, 29, -31, 29],\n [0, 0, 7, -31, -32, -35, 20, 9, 29, -33, -14, 20],\n [0, 0, 0, -5, -6, 30, -26, 35, 23, 15, -27, 18],\n [0, 0, 0, 0, 3, -28, -11, 30, -26, -12, 23, -5],\n [0, 0, 0, 0, 0, 12, -23, 23, 31, 20, 5, 20],\n [0, 0, 0, 0, 0, 0, -9, 12, -12, -18, -9, 18],\n [0, 0, 0, 0, 0, 0, 0, -18, -33, -12, -35, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, -32, -28, 25, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 11, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "166761", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[13, 21, -20, -28, 31, -17, 31, 0, 24, 0, -25, 15],\n [19, 18, -19, 26, 6, -12, -19, 12, 34, -29, -22, -25],\n [-24, -31, -31, -16, 18, 19, 22, -6, -12, -33, 12, 35],\n [-14, -22, 12, -7, 14, -26, 35, -9, -8, -27, 35, -10],\n [-28, -34, 21, 16, 22, -33, -28, 23, -34, 26, 13, -16],\n [-7, -19, -14, -30, 26, -5, 26, -24, -24, 27, -20, -11],\n [-14, -18, 9, 32, -24, 13, -3, 27, -18, 18, -9, -11],\n [-2, 24, 18, -31, 0, 18, 0, 33, 3, 34, -32, 29],\n [4, 1, 31, -5, 11, -9, 15, -16, -23, 27, 8, -12],\n [-33, -26, 29, 13, 22, -34, 30, -5, 32, 1, -12, 8],\n [5, 15, 6, 4, 12, -32, 24, 3, -31, -30, -22, 34],\n [-24, 26, -9, 18, -24, -28, -20, 16, -10, -28, 9, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1037", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (9, 3) rounded to the nearest integer?\n[[-19, 4, -6, -6, -13, -3, 26, 4, 14, 1, -6, -22],\n [4, -31, 15, -10, 6, 6, 0, -26, -6, -20, -19, 18],\n [-6, 15, 12, 3, 2, -6, -5, -13, 3, 2, -33, 0],\n [-6, -10, 3, 25, 14, -25, 2, 0, 5, 20, -9, 23],\n [-13, 6, 2, 14, 19, -13, 3, -20, -31, 22, -4, -2],\n [-3, 6, -6, -25, -13, 6, 5, 2, 2, 30, 4, 6],\n [26, 0, -5, 2, 3, 5, -33, -22, 2, 0, 18, 31],\n [4, -26, -13, 0, -20, 2, -22, 23, -25, 6, -12, 4],\n [14, -6, 3, 5, -31, 2, 2, -25, -4, -24, -16, -12],\n [1, -20, 2, 20, 22, 30, 0, 6, -24, -14, -32, 26],\n [-6, -19, -33, -9, -4, 4, 18, -12, -16, -32, 31, 32],\n [-22, 18, 0, 23, -2, 6, 31, 4, -12, 26, 32, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[11, -14, 10, 22, 25, 10, -35, -11, 25, -22, 9, 3],\n [30, -4, 22, 20, -30, 31, 14, 2, -33, -31, -12, 18],\n [-2, 3, 12, 13, -2, -29, -18, 34, -2, 15, 32, -22],\n [33, -28, -21, 23, -25, -16, 19, 0, -22, 22, 2, -35],\n [29, -35, 24, -11, -26, 14, -24, -4, -3, -10, 6, 14],\n [25, 5, 21, -34, 34, -5, -13, 18, -8, -17, 12, -34],\n [-25, 8, 23, 23, 2, -11, -15, 6, 0, -27, -24, -26],\n [23, -31, -3, 33, 27, -7, -18, -30, 17, -4, 6, 11],\n [-5, 26, 20, -25, -10, -9, 21, -9, 23, 26, -16, -33],\n [-20, 8, -6, 4, 29, -7, -6, -4, -26, 15, -28, 15],\n [0, 19, -1, 0, 20, 0, 25, 26, -11, 28, 24, 21],\n [34, 16, 20, 27, 32, -16, 18, -35, -26, -13, 15, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-23, -18, 12, 6, -2, 12, 4, -17, -16, -16, 12, 4],\n [-18, 2, -17, 2, -12, -10, -12, -6, 16, -20, 3, 7],\n [12, -17, -32, -9, -16, 11, -10, -7, -6, 26, -4, -13],\n [6, 2, -9, 30, 4, -2, -6, -6, -16, -4, -8, -24],\n [-2, -12, -16, 4, 34, -3, 4, -32, 3, -12, 22, 14],\n [12, -10, 11, -2, -3, -32, -10, 0, 22, -2, 2, -15],\n [4, -12, -10, -6, 4, -10, -1, -4, 8, 9, 2, 10],\n [-17, -6, -7, -6, -32, 0, -4, -19, -10, -27, -32, -3],\n [-16, 16, -6, -16, 3, 22, 8, -10, 0, -14, -2, -7],\n [-16, -20, 26, -4, -12, -2, 9, -27, -14, 15, 6, 21],\n [12, 3, -4, -8, 22, 2, 2, -32, -2, 6, 7, 8],\n [4, 7, -13, -24, 14, -15, 10, -3, -7, 21, 8, -30]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-328", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-2, 20, -11, -23, 27, 30, -31, -25, 8, 33, -34, 4],\n [1, 13, 0, 34, -2, 22, 1, 24, -24, -4, -32, -3],\n [7, -27, 15, -16, 3, -13, 5, 8, -1, -13, 22, 12],\n [22, 21, 3, -8, 28, 26, 26, -10, 15, 14, 0, -10],\n [-3, 32, -28, 30, -13, 34, 19, 7, -15, -14, -27, -2],\n [23, -10, -35, -31, 5, 27, -14, 32, 12, 30, -20, 17],\n [29, 28, 32, 27, 26, 35, 9, 16, 29, -34, 13, -14],\n [-7, -1, -12, -6, 6, 35, 14, 35, 24, -6, -24, 13],\n [10, 7, -34, 18, -1, 16, -3, 15, -10, 26, 25, -10],\n [1, -6, -25, 17, 5, -31, 30, -23, 27, -11, 8, -22],\n [33, 23, 20, 16, 30, 32, -24, 32, 7, -30, -21, 6],\n [-5, 17, -30, -3, -7, -15, 18, 20, -15, 19, 22, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2385", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (7, 10) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -9, 12, -30, 7, -13, -24, 2, 5, 2, -12, -20],\n [-9, -21, -14, 15, 16, 2, -16, 22, 7, -2, 16, 10],\n [12, -14, 5, 0, -6, 2, -4, 0, -14, 16, 6, -8],\n [-30, 15, 0, -27, -26, -24, -6, 2, 14, -18, 14, 10],\n [7, 16, -6, -26, 24, 16, -9, 20, -24, -7, -13, 13],\n [-13, 2, 2, -24, 16, -19, -1, -18, 9, -2, 3, -32],\n [-24, -16, -4, -6, -9, -1, -8, -7, 19, -24, 16, 34],\n [2, 22, 0, 2, 20, -18, -7, 2, -26, 0, -10, -1],\n [5, 7, -14, 14, -24, 9, 19, -26, -11, -4, 4, -16],\n [2, -2, 16, -18, -7, -2, -24, 0, -4, 9, -15, 4],\n [-12, 16, 6, 14, -13, 3, 16, -10, 4, -15, 11, 26],\n [-20, 10, -8, 10, 13, -32, 34, -1, -16, 4, 26, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "221", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, -30, -22, 22, -5, 5, -1, -26, -6, 8, 19, 35],\n [-18, 3, 6, 18, -6, -16, 6, -31, 14, 5, 3, 21],\n [21, 1, -29, -31, 15, -28, 20, -25, -14, -25, 24, -21],\n [2, -35, 10, 7, -14, -33, -22, -34, 25, -4, 2, 10],\n [6, -30, 5, -11, -25, 5, 35, 21, 10, 12, 27, 3],\n [-26, 34, 29, 23, 0, -9, 19, 34, 17, 24, 25, 0],\n [-9, 5, -8, -20, -1, 0, 20, -17, 21, -3, -13, 27],\n [34, -14, 31, 23, -11, -19, 3, 3, -12, 2, 21, 8],\n [0, 34, 9, -10, -25, 16, -11, -5, 9, 31, 4, 10],\n [18, 5, 2, 0, 8, 21, 30, -6, -26, 25, 27, 0],\n [18, 29, -32, 19, 18, 28, -14, -11, 23, 21, 18, 8],\n [16, -20, -20, 19, 25, 4, -15, 30, -28, 35, -26, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1095", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-32, -14, 31, 18, -1, -5, 5, -1, 0, -2, 8, -16],\n [-14, -26, -8, -14, -25, -12, 2, 8, 0, -11, -3, 9],\n [31, -8, 32, 10, 28, 18, -24, 0, 0, 6, -30, 13],\n [18, -14, 10, -1, -5, -10, 3, 23, 2, 22, -4, -22],\n [-1, -25, 28, -5, -17, 0, -12, -22, -8, -6, -19, 0],\n [-5, -12, 18, -10, 0, 32, 30, 2, 4, 1, 5, 4],\n [5, 2, -24, 3, -12, 30, -11, -22, -2, -4, 12, 22],\n [-1, 8, 0, 23, -22, 2, -22, -18, 24, 0, 4, 11],\n [0, 0, 0, 2, -8, 4, -2, 24, 7, -16, 7, -16],\n [-2, -11, 6, 22, -6, 1, -4, 0, -16, 3, -10, 11],\n [8, -3, -30, -4, -19, 5, 12, 4, 7, -10, -8, 16],\n [-16, 9, 13, -22, 0, 4, 22, 11, -16, 11, 16, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-347", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-27, -1, 24, 27, 16, 12, 25, -12, 22, 28, -6, -7],\n [0, 3, 19, -8, -18, 5, 29, 10, 24, -27, 9, 24],\n [0, 0, 15, -28, 34, 23, 25, 22, 34, -24, -27, 13],\n [0, 0, 0, -4, -1, 13, 18, -20, -24, -28, -15, 12],\n [0, 0, 0, 0, -21, -32, 26, -32, 5, 19, -8, 11],\n [0, 0, 0, 0, 0, -8, -22, 10, -23, -20, 4, -6],\n [0, 0, 0, 0, 0, 0, -19, -5, -26, 34, 1, 28],\n [0, 0, 0, 0, 0, 0, 0, -9, 19, -17, -13, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 27, -24, 7, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -5, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "113", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-31, -20, -25, -1, 6, -26, -28, -10, -33, 23, -33, 2],\n [0, -19, 0, -34, -2, -9, 1, 35, -14, 32, -22, -13],\n [0, 0, 25, 19, 35, 14, -24, -21, -19, -2, -1, 3],\n [0, 0, 0, -6, -32, -21, -1, 19, 30, 24, -12, -14],\n [0, 0, 0, 0, 34, -4, -34, 23, -22, 15, -25, -26],\n [0, 0, 0, 0, 0, -10, -29, 9, 9, 35, -1, 16],\n [0, 0, 0, 0, 0, 0, 12, 16, -21, 19, 7, 14],\n [0, 0, 0, 0, 0, 0, 0, 17, -2, 5, -26, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, -20, 2, -32, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -29, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "185647", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[10, 16, 25, -23, 4, 25, 8, 26, 8, 12, 23, 21],\n [-25, -11, 25, 10, 18, -2, -29, 26, 21, -31, -1, 1],\n [24, 29, -20, -6, 6, 25, 12, 26, 28, 21, 32, 10],\n [-8, -33, 1, 12, -17, -19, 4, 14, -7, 15, 6, -7],\n [30, -19, -5, 16, 3, 24, 15, -20, -22, 6, 15, -12],\n [7, -17, 25, 27, -10, -1, 31, 20, 4, -7, -30, 16],\n [-35, 16, -12, -2, -29, -25, 0, -16, 27, 27, 33, -6],\n [-6, -14, 25, -15, 1, -9, -1, 2, 24, 34, -4, -9],\n [-33, 13, -6, -14, -17, -5, -16, -17, -34, 4, 3, 18],\n [-9, -24, 35, -19, -26, -17, -6, -6, -11, 30, -1, 15],\n [35, 35, -9, -26, 7, 19, 35, -30, -30, 12, -34, 15],\n [25, -17, -34, 15, -10, 34, -16, -13, 18, -21, -30, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-28, 21, 14, 13, -15, 0, 35, 33, 22, 27, -20, -30],\n [16, -34, -18, -1, 3, -35, 1, -15, -35, -32, 22, -35],\n [-23, 10, 11, -29, 15, -33, 14, -10, -5, 26, -10, 31],\n [19, -8, 8, 2, -6, 30, -28, -22, 26, 27, 30, 4],\n [-23, -19, -21, -3, -20, -23, -13, 0, 7, 14, -23, -6],\n [21, -6, 35, -26, 30, 3, 1, -33, -2, 2, -22, 28],\n [3, 18, -34, 7, 17, -33, 5, -28, 27, 29, -32, 32],\n [-26, 14, -13, 25, 11, -33, -19, -14, -20, -33, 16, -3],\n [6, -34, 3, 10, 12, -9, -21, -29, 21, 6, -27, -30],\n [21, -6, 19, 18, -9, 23, -29, 4, -34, -22, -26, 14],\n [-18, -18, -20, 16, 33, 16, -5, -13, 6, 26, 14, -21],\n [8, 6, 9, -1, -14, 2, 34, 28, -29, 8, -29, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-73", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[24, -35, 26, -18, -29, 18, 31, -26, 25, 23, 23, 33],\n [27, -28, 19, -30, -35, 20, -26, -13, -20, -20, 20, -30],\n [-6, 27, -35, 15, 10, -15, 2, 33, 27, 14, -24, 33],\n [8, 16, -27, 29, -26, 10, 22, 1, 16, -23, -30, 22],\n [12, -4, -25, -31, -30, -15, 6, -9, -33, 24, 30, 13],\n [-2, 1, 6, 29, 24, -35, 23, -32, -22, -18, -2, -35],\n [17, -14, 25, -14, 14, -20, -8, 34, 6, 30, 35, -1],\n [-16, -34, -29, 13, -27, -9, -34, 32, 24, 13, -34, -19],\n [-16, -4, 15, 6, 27, 25, 26, -33, -10, 12, -28, -31],\n [-25, 6, 5, -17, 12, 17, 19, 25, -4, 10, 0, -18],\n [-18, -24, 10, 19, 2, -34, -27, -31, -17, 35, 3, 6],\n [-19, 27, 10, -16, 34, -28, -17, -4, -17, -12, -12, 20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "133", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, 0, -12, 14, -3, -10, -5, -14, 4, 4, 19, 24],\n [0, 4, 2, -10, -22, -8, 24, -10, 24, -3, -10, 4],\n [-12, 2, -21, 26, 2, 0, -3, 2, -2, 2, 1, 25],\n [14, -10, 26, 18, 14, -23, 4, -4, 6, 24, 4, -9],\n [-3, -22, 2, 14, -3, -30, 14, -14, -8, 2, -23, 4],\n [-10, -8, 0, -23, -30, -6, -8, -21, 14, 4, -4, -4],\n [-5, 24, -3, 4, 14, -8, -28, 9, 10, 8, 12, -26],\n [-14, -10, 2, -4, -14, -21, 9, 14, 1, 3, 2, 6],\n [4, 24, -2, 6, -8, 14, 10, 1, 26, -17, 6, -14],\n [4, -3, 2, 24, 2, 4, 8, 3, -17, 2, -18, 0],\n [19, -10, 1, 4, -23, -4, 12, 2, 6, -18, -10, 0],\n [24, 4, 25, -9, 4, -4, -26, 6, -14, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2278", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[11, 24, -33, -27, -12, -32, -27, -35, -1, -24, -18, -26],\n [-18, -12, -35, -20, -21, 26, -31, 9, 16, 35, -29, -9],\n [-23, -19, 8, -23, -31, -3, -32, -10, 32, -20, -14, 0],\n [22, 19, -1, -11, 25, -18, 22, 21, 27, -24, -25, -23],\n [-1, -9, 31, 9, 31, -14, 6, -16, 12, -18, 34, -30],\n [3, -25, -11, 19, 22, 1, -20, 34, 1, 17, -20, -18],\n [-17, 8, -34, 22, -26, 10, -17, 2, 1, 9, -2, -34],\n [8, -9, 12, -29, -9, 35, -18, -3, -3, -11, -22, 2],\n [2, -32, 26, -26, -1, -13, 29, -11, 17, -19, 21, -16],\n [-11, 6, 9, -5, 29, 16, -15, -6, -33, 34, 7, -7],\n [-33, 22, -3, 9, 33, -4, 16, 28, 4, -23, -7, 27],\n [-10, 23, 13, 17, -5, -24, 22, 0, -26, -30, -29, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1349", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-33, 6, -4, -6, 18, -8, -24, 19, -11, 16, 2, 22],\n [6, 31, -3, -12, 5, 24, -12, 4, -4, 16, 16, 12],\n [-4, -3, 2, 8, 10, -6, -32, -1, 14, -10, 18, -6],\n [-6, -12, 8, -28, 5, 12, -8, -6, 5, 2, 12, 13],\n [18, 5, 10, 5, -19, -8, 1, -3, 18, 0, 15, 20],\n [-8, 24, -6, 12, -8, -14, 10, 11, -8, -4, 13, 2],\n [-24, -12, -32, -8, 1, 10, -9, 12, -8, -8, 0, -12],\n [19, 4, -1, -6, -3, 11, 12, 1, -13, -2, -11, -2],\n [-11, -4, 14, 5, 18, -8, -8, -13, -20, -9, 2, 0],\n [16, 16, -10, 2, 0, -4, -8, -2, -9, 6, -10, -15],\n [2, 16, 18, 12, 15, 13, 0, -11, 2, -10, 33, -3],\n [22, 12, -6, 13, 20, 2, -12, -2, 0, -15, -3, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-31, -11, -11, -12, 8, -24, -8, 9, 5, -16, -22, 7],\n [-11, 18, -17, -20, 2, -1, -3, -22, -22, -8, -9, 11],\n [-11, -17, -12, 26, 10, -11, 0, 0, 3, 0, 8, -9],\n [-12, -20, 26, -1, -15, -16, -9, -32, -6, -2, 8, 15],\n [8, 2, 10, -15, 18, 2, 26, -10, 1, -3, -16, -8],\n [-24, -1, -11, -16, 2, -14, -9, 1, 8, 14, -6, -7],\n [-8, -3, 0, -9, 26, -9, -15, -31, -6, 33, 0, -8],\n [9, -22, 0, -32, -10, 1, -31, 14, 7, 3, -7, -2],\n [5, -22, 3, -6, 1, 8, -6, 7, -26, -16, 10, 13],\n [-16, -8, 0, -2, -3, 14, 33, 3, -16, -19, 28, 16],\n [-22, -9, 8, 8, -16, -6, 0, -7, 10, 28, -20, -32],\n [7, 11, -9, 15, -8, -7, -8, -2, 13, 16, -32, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-207", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (6, 1) of the inverse. Round your answer to the nearest integer:\n[[-11, -9, 15, 33, -13, -27, -3, -1, 14, -12, -12, -17],\n [0, 25, -11, -11, -9, -4, -25, 33, -3, -17, -20, -25],\n [0, 0, -11, -2, -24, -15, -7, 15, -13, -3, -28, 6],\n [0, 0, 0, -22, 26, 10, 31, 17, 16, -29, 18, -25],\n [0, 0, 0, 0, 22, -25, 19, -17, 3, 34, -25, -22],\n [0, 0, 0, 0, 0, 24, -16, -14, -32, 20, 22, 29],\n [0, 0, 0, 0, 0, 0, 25, -15, -26, -6, -12, 12],\n [0, 0, 0, 0, 0, 0, 0, 33, 32, 13, 22, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, -21, 31, -22, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27, -30, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-18, -2, -13, 4, -10, -29, -8, -19, 6, 9, -3, 8],\n [-2, 26, -18, 32, 0, 2, 10, 20, -10, 8, 12, 4],\n [-13, -18, -13, 2, -9, -21, -12, -14, -26, -14, -1, 22],\n [4, 32, 2, 14, 0, 14, 4, 15, -6, -18, 23, -3],\n [-10, 0, -9, 0, 20, -12, -7, 0, 6, -20, -6, -8],\n [-29, 2, -21, 14, -12, 17, -8, 24, -11, 23, 12, -1],\n [-8, 10, -12, 4, -7, -8, 33, 6, 17, 1, 25, 0],\n [-19, 20, -14, 15, 0, 24, 6, 10, 0, -8, 8, 2],\n [6, -10, -26, -6, 6, -11, 17, 0, -8, 12, 8, 18],\n [9, 8, -14, -18, -20, 23, 1, -8, 12, 0, -8, 9],\n [-3, 12, -1, 23, -6, 12, 25, 8, 8, -8, 28, -10],\n [8, 4, 22, -3, -8, -1, 0, 2, 18, 9, -10, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3000", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-13, -32, -33, 25, -32, 29, -24, -23, -2, 23, -5, 35],\n [-23, 18, -34, -3, 14, -29, -18, 15, -28, 19, 7, 23],\n [-6, 23, -27, 32, 3, -25, -34, -13, 27, -14, 25, -10],\n [-24, -4, -27, 33, 35, -3, -12, 33, 2, -25, -4, 28],\n [-16, -2, 6, -28, 30, -15, 34, -31, 31, 7, -20, -1],\n [7, 3, -26, -16, -35, -30, 17, 10, 30, 2, -3, 31],\n [-1, 9, -14, 32, -19, -31, 21, 4, -6, 6, -29, 35],\n [-17, 5, -2, -14, 16, -30, -11, 30, -26, -10, -31, 32],\n [35, 14, -19, -25, 17, 14, -28, 26, -7, 8, 9, -7],\n [23, -21, 34, 8, 0, 21, 28, 2, -19, -9, -19, 27],\n [-25, 28, 3, -34, 30, 18, -7, 9, -5, 13, -27, -9],\n [20, 9, 7, -14, -3, -9, 4, -10, 9, 9, -10, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-331", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[31, -28, 0, 20, -18, 17, -14, -6, -8, 18, 0, -24],\n [-28, 28, 13, -4, -17, -19, -4, 2, 17, -4, -2, 10],\n [0, 13, -33, -17, -10, -32, -22, 10, 2, 12, 8, 10],\n [20, -4, -17, 23, 26, 7, -6, 6, 4, -26, -8, -12],\n [-18, -17, -10, 26, -33, 16, -2, 18, -2, -14, -14, -16],\n [17, -19, -32, 7, 16, -32, -16, -21, -13, -12, -29, -28],\n [-14, -4, -22, -6, -2, -16, -24, -26, -4, 15, -26, -18],\n [-6, 2, 10, 6, 18, -21, -26, 23, 15, 28, 3, -11],\n [-8, 17, 2, 4, -2, -13, -4, 15, 34, 8, -30, -2],\n [18, -4, 12, -26, -14, -12, 15, 28, 8, 17, -24, -25],\n [0, -2, 8, -8, -14, -29, -26, 3, -30, -24, 2, 8],\n [-24, 10, 10, -12, -16, -28, -18, -11, -2, -25, 8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (2, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -12, 10, -24, 17, 9, -4, -18, -23, -32, -13, 26],\n [0, 19, 33, 4, -22, -8, 35, 31, -7, 25, 32, -27],\n [0, 0, 27, 10, -23, 9, 17, -19, 11, 26, 14, 7],\n [0, 0, 0, 5, 0, -3, -11, -17, 11, -3, 31, -22],\n [0, 0, 0, 0, -1, -4, 19, 18, 15, 23, -22, -18],\n [0, 0, 0, 0, 0, 35, -30, 34, -28, -21, -10, 3],\n [0, 0, 0, 0, 0, 0, 31, 29, -17, 26, 21, -23],\n [0, 0, 0, 0, 0, 0, 0, -32, 7, 10, 11, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 19, 16, 0, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 31, -5, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-101", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[23, 22, 23, -20, 4, -28, 10, -11, 21, -14, -4, 14],\n [22, 28, -3, 0, 6, 2, -5, 18, -4, -12, 13, 24],\n [23, -3, -33, -26, -16, 19, 32, 1, 10, -8, 4, -4],\n [-20, 0, -26, 15, 3, 16, 14, 7, -16, 2, -4, -11],\n [4, 6, -16, 3, -1, -17, 12, -6, 12, -30, -27, 17],\n [-28, 2, 19, 16, -17, 11, -10, 9, 4, 17, -20, 2],\n [10, -5, 32, 14, 12, -10, -34, -12, 23, 24, -4, -1],\n [-11, 18, 1, 7, -6, 9, -12, 18, 33, 4, 11, -18],\n [21, -4, 10, -16, 12, 4, 23, 33, 27, 26, -16, -8],\n [-14, -12, -8, 2, -30, 17, 24, 4, 26, -9, 20, 16],\n [-4, 13, 4, -4, -27, -20, -4, 11, -16, 20, 31, -3],\n [14, 24, -4, -11, 17, 2, -1, -18, -8, 16, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "234", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (9, 11) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 11, -7, 15, 5, 28, 12, -14, -19, -31, 25, -30],\n [17, -19, 23, 3, 18, 12, 1, 12, 32, -9, -9, 27],\n [16, 11, -15, 21, 6, 12, -9, -3, -1, -20, 0, 30],\n [20, -19, -16, -28, -18, -18, -18, -34, 15, -26, -22, -10],\n [11, -6, 20, 6, -32, -25, -12, 31, 1, -34, -24, -15],\n [33, 35, 28, 32, 7, 18, 26, -24, -35, -3, 28, 32],\n [-22, -22, -27, -10, 13, -19, 32, 24, -33, -11, -15, -24],\n [18, -35, -35, 9, 10, 12, -29, -26, -21, 4, -25, 20],\n [10, 9, -23, -9, 14, 25, -23, -24, -7, -16, -5, -28],\n [-12, 3, -3, 6, -21, 32, 29, -4, -25, 1, -17, 15],\n [-2, 35, 24, 17, -24, 26, 30, 12, 4, -12, 14, 32],\n [7, -19, 19, -2, 34, 24, 15, -1, -2, -20, -18, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-66", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[7, -9, -20, 12, 20, -18, 18, 2, 2, -11, 2, 9],\n [-9, 2, 6, -6, 16, 4, 14, 24, -1, 4, 14, 30],\n [-20, 6, 21, -1, -14, 18, -8, 15, 28, -18, -8, 18],\n [12, -6, -1, -28, 4, -23, 4, -2, -8, -26, -30, -11],\n [20, 16, -14, 4, 1, 19, 4, 4, 3, 16, -7, -3],\n [-18, 4, 18, -23, 19, 13, -11, 6, -16, -8, 4, 0],\n [18, 14, -8, 4, 4, -11, -16, -12, 4, -8, -6, -1],\n [2, 24, 15, -2, 4, 6, -12, 7, -18, -11, -13, -16],\n [2, -1, 28, -8, 3, -16, 4, -18, 23, 1, -16, -4],\n [-11, 4, -18, -26, 16, -8, -8, -11, 1, 12, 1, -10],\n [2, 14, -8, -30, -7, 4, -6, -13, -16, 1, 13, -16],\n [9, 30, 18, -11, -3, 0, -1, -16, -4, -10, -16, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-25, -30, -9, -29, 13, 24, -3, 11, 8, -9, -14, 11],\n [0, -6, -34, -21, 11, -9, 35, -9, -23, 19, -19, 23],\n [0, 0, 1, -28, -3, -29, -2, 35, -29, 5, 19, -29],\n [0, 0, 0, 17, -22, -15, 21, 10, -10, -12, -31, 6],\n [0, 0, 0, 0, -29, -7, -2, -29, 22, -5, 9, 11],\n [0, 0, 0, 0, 0, -31, -35, -5, -1, -6, -21, 20],\n [0, 0, 0, 0, 0, 0, -23, -13, 14, 1, -6, -13],\n [0, 0, 0, 0, 0, 0, 0, -3, -4, 8, 1, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 2, 19, 32, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 35, -28, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "701", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-20, -1, 26, -27, 26, 3, 15, -26, 16, -24, 26, -33],\n [0, -28, -13, -26, -18, 3, -10, -25, -26, -33, 26, 35],\n [0, 0, 25, -28, -23, -24, -1, 18, 15, 7, 30, -21],\n [0, 0, 0, -10, 33, 12, 15, -32, -9, 6, 20, 33],\n [0, 0, 0, 0, 14, 34, -16, -16, 10, -9, -10, -4],\n [0, 0, 0, 0, 0, 10, -28, 19, -5, -20, -16, 2],\n [0, 0, 0, 0, 0, 0, 1, 30, -29, 12, -25, -5],\n [0, 0, 0, 0, 0, 0, 0, -25, 32, 0, 23, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, -19, -31, -34, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 18, -25, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-50252", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[13, -25, 11, -1, 35, -7, 18, -13, -12, -26, 25, -28],\n [0, -7, -10, 1, 16, 2, -30, -28, -19, 26, -2, -17],\n [0, 0, 2, -21, 4, -27, 17, 34, 30, 16, -35, -6],\n [0, 0, 0, -19, -14, -5, 4, -9, 0, -32, 33, -11],\n [0, 0, 0, 0, 9, 27, 19, -6, -22, 20, -17, -10],\n [0, 0, 0, 0, 0, 21, -13, -22, 33, -14, -8, 7],\n [0, 0, 0, 0, 0, 0, 34, 11, 17, 5, -4, -22],\n [0, 0, 0, 0, 0, 0, 0, -19, -8, -35, 17, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, -28, -11, -3, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 26, -15, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "781", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-4, -6, -3, 28, 4, -20, -17, -14, -4, -6, -1, -8],\n [-6, -24, -6, 23, -27, -22, -14, 18, -6, -14, 4, -12],\n [-3, -6, 1, -24, -20, 7, 24, -18, 18, -17, -7, -2],\n [28, 23, -24, -5, 14, 10, 8, 11, 10, 18, -17, -12],\n [4, -27, -20, 14, -35, -1, -28, 1, -14, -9, -9, 20],\n [-20, -22, 7, 10, -1, 31, -4, 10, -10, 17, -1, -8],\n [-17, -14, 24, 8, -28, -4, -33, 32, -22, -8, 15, -19],\n [-14, 18, -18, 11, 1, 10, 32, 14, 6, 2, -14, -13],\n [-4, -6, 18, 10, -14, -10, -22, 6, -29, -24, 18, 2],\n [-6, -14, -17, 18, -9, 17, -8, 2, -24, -21, -11, -11],\n [-1, 4, -7, -17, -9, -1, 15, -14, 18, -11, -18, 13],\n [-8, -12, -2, -12, 20, -8, -19, -13, 2, -11, 13, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "287", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[26, 18, -28, 6, 5, 23, 4, -14, -12, 2, -34, 5],\n [0, -34, 26, -20, -14, -22, 20, 29, 9, 18, 30, 10],\n [0, 0, -14, 4, 3, 5, 32, -29, 35, -32, 23, -10],\n [0, 0, 0, -15, -20, 15, -20, -18, 11, 20, -8, 20],\n [0, 0, 0, 0, 25, -25, 30, -4, -17, 20, -31, -33],\n [0, 0, 0, 0, 0, 35, -13, 34, 4, -22, -7, -20],\n [0, 0, 0, 0, 0, 0, -30, -22, -1, 11, 22, 29],\n [0, 0, 0, 0, 0, 0, 0, -10, 2, 30, -10, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, -21, 20, -1, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -31, -21, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64842", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -14, 10, -3, -7, 5, 4, 6, 17, 22, -5, 4],\n [-14, 24, -26, -27, 32, 5, -4, -2, -16, -16, -24, -14],\n [10, -26, -25, -9, -22, -28, 4, 11, -21, 6, 2, 0],\n [-3, -27, -9, -16, 0, 10, -4, 0, 20, 5, 25, -3],\n [-7, 32, -22, 0, -2, 0, -11, -10, -10, 12, 8, -26],\n [5, 5, -28, 10, 0, -25, 27, -6, 0, 12, 8, 1],\n [4, -4, 4, -4, -11, 27, -34, -20, 30, 0, -20, -30],\n [6, -2, 11, 0, -10, -6, -20, -16, -4, 2, 26, 1],\n [17, -16, -21, 20, -10, 0, 30, -4, 2, 6, -1, 10],\n [22, -16, 6, 5, 12, 12, 0, 2, 6, -18, -26, -2],\n [-5, -24, 2, 25, 8, 8, -20, 26, -1, -26, 17, 6],\n [4, -14, 0, -3, -26, 1, -30, 1, 10, -2, 6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (5, 7) of the inverse. Round your answer to the nearest integer:\n[[-22, -16, -25, 30, -12, 1, -12, -21, -24, 28, -5, 17],\n [0, -6, -1, -15, 27, -19, -24, -18, 24, 31, -21, -20],\n [0, 0, -5, -35, -30, -27, 16, 26, 22, -17, -23, -4],\n [0, 0, 0, -5, -5, 23, 19, -17, 27, -34, 9, 7],\n [0, 0, 0, 0, -29, -3, -27, -6, -18, 20, -5, 27],\n [0, 0, 0, 0, 0, -30, -19, 10, 19, -30, 34, 32],\n [0, 0, 0, 0, 0, 0, 22, -10, 2, 0, 19, -30],\n [0, 0, 0, 0, 0, 0, 0, -7, -13, 0, 34, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 3, -24, -25, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -17, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -10, -19, 14, -19, 4, 14, -22, -6, 21, -6, -28],\n [-10, 30, 14, 10, 8, 1, -1, 18, -6, -11, -4, -34],\n [-19, 14, 26, -11, -10, -12, 8, -12, 8, -20, -4, 16],\n [14, 10, -11, 30, 4, 4, -7, 8, -12, 2, 11, -9],\n [-19, 8, -10, 4, -32, 31, 24, -4, 5, 8, -10, 2],\n [4, 1, -12, 4, 31, 18, 0, 16, 26, 4, -6, -18],\n [14, -1, 8, -7, 24, 0, -24, -2, -16, -2, 22, 16],\n [-22, 18, -12, 8, -4, 16, -2, -27, -14, 4, -28, 6],\n [-6, -6, 8, -12, 5, 26, -16, -14, 19, -4, -17, -3],\n [21, -11, -20, 2, 8, 4, -2, 4, -4, 14, -10, 2],\n [-6, -4, -4, 11, -10, -6, 22, -28, -17, -10, -29, -1],\n [-28, -34, 16, -9, 2, -18, 16, 6, -3, 2, -1, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "262", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (10, 11) of the inverse of matrix 1/839 * A where A =\n[[-26, 4, 2, 1, -6, 6, -28, 4, -25, 30, 6, -6],\n [4, 5, -13, -11, 8, -16, 13, -2, -9, 23, 0, 20],\n [2, -13, -11, -12, -26, -12, -2, 16, -5, 3, -21, 13],\n [1, -11, -12, -15, -25, 31, -12, 12, -4, -19, -8, 20],\n [-6, 8, -26, -25, 22, -10, -16, 6, 14, 12, 0, -29],\n [6, -16, -12, 31, -10, -1, -18, 12, 2, 0, 2, -16],\n [-28, 13, -2, -12, -16, -18, 27, -4, -12, -26, -12, 2],\n [4, -2, 16, 12, 6, 12, -4, -1, 34, -4, 24, 11],\n [-25, -9, -5, -4, 14, 2, -12, 34, 35, -8, 14, -12],\n [30, 23, 3, -19, 12, 0, -26, -4, -8, -9, -4, 32],\n [6, 0, -21, -8, 0, 2, -12, 24, 14, -4, 29, 16],\n [-6, 20, 13, 20, -29, -16, 2, 11, -12, 32, 16, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[29, -31, 10, 10, 3, 6, 10, 18, -1, 6, 32, -13],\n [-31, 18, -18, -5, 6, 24, 20, 7, 8, 16, -32, 23],\n [10, -18, -14, 4, 6, -10, 7, 22, 10, 12, -3, -4],\n [10, -5, 4, 1, 4, 18, 5, 6, -12, 12, 2, -6],\n [3, 6, 6, 4, 29, 8, -19, 4, -5, 15, 3, -6],\n [6, 24, -10, 18, 8, -33, -8, 13, 0, 14, -20, -25],\n [10, 20, 7, 5, -19, -8, 13, 22, -24, -26, -7, -14],\n [18, 7, 22, 6, 4, 13, 22, 19, 18, 0, 0, -18],\n [-1, 8, 10, -12, -5, 0, -24, 18, 23, -22, -18, -7],\n [6, 16, 12, 12, 15, 14, -26, 0, -22, -6, -7, 16],\n [32, -32, -3, 2, 3, -20, -7, 0, -18, -7, 12, 13],\n [-13, 23, -4, -6, -6, -25, -14, -18, -7, 16, 13, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1409", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[14, 27, -24, 5, -5, -34, -20, -35, -32, 11, 29, 16],\n [0, 14, 9, 6, 20, 35, 21, -3, -8, 8, 20, 8],\n [0, 0, 32, -7, -19, -27, -9, 13, 1, -8, 14, 19],\n [0, 0, 0, -32, 1, 15, -4, 9, -24, 5, 20, -22],\n [0, 0, 0, 0, -15, -32, 10, -24, -6, 24, 35, 29],\n [0, 0, 0, 0, 0, -4, -20, 26, -6, 35, -24, 31],\n [0, 0, 0, 0, 0, 0, -4, -28, 26, -16, -18, -30],\n [0, 0, 0, 0, 0, 0, 0, -21, 4, -31, 14, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, -1, 33, 18, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -26, 5, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "775443", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[34, -8, 4, 15, -7, 6, 33, -31, 5, 25, 19, -8],\n [0, -27, -7, 2, 26, 18, 16, -2, 1, 13, 6, -22],\n [0, 0, -4, 32, 3, -26, -12, 22, 33, 28, -17, -28],\n [0, 0, 0, -9, -34, -20, -22, -19, 24, 34, -19, 9],\n [0, 0, 0, 0, 13, -15, -13, 21, 28, -7, -9, -30],\n [0, 0, 0, 0, 0, -15, 22, -32, 33, -29, -1, 0],\n [0, 0, 0, 0, 0, 0, 5, 6, 29, 4, 2, 6],\n [0, 0, 0, 0, 0, 0, 0, 11, 2, 3, -21, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, -13, -23, 32, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 32, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1954362", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 11) of the inverse of matrix 1/839 * A where A =\n[[-18, -10, 19, -14, -10, -2, 12, 32, 8, 0, -8, -14],\n [-10, 16, 10, 6, -12, -12, 8, -14, -24, 16, 18, 16],\n [19, 10, -5, 4, 14, -3, 5, -22, 4, -12, 32, 22],\n [-14, 6, 4, 34, 26, 10, -8, -1, 20, -5, -18, -21],\n [-10, -12, 14, 26, 24, 8, 25, 7, 7, -10, -13, -24],\n [-2, -12, -3, 10, 8, 17, -4, 32, 6, 9, -6, 8],\n [12, 8, 5, -8, 25, -4, -21, -2, 10, -2, -25, 28],\n [32, -14, -22, -1, 7, 32, -2, -7, 8, -18, -10, -28],\n [8, -24, 4, 20, 7, 6, 10, 8, 15, 2, -14, -18],\n [0, 16, -12, -5, -10, 9, -2, -18, 2, 31, 6, -8],\n [-8, 18, 32, -18, -13, -6, -25, -10, -14, 6, 15, -34],\n [-14, 16, 22, -21, -24, 8, 28, -28, -18, -8, -34, 23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-13, -18, 5, -28, -4, 5, 9, -27, 12, -12, 8, 22],\n [30, -18, -7, -34, 32, 3, 5, 35, -14, 13, -8, -20],\n [32, 26, 0, -14, -25, 6, 19, -1, 21, -2, 34, -32],\n [10, -25, 25, -1, 33, 21, -25, -24, 7, -17, 32, 23],\n [-34, -28, -14, -15, -7, 1, -7, 1, -15, -24, 12, 11],\n [-21, 31, -23, 23, -23, -17, 21, -4, -15, -22, -12, 13],\n [-4, -25, 24, 32, 25, -31, 0, 28, -4, 35, 30, -26],\n [-15, 4, 6, 10, 5, -32, -22, -22, 17, -7, -13, -5],\n [35, 25, -13, -28, -20, -10, -7, -30, 1, -3, 10, 25],\n [5, -18, -20, 15, 1, -22, 32, -6, 24, 17, 0, -6],\n [28, -22, -13, 12, -8, -29, 6, -26, 32, 8, -23, -3],\n [-4, 12, -31, 25, -33, -12, -2, 6, -16, 5, -16, -30]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1181", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[21, 6, -11, 5, 5, -33, 7, 10, 21, 15, -31, -21],\n [3, 34, 2, 3, 16, -33, -7, -5, 30, 9, -14, -26],\n [-15, -19, 31, -29, 0, 31, -6, 35, -7, -3, 23, -16],\n [-7, 17, -35, -2, 8, -22, 1, -1, 23, -12, 29, -30],\n [32, 2, -35, 5, -5, 0, 18, -5, -7, -33, 22, 25],\n [-30, -16, 25, 10, -23, -13, -5, -32, 30, -20, -5, 12],\n [7, -32, 26, 12, -8, -20, 33, -6, 29, 33, -22, -2],\n [20, -7, -11, 30, 4, -21, -4, -16, 17, 31, 13, 31],\n [-35, 3, 25, 19, 33, -34, -19, -7, -32, 28, 7, -24],\n [14, 32, 25, 15, -31, -8, -26, 16, -19, 29, -15, 18],\n [13, -14, 33, 28, 0, -15, 20, 12, -18, -21, 8, 9],\n [0, 4, 15, -6, -10, -5, 20, 25, -19, -12, -32, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3260", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-34, -1, 2, 9, -21, 6, -33, -5, 16, 5, 21, 6],\n [17, 20, 17, -4, 18, 1, -28, -25, 18, 24, -26, 34],\n [6, 1, 22, 23, -12, -8, 1, -15, -3, -34, -8, -21],\n [-35, -8, 14, -1, -8, -27, -12, 27, -32, 20, 5, 31],\n [12, 22, 3, -11, 24, 11, 25, -9, 6, 16, 12, -4],\n [-12, -33, -9, 4, -13, -29, 1, -29, -14, -19, -17, 3],\n [0, -21, 27, -7, 24, 20, 4, -20, -3, -20, -6, 30],\n [8, 2, 15, 24, -18, -31, 4, -30, -24, -24, -14, 13],\n [14, -32, 14, -33, -20, -22, 28, 5, 32, 23, -34, -26],\n [-10, -32, -8, -34, 30, -20, 21, -13, -13, -15, -11, 22],\n [1, 13, -21, -8, 31, -32, 11, 14, 24, 26, 31, 7],\n [22, 16, 33, 10, -11, -11, -1, 25, -21, -1, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-89", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (2, 8) rounded to the nearest integer?\n[[33, -21, -26, -11, 2, -2, -16, -2, 5, -14, -20, -5],\n [-21, -4, -12, 0, -2, 5, 2, -8, 6, -16, 4, -22],\n [-26, -12, 30, 0, -2, -17, -12, -16, 18, -14, -19, -10],\n [-11, 0, 0, 17, 2, 8, 24, -10, -4, 7, -18, 14],\n [2, -2, -2, 2, 0, 1, -3, 30, 8, -11, 16, -20],\n [-2, 5, -17, 8, 1, 13, -4, 21, 5, -12, -22, 10],\n [-16, 2, -12, 24, -3, -4, -33, -16, -28, -5, -8, -30],\n [-2, -8, -16, -10, 30, 21, -16, 9, -14, -16, 20, -26],\n [5, 6, 18, -4, 8, 5, -28, -14, 5, -6, 20, -12],\n [-14, -16, -14, 7, -11, -12, -5, -16, -6, 24, -4, 7],\n [-20, 4, -19, -18, 16, -22, -8, 20, 20, -4, 26, -8],\n [-5, -22, -10, 14, -20, 10, -30, -26, -12, 7, -8, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (4, 12) rounded to the nearest integer?\n[[5, -31, 27, -35, -11, 10, -21, 33, -19, -15, 17, 19],\n [0, 21, 29, 1, -29, 4, 14, -35, -16, -5, 32, -24],\n [0, 0, -35, -33, -15, -23, 25, -23, -3, -30, -11, -13],\n [0, 0, 0, -11, -16, -35, 32, -13, -14, 26, -35, 23],\n [0, 0, 0, 0, 12, -17, 16, -14, 14, 30, -30, 28],\n [0, 0, 0, 0, 0, 24, -2, -35, 12, -15, -2, -10],\n [0, 0, 0, 0, 0, 0, 25, 1, 16, 26, 30, -12],\n [0, 0, 0, 0, 0, 0, 0, -5, -21, 19, -3, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 24, -12, 3, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 8, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22632", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-32, -10, -22, -6, 4, -8, -3, 10, 18, -8, -20, 7],\n [-10, 12, -10, -4, -16, 2, -22, 19, -2, 31, -29, 2],\n [-22, -10, -20, -12, 6, 10, -2, -4, -10, -14, -14, -2],\n [-6, -4, -12, 35, 2, 6, 0, 12, 2, 18, 4, -10],\n [4, -16, 6, 2, 24, -20, 24, -17, 26, 7, -2, -4],\n [-8, 2, 10, 6, -20, -23, 14, 20, -14, 5, -5, -2],\n [-3, -22, -2, 0, 24, 14, -6, 8, 2, -2, 0, 8],\n [10, 19, -4, 12, -17, 20, 8, 9, 12, -8, 20, 12],\n [18, -2, -10, 2, 26, -14, 2, 12, -24, -2, -1, -14],\n [-8, 31, -14, 18, 7, 5, -2, -8, -2, -17, 14, 2],\n [-20, -29, -14, 4, -2, -5, 0, 20, -1, 14, -10, 0],\n [7, 2, -2, -10, -4, -2, 8, 12, -14, 2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-199", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-11, -15, 6, -35, -13, -12, 11, -29, 2, 11, -1, 26],\n [-33, -16, 8, -4, -10, 12, -31, 23, 25, 13, -6, -19],\n [34, 22, 27, 25, 27, -21, -35, -23, 12, -2, -6, -17],\n [28, 30, 21, 8, -24, 4, -12, -25, 30, -35, 22, -8],\n [32, 23, 35, -14, -7, 33, 9, 34, -19, 3, 4, -8],\n [-34, -9, -15, -29, 25, 16, 12, -17, -24, 35, -34, -19],\n [-33, -15, 15, -26, 19, 0, 15, -19, 25, -23, 29, 12],\n [34, 11, -26, 21, -23, 25, 22, 32, -7, -20, 27, 11],\n [7, -13, -6, 21, -6, 31, 20, -12, -28, 8, -2, -1],\n [14, -19, -34, 18, 8, 13, -34, 34, -27, -35, 33, -27],\n [-22, -9, -27, 0, -33, -13, -6, -17, 31, 14, 12, -33],\n [30, -9, 4, -18, -9, -25, 3, -17, -29, 21, -34, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-31, 3, 0, 6, -1, -15, -6, 6, 3, -4, -8, 2],\n [3, -1, -15, -2, -1, -1, -14, -16, 8, -6, 10, -19],\n [0, -15, 34, -16, -19, -18, -28, 16, -1, 6, 12, 16],\n [6, -2, -16, 29, -16, -12, -10, -20, 6, 1, 13, -5],\n [-1, -1, -19, -16, -26, 14, 10, -18, 19, -2, -12, -8],\n [-15, -1, -18, -12, 14, -27, 6, -12, -2, -10, 4, 27],\n [-6, -14, -28, -10, 10, 6, -30, -6, 0, -13, 19, 13],\n [6, -16, 16, -20, -18, -12, -6, 11, 10, 3, 17, 6],\n [3, 8, -1, 6, 19, -2, 0, 10, 11, 8, 6, -11],\n [-4, -6, 6, 1, -2, -10, -13, 3, 8, 25, 28, 16],\n [-8, 10, 12, 13, -12, 4, 19, 17, 6, 28, 8, 10],\n [2, -19, 16, -5, -8, 27, 13, 6, -11, 16, 10, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8735", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (8, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 10, 5, 10, -35, 32, -24, -1, -3, 22, -1, 10],\n [0, 8, -10, 6, -6, -4, 0, -17, -14, 29, 21, -25],\n [0, 0, -17, -24, 31, 20, -18, -31, -12, 2, 31, 34],\n [0, 0, 0, -10, 29, 12, 17, -27, -31, 25, -15, 27],\n [0, 0, 0, 0, 27, -6, 27, 8, 31, 22, 29, 0],\n [0, 0, 0, 0, 0, -11, -3, -23, 2, 22, -16, -19],\n [0, 0, 0, 0, 0, 0, 21, 22, 31, -14, 22, 13],\n [0, 0, 0, 0, 0, 0, 0, 15, -22, -27, -18, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 6, 12, -18, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 23, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 16, 30, 27, -29, 17, -30, -29, 8, -18, 18, -7],\n [-11, 27, 32, -23, -4, -9, 15, -2, -8, -6, -27, -23],\n [28, 2, -14, -5, 6, 26, 28, -27, 8, 27, 4, 5],\n [14, -16, 34, 6, -3, 27, 21, 29, 16, -30, -29, -27],\n [25, -2, -1, -16, 22, 24, 18, -1, 11, 10, -32, -26],\n [4, 19, 4, -13, -21, -31, 4, -18, -15, -33, 10, 17],\n [-16, 23, -15, 15, -11, 32, -26, 31, -27, -7, 1, 35],\n [2, 23, 21, 24, -8, -8, 10, 35, 31, 19, 2, -18],\n [27, -31, 8, -7, -22, 22, 8, -18, -29, 26, 9, -20],\n [28, 1, -11, -27, 19, -8, -27, -24, -18, 20, 22, 15],\n [-4, 12, -28, -6, -10, -12, -9, 3, 30, 15, 14, 9],\n [-3, -17, -23, -14, -16, -31, -4, -6, -10, -32, 31, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 10) of the inverse of matrix 1/839 * A where A =\n[[-6, -16, 10, 17, -2, 2, -6, -26, 14, -16, 12, 6],\n [-16, 2, -24, 0, -26, -3, -16, 14, 6, 8, -16, 23],\n [10, -24, 34, 28, 1, -14, -2, 0, 0, -3, 15, 12],\n [17, 0, 28, -20, 12, -16, -14, 16, 12, -10, 8, 12],\n [-2, -26, 1, 12, -23, 0, 6, -1, -2, 24, 9, -2],\n [2, -3, -14, -16, 0, -23, 10, 12, -2, -18, -8, 1],\n [-6, -16, -2, -14, 6, 10, 13, -8, -8, 25, -18, -6],\n [-26, 14, 0, 16, -1, 12, -8, 4, 9, -30, -14, 2],\n [14, 6, 0, 12, -2, -2, -8, 9, -13, 22, 16, 1],\n [-16, 8, -3, -10, 24, -18, 25, -30, 22, 15, -2, -4],\n [12, -16, 15, 8, 9, -8, -18, -14, 16, -2, 17, 22],\n [6, 23, 12, 12, -2, 1, -6, 2, 1, -4, 22, 28]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (12, 9) rounded to the nearest integer?\n[[21, -18, -18, -9, -15, 4, 0, 9, -10, 15, 8, -2],\n [-18, 27, -20, -4, -9, 0, 27, 8, -13, -21, -22, 14],\n [-18, -20, 23, 6, 11, 3, 10, 26, 10, -4, 8, 0],\n [-9, -4, 6, 18, -5, -2, 10, 6, 5, -13, 2, -19],\n [-15, -9, 11, -5, -4, 6, 6, -4, -2, 6, 4, -14],\n [4, 0, 3, -2, 6, -34, -25, 18, 14, -2, 2, -11],\n [0, 27, 10, 10, 6, -25, 3, 26, 15, -2, 20, 2],\n [9, 8, 26, 6, -4, 18, 26, 28, -12, -12, -11, -12],\n [-10, -13, 10, 5, -2, 14, 15, -12, 18, -10, 3, -18],\n [15, -21, -4, -13, 6, -2, -2, -12, -10, 13, 5, 22],\n [8, -22, 8, 2, 4, 2, 20, -11, 3, 5, -28, 26],\n [-2, 14, 0, -19, -14, -11, 2, -12, -18, 22, 26, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[25, 31, -21, 17, -32, -13, -9, 1, 7, 1, -7, -7],\n [0, 15, 14, -8, -31, 20, 28, -19, 19, -27, 32, -20],\n [0, 0, 27, 5, 17, 32, -27, 15, 12, 13, -18, -26],\n [0, 0, 0, 4, 11, -16, -14, 12, -20, -31, 29, -15],\n [0, 0, 0, 0, -25, 11, -34, 34, 17, -25, -21, -24],\n [0, 0, 0, 0, 0, -9, -15, 13, 26, 8, 8, 25],\n [0, 0, 0, 0, 0, 0, -18, 2, 31, -16, -17, -23],\n [0, 0, 0, 0, 0, 0, 0, -2, 35, -23, 20, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 21, 34, 16, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -30, -27, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4259", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[11, 30, -21, -12, -26, -12, 21, -2, 5, 4, -25, -35],\n [0, 7, -10, 17, 11, -27, -27, -35, 35, 8, 23, 20],\n [0, 0, 2, -25, -11, 23, -7, 4, -28, -30, 9, 17],\n [0, 0, 0, 27, -30, 17, -32, -27, 33, -32, 22, 1],\n [0, 0, 0, 0, -22, -25, -26, 25, -23, -2, 24, 15],\n [0, 0, 0, 0, 0, 18, 18, 5, 12, 15, 11, 14],\n [0, 0, 0, 0, 0, 0, 21, -2, -17, -27, -3, -9],\n [0, 0, 0, 0, 0, 0, 0, -9, 2, -17, 1, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, 18, 5, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 33, 15, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28553", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[10, -30, 4, -2, -28, 8, 9, 16, -6, -17, 16, -18],\n [-30, 28, -11, 16, 6, -11, -4, -8, -8, 2, 6, -14],\n [4, -11, 0, -22, -22, 4, -2, 2, -10, 14, -4, -6],\n [-2, 16, -22, -24, -14, 7, 6, 10, 2, -14, 1, -23],\n [-28, 6, -22, -14, -8, -10, -12, 2, 8, -2, 2, -10],\n [8, -11, 4, 7, -10, -29, 16, -8, 6, 12, 0, 9],\n [9, -4, -2, 6, -12, 16, -21, 14, 18, -6, 13, 20],\n [16, -8, 2, 10, 2, -8, 14, -31, -4, -4, 10, -8],\n [-6, -8, -10, 2, 8, 6, 18, -4, -7, 25, 20, 0],\n [-17, 2, 14, -14, -2, 12, -6, -4, 25, 34, -8, 8],\n [16, 6, -4, 1, 2, 0, 13, 10, 20, -8, 4, -2],\n [-18, -14, -6, -23, -10, 9, 20, -8, 0, 8, -2, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5890", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-19, 25, 10, 19, 14, -25, -24, 4, 12, 20, -28, -22],\n [0, 18, -19, 9, -31, -33, -27, -16, -15, -3, -31, -12],\n [0, 0, -3, -18, -18, 2, -3, -9, 13, 14, -21, 16],\n [0, 0, 0, -11, -3, 24, 1, 7, -27, -22, -33, 33],\n [0, 0, 0, 0, -15, 3, -13, 22, 33, -7, 26, 17],\n [0, 0, 0, 0, 0, 24, 6, 15, -25, -1, -17, 29],\n [0, 0, 0, 0, 0, 0, -26, -19, 4, 32, 27, -21],\n [0, 0, 0, 0, 0, 0, 0, -33, 15, 10, 19, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 6, -12, 16, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 2, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12012", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[29, -6, 10, 6, -2, -14, 1, 16, -7, -22, 6, 2],\n [-6, -24, -29, 4, 11, -16, 3, 12, 2, -1, 10, 9],\n [10, -29, -30, 6, 13, 4, 7, 6, -12, 22, -4, -6],\n [6, 4, 6, -31, 4, -12, -22, -4, -3, 18, -8, -28],\n [-2, 11, 13, 4, -10, -9, -15, 10, 18, -19, 6, 14],\n [-14, -16, 4, -12, -9, -14, -4, 18, -14, 4, -2, 14],\n [1, 3, 7, -22, -15, -4, 7, -16, -2, -2, 0, -15],\n [16, 12, 6, -4, 10, 18, -16, 27, -32, -18, -28, 2],\n [-7, 2, -12, -3, 18, -14, -2, -32, -32, -28, -30, 26],\n [-22, -1, 22, 18, -19, 4, -2, -18, -28, 33, -13, 10],\n [6, 10, -4, -8, 6, -2, 0, -28, -30, -13, -1, 14],\n [2, 9, -6, -28, 14, 14, -15, 2, 26, 10, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-163", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 4, 33, 26, -21, -33, -12, 5, 27, 12, 25, 12],\n [0, 20, -28, -18, -13, 33, 29, 10, 30, 33, -14, 29],\n [0, 0, -14, 19, 26, 15, 12, -19, -23, -8, 31, -31],\n [0, 0, 0, 10, -7, 32, 13, 7, 32, -16, -18, 28],\n [0, 0, 0, 0, -28, -8, 24, 13, 2, 22, -31, 10],\n [0, 0, 0, 0, 0, 32, 33, 33, -20, 18, 27, -18],\n [0, 0, 0, 0, 0, 0, 6, 5, -6, -10, 13, -5],\n [0, 0, 0, 0, 0, 0, 0, 8, 27, 14, -14, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 18, -24, -17, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 1, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "601", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[5, 0, 4, 0, -2, 1, -2, 16, 1, 26, -26, 4],\n [0, -4, -6, 20, -32, -4, 14, 22, -5, -12, -22, 4],\n [4, -6, 31, -6, 4, -2, -18, -5, 21, 15, 5, 12],\n [0, 20, -6, -23, 6, -4, -1, -6, 16, 28, 0, -22],\n [-2, -32, 4, 6, 31, -14, -2, 11, -7, 11, 12, -8],\n [1, -4, -2, -4, -14, 7, -2, -18, -3, 14, -28, 9],\n [-2, 14, -18, -1, -2, -2, -32, 4, 12, 8, -10, 32],\n [16, 22, -5, -6, 11, -18, 4, 24, -4, 15, 6, -2],\n [1, -5, 21, 16, -7, -3, 12, -4, -14, -34, 18, -8],\n [26, -12, 15, 28, 11, 14, 8, 15, -34, 9, -8, -24],\n [-26, -22, 5, 0, 12, -28, -10, 6, 18, -8, -31, 18],\n [4, 4, 12, -22, -8, 9, 32, -2, -8, -24, 18, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-721", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -27, 22, -13, -33, 25, -27, 17, 32, 13, 34, 12],\n [0, -5, 20, 25, -31, -6, -14, -19, -26, 35, 32, 6],\n [0, 0, -13, -28, -28, -31, 35, -34, 15, 30, -24, 11],\n [0, 0, 0, 26, 34, -34, -10, -22, 21, -4, 26, -6],\n [0, 0, 0, 0, 9, 23, -8, 25, -17, 7, 23, -20],\n [0, 0, 0, 0, 0, -17, 15, -23, 27, -20, 17, -1],\n [0, 0, 0, 0, 0, 0, 10, 16, -7, -31, 31, 4],\n [0, 0, 0, 0, 0, 0, 0, -22, -21, -30, -20, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, -28, 3, 1, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 7, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-121531", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-7, -21, 22, -13, 2, 5, -21, -33, -35, -25, 24, 29],\n [-32, -11, 7, 4, 8, 23, -13, 26, -13, 22, 19, -3],\n [27, 24, 25, 25, 33, -15, -33, 12, -26, 6, 30, 10],\n [-27, 13, -32, 24, -7, 11, 27, -5, 15, 5, 0, 4],\n [24, -21, -6, -6, -9, 4, 9, 11, 20, 18, -27, 29],\n [34, -35, -23, 2, 9, 4, -21, 14, -34, 17, -10, 30],\n [-3, 23, -10, -15, 13, 35, 35, 30, 1, -22, -29, 2],\n [9, -14, 8, -1, 24, -33, 31, 19, -27, 33, -8, -21],\n [-5, 23, 18, 32, 11, 6, -13, 29, 18, -25, 27, -14],\n [18, 0, 22, -16, -20, 20, 14, 30, -23, -21, -9, -28],\n [34, 14, 31, -10, 0, -15, 16, -25, -28, 21, 10, -34],\n [28, 16, 29, -25, -30, 28, 19, 8, -22, -31, -11, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3065", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[35, -34, -26, -34, 24, 9, -28, 22, -29, -15, 11, -35],\n [0, 12, -32, -2, -4, -33, 32, 21, -12, -3, -33, -32],\n [0, 0, 13, -6, -20, 17, -30, -12, -8, -15, -28, 0],\n [0, 0, 0, -35, 27, 32, -10, 4, -33, -27, -4, 31],\n [0, 0, 0, 0, 30, -33, -1, 23, 2, -3, -21, -22],\n [0, 0, 0, 0, 0, -7, -2, 23, 7, -3, -17, -28],\n [0, 0, 0, 0, 0, 0, -29, 3, -16, -25, -20, 6],\n [0, 0, 0, 0, 0, 0, 0, -34, -11, 5, 16, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, -5, -23, -9, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 2, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13416", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-20, -14, -13, 11, 31, -33, -24, -13, -25, 16, 14, 21],\n [28, 10, -7, 34, 10, -20, 15, -25, -25, 27, 17, 22],\n [-17, -4, 14, 19, 5, 34, -15, -10, -35, -9, 14, 30],\n [29, -26, 1, 33, 5, 10, 9, -9, 29, -28, 31, 13],\n [-22, 26, 7, -9, -9, 32, 12, 31, -11, 28, -12, -27],\n [-28, 23, -19, 7, 32, -32, -28, 6, 13, -30, 6, -4],\n [-21, 33, -9, 30, 23, -8, -12, 15, -15, -5, 14, 4],\n [32, -20, 27, 20, -12, -8, -5, -21, 6, 14, -31, 12],\n [-23, -4, 31, -6, -30, -11, -8, 26, -14, 32, -21, -10],\n [27, -18, 27, 26, 32, 12, 14, 27, 33, -30, 22, 15],\n [-24, 11, -27, -29, -7, 15, 19, 23, 20, -14, -18, 22],\n [4, -5, 20, -1, -10, 32, -2, -20, 6, -31, 25, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-292", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (8, 7) of the inverse. Round your answer to the nearest integer:\n[[-1, -21, 2, -19, 11, -18, 19, -3, -12, -2, 17, 6],\n [-21, -6, -6, -10, 10, -24, -26, 13, -22, -8, -18, 6],\n [2, -6, -4, 10, -13, 31, 18, 0, 14, -5, 16, 18],\n [-19, -10, 10, 28, -6, 25, -27, 1, -24, 28, -6, -29],\n [11, 10, -13, -6, -13, -3, 0, -6, 4, -12, 10, 6],\n [-18, -24, 31, 25, -3, 22, 24, -24, -17, -22, -12, -29],\n [19, -26, 18, -27, 0, 24, 5, 20, -6, 2, -7, 14],\n [-3, 13, 0, 1, -6, -24, 20, -28, 8, 8, 2, -18],\n [-12, -22, 14, -24, 4, -17, -6, 8, -21, 4, -21, 2],\n [-2, -8, -5, 28, -12, -22, 2, 8, 4, -31, -6, -6],\n [17, -18, 16, -6, 10, -12, -7, 2, -21, -6, 34, 7],\n [6, 6, 18, -29, 6, -29, 14, -18, 2, -6, 7, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "858", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-18, -27, 31, -29, 22, -6, 25, -19, 17, -30, 3, -11],\n [6, 6, 23, 2, -5, -7, -27, -35, 11, -26, -20, 11],\n [7, -12, -28, -10, -29, -21, 12, -33, -20, -22, -33, 34],\n [-5, -19, 13, -33, 19, 4, 30, 4, -6, -11, -29, 14],\n [-35, 8, 13, -29, -33, -35, 15, 2, 7, 19, 21, 17],\n [-3, 26, -25, 16, -35, -22, -15, -2, -22, 4, -1, 6],\n [-16, 24, -27, -3, 13, 32, -32, 12, -20, 11, -10, 34],\n [1, -14, -29, 6, -6, -30, -12, 30, 4, -21, 17, -31],\n [0, 10, -13, 9, -26, 18, 34, -4, 7, -21, 30, -21],\n [-16, 14, -30, -19, -10, -14, 28, 22, 1, -8, 13, 31],\n [31, 5, 10, 19, -25, -10, -23, 0, 28, 15, -14, 24],\n [-34, 20, 4, -8, -33, 27, -13, 19, -4, -8, -28, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[17, -7, 23, -12, 2, -8, 26, 15, -29, -13, 10, -8],\n [0, -29, 13, -33, -34, -29, -15, -27, -24, -12, -3, 7],\n [0, 0, -22, 0, -1, 14, -25, -12, 8, 15, -19, 34],\n [0, 0, 0, 7, 1, 27, 27, -26, 1, -25, -17, 16],\n [0, 0, 0, 0, 22, -15, -15, -7, 11, -24, 22, 5],\n [0, 0, 0, 0, 0, 27, 16, -26, 3, -13, -25, 12],\n [0, 0, 0, 0, 0, 0, 1, 27, -7, 22, -5, 32],\n [0, 0, 0, 0, 0, 0, 0, -33, -29, -20, 13, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, -9, 33, -1, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 2, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-42627", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-12, -8, 4, -3, -12, -12, 7, -10, 9, 10, 8, 20],\n [-8, 15, -22, 6, 8, 1, -18, 32, 12, -2, 25, 28],\n [4, -22, 5, 8, -24, 1, 11, -24, -12, -8, 16, -7],\n [-3, 6, 8, -3, -20, -6, 24, -12, 0, -1, 0, 1],\n [-12, 8, -24, -20, 29, -1, -16, 11, 16, -16, 13, 2],\n [-12, 1, 1, -6, -1, 3, -20, -3, -6, 34, 10, 18],\n [7, -18, 11, 24, -16, -20, -24, 14, -13, 19, 2, -16],\n [-10, 32, -24, -12, 11, -3, 14, 5, -4, -4, 13, 16],\n [9, 12, -12, 0, 16, -6, -13, -4, -25, 0, 3, -6],\n [10, -2, -8, -1, -16, 34, 19, -4, 0, 23, -22, -32],\n [8, 25, 16, 0, 13, 10, 2, 13, 3, -22, 26, -14],\n [20, 28, -7, 1, 2, 18, -16, 16, -6, -32, -14, 22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[7, -10, -4, -26, -10, -10, -22, -3, 2, 26, -1, -16],\n [-10, -9, 26, 9, 29, 6, -28, 24, -12, -13, 7, -14],\n [-4, 26, -31, -14, 32, -18, -11, -10, -18, -25, 12, 17],\n [-26, 9, -14, -3, 3, 0, -4, 31, 34, -10, 8, -1],\n [-10, 29, 32, 3, -12, 4, -12, 3, -3, -1, 9, 16],\n [-10, 6, -18, 0, 4, 8, 0, 15, 22, -20, -22, 8],\n [-22, -28, -11, -4, -12, 0, -21, 6, -28, 6, 3, -18],\n [-3, 24, -10, 31, 3, 15, 6, -24, 11, -26, 8, -4],\n [2, -12, -18, 34, -3, 22, -28, 11, -28, -6, -26, 4],\n [26, -13, -25, -10, -1, -20, 6, -26, -6, -3, 20, 4],\n [-1, 7, 12, 8, 9, -22, 3, 8, -26, 20, 12, 5],\n [-16, -14, 17, -1, 16, 8, -18, -4, 4, 4, 5, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-74", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (10, 4) rounded to the nearest integer?\n[[-11, -10, -6, 2, -2, -21, 8, -26, 1, -29, -4, -25],\n [0, 32, 12, 9, -3, -32, 11, 17, -5, -5, -9, 12],\n [0, 0, -5, 8, 23, -13, 32, 6, 6, -23, -35, 17],\n [0, 0, 0, 16, -8, 17, 27, -19, 28, -30, -22, -19],\n [0, 0, 0, 0, -27, 8, -10, -17, 12, -6, -4, 33],\n [0, 0, 0, 0, 0, -13, -11, 1, 29, -34, -4, 19],\n [0, 0, 0, 0, 0, 0, -33, 6, 4, 30, 24, -25],\n [0, 0, 0, 0, 0, 0, 0, -9, 31, -8, 30, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 20, 3, -32, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -15, 11, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-6, -25, -1, -9, 31, 11, 14, -28, 19, 6, 31, -16],\n [9, -1, -16, -12, 21, 19, -27, -20, 19, 22, 28, 13],\n [-7, -29, 33, -34, -3, 12, 1, -6, 5, -32, 3, -12],\n [14, 1, 17, -11, -5, 2, 22, 17, 14, -32, 16, -5],\n [-22, -35, 7, 23, 25, 5, -18, 24, 33, 23, 6, 0],\n [4, -6, -25, -11, 9, 15, 7, 30, 11, -12, 1, 20],\n [10, -8, 16, -21, 9, 22, 31, 5, 29, 4, -31, -8],\n [2, -18, 1, -9, -11, 33, -9, 18, -29, -9, 23, -5],\n [32, -32, -18, 27, 16, 27, 9, -24, -28, -14, 5, 5],\n [21, -4, 19, -30, 3, -27, -4, 0, -20, -24, 5, 31],\n [22, -27, -19, -31, -10, -35, -35, -1, -27, 2, -32, 16],\n [-17, -31, 12, 27, 2, 16, 10, -27, 14, 30, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-16, 30, 7, -8, -12, -18, 0, 1, 7, -20, 14, -2],\n [30, -29, -5, -18, 14, -29, 17, 12, -2, -1, -18, -6],\n [7, -5, -31, -22, 30, -6, 23, 22, -16, 22, 8, 20],\n [-8, -18, -22, -24, -8, -13, 2, -16, 5, 0, 5, 2],\n [-12, 14, 30, -8, -28, -1, 19, -11, 2, -6, -2, 18],\n [-18, -29, -6, -13, -1, 5, 3, 12, -26, -2, 6, -8],\n [0, 17, 23, 2, 19, 3, -23, -5, -10, -2, 10, -18],\n [1, 12, 22, -16, -11, 12, -5, -25, 12, -10, -7, 16],\n [7, -2, -16, 5, 2, -26, -10, 12, -15, 12, 12, -13],\n [-20, -1, 22, 0, -6, -2, -2, -10, 12, -17, 12, -7],\n [14, -18, 8, 5, -2, 6, 10, -7, 12, 12, -15, -6],\n [-2, -6, 20, 2, 18, -8, -18, 16, -13, -7, -6, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 20, -2, 9, 2, -12, 0, 7, 8, -32, -8, -10],\n [20, 24, -28, -34, 0, -6, 1, 3, -6, 30, -11, 2],\n [-2, -28, 1, -4, -4, -6, -26, -1, 0, -3, -8, -20],\n [9, -34, -4, -18, 24, 6, 25, 4, 18, 2, -16, -3],\n [2, 0, -4, 24, -14, -20, 34, 5, -32, 4, -16, -2],\n [-12, -6, -6, 6, -20, 25, 2, -30, 25, -6, 24, -2],\n [0, 1, -26, 25, 34, 2, -29, 0, -30, 8, -6, -16],\n [7, 3, -1, 4, 5, -30, 0, 23, -12, 12, -6, -6],\n [8, -6, 0, 18, -32, 25, -30, -12, -18, -8, 21, -15],\n [-32, 30, -3, 2, 4, -6, 8, 12, -8, 24, 30, 5],\n [-8, -11, -8, -16, -16, 24, -6, -6, 21, 30, 19, -18],\n [-10, 2, -20, -3, -2, -2, -16, -6, -15, 5, -18, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-591", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[24, -6, 0, -16, -30, -4, 8, 3, -16, -12, 5, 2],\n [-6, 10, 2, -15, 11, -18, 18, 6, 1, -10, -4, 26],\n [0, 2, 23, 27, -20, -30, -18, 8, 12, -29, -2, 20],\n [-16, -15, 27, -18, -10, -11, 2, -5, -3, 8, 0, -27],\n [-30, 11, -20, -10, -29, -18, 24, -9, 18, 18, 2, 16],\n [-4, -18, -30, -11, -18, 25, 18, 2, 9, 30, -12, 4],\n [8, 18, -18, 2, 24, 18, 30, 12, 10, -9, 4, -12],\n [3, 6, 8, -5, -9, 2, 12, -7, 22, -15, -4, 10],\n [-16, 1, 12, -3, 18, 9, 10, 22, 24, 11, 28, 22],\n [-12, -10, -29, 8, 18, 30, -9, -15, 11, -24, -24, 2],\n [5, -4, -2, 0, 2, -12, 4, -4, 28, -24, 34, -20],\n [2, 26, 20, -27, 16, 4, -12, 10, 22, 2, -20, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1063", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (10, 11) of the inverse. Round your answer to the nearest integer:\n[[-9, 8, -28, 20, 10, -2, -6, 10, -4, -2, -2, 16],\n [8, -9, -8, -6, 12, -4, -6, 18, 6, -4, 16, -22],\n [-28, -8, -21, -11, 7, -22, 0, -14, -7, -6, -4, 14],\n [20, -6, -11, 30, -6, -8, 5, -17, -2, 12, 12, -28],\n [10, 12, 7, -6, 10, 18, 18, -4, 11, 27, 18, -18],\n [-2, -4, -22, -8, 18, -9, 10, -7, 14, 14, -21, 14],\n [-6, -6, 0, 5, 18, 10, -12, 12, 17, -1, -4, 4],\n [10, 18, -14, -17, -4, -7, 12, 26, -22, 4, 20, 2],\n [-4, 6, -7, -2, 11, 14, 17, -22, -19, -8, -20, -3],\n [-2, -4, -6, 12, 27, 14, -1, 4, -8, 31, 13, -2],\n [-2, 16, -4, 12, 18, -21, -4, 20, -20, 13, 34, 16],\n [16, -22, 14, -28, -18, 14, 4, 2, -3, -2, 16, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-33, -5, -21, 18, 17, 9, 2, 14, -12, -19, -18, 6],\n [-19, -20, 16, 0, 3, -11, 6, -15, 32, 23, -6, 21],\n [-3, 17, -20, 13, -31, 24, 35, 19, -1, 33, 6, 33],\n [-12, 35, 35, 19, -22, 19, -21, -31, -32, -6, 17, -6],\n [25, 35, 32, 19, 35, 6, -7, -1, 9, -7, 34, -33],\n [21, 30, -14, -9, -14, 13, -12, -9, 0, -19, 20, -26],\n [18, 2, -32, 14, 25, -15, 0, 10, 35, 8, 28, -18],\n [-23, -23, -11, -31, 3, -7, 21, 10, -3, -26, 22, -11],\n [3, -20, 24, -8, 8, 22, -4, 27, 9, 17, 25, 14],\n [-9, -10, -33, 3, 29, -1, 17, 10, 32, -14, 24, -30],\n [16, -7, 7, -2, -5, 10, -32, -34, -31, 10, -17, 2],\n [23, -16, 32, 17, 19, 3, 0, 22, -21, -35, -27, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-56", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[16, 12, 28, -23, 0, 11, 32, -3, 14, 24, -2, 8],\n [12, -21, 8, 19, 5, -4, -8, -6, 16, 21, -18, -12],\n [28, 8, 12, 6, 0, -8, 18, 1, -4, 23, 18, -26],\n [-23, 19, 6, -33, -18, -12, -16, 4, -4, 10, -9, -8],\n [0, 5, 0, -18, -17, 29, 14, 16, 32, -18, 2, 0],\n [11, -4, -8, -12, 29, 12, -10, 4, 7, -3, -3, 9],\n [32, -8, 18, -16, 14, -10, -29, -22, 6, -16, -1, -26],\n [-3, -6, 1, 4, 16, 4, -22, 23, -14, -10, -4, 13],\n [14, 16, -4, -4, 32, 7, 6, -14, -20, 2, -10, -16],\n [24, 21, 23, 10, -18, -3, -16, -10, 2, 31, -4, 12],\n [-2, -18, 18, -9, 2, -3, -1, -4, -10, -4, 22, 12],\n [8, -12, -26, -8, 0, 9, -26, 13, -16, 12, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1537", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-6, -19, -18, 3, 20, -2, -18, -6, 0, 11, 2, 8],\n [-19, 21, -1, -11, -18, 4, -4, -28, 14, 18, 1, -26],\n [-18, -1, -24, -19, -4, 22, 4, 2, 16, 24, -20, -2],\n [3, -11, -19, -3, -17, -3, 23, 16, -8, -28, -28, 30],\n [20, -18, -4, -17, -33, 8, 0, 33, 8, -11, -34, -28],\n [-2, 4, 22, -3, 8, -3, -10, 0, -19, -17, -4, 16],\n [-18, -4, 4, 23, 0, -10, 32, 4, 0, -6, 8, 0],\n [-6, -28, 2, 16, 33, 0, 4, -12, -1, 10, 9, -4],\n [0, 14, 16, -8, 8, -19, 0, -1, -9, -6, 8, -6],\n [11, 18, 24, -28, -11, -17, -6, 10, -6, 1, 3, 4],\n [2, 1, -20, -28, -34, -4, 8, 9, 8, 3, -5, -12],\n [8, -26, -2, 30, -28, 16, 0, -4, -6, 4, -12, -30]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-52", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-24, 25, 0, -1, 31, 27, 4, -5, 1, -31, -32, -10],\n [-12, 3, 20, 18, 2, 18, -17, -10, 16, 25, 31, -14],\n [-19, -25, 3, 25, 13, 25, -24, -23, 22, -25, 28, -5],\n [-25, 7, 0, -34, 25, 0, 13, -9, -24, 22, -30, 8],\n [11, -13, -10, -29, -4, -3, -16, 33, 16, 6, -35, 27],\n [-29, 22, 14, -2, 15, -26, -10, -4, 6, 26, -24, 4],\n [-2, 34, -9, -28, 11, -10, 21, -29, -10, 23, 33, 11],\n [-1, -6, 14, -12, -6, 18, 31, -4, -28, 14, 11, 10],\n [-1, 25, 15, 27, -28, -2, -11, 8, 7, 14, -23, 10],\n [17, 27, -34, 4, -13, 23, 33, -2, -9, 19, -32, 32],\n [34, -9, 11, 4, -9, -29, -13, 28, -7, 25, 8, 33],\n [-9, -24, -19, 1, -2, 0, -30, -4, -14, -26, -7, -25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-92", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[30, -4, 22, 4, 26, -19, 6, -7, -12, 9, 14, -13],\n [-4, 35, 1, -9, -5, 20, 13, -6, 8, -4, -8, 12],\n [22, 1, -32, -6, -14, -6, -7, -4, 26, -4, 6, 4],\n [4, -9, -6, 5, -11, 4, -25, 2, 18, 34, -16, 4],\n [26, -5, -14, -11, 1, -14, -8, 25, -3, -4, -10, 8],\n [-19, 20, -6, 4, -14, -8, 3, 16, -16, -2, 28, -4],\n [6, 13, -7, -25, -8, 3, 4, -2, -6, -14, 33, -15],\n [-7, -6, -4, 2, 25, 16, -2, 35, -9, 18, 0, -34],\n [-12, 8, 26, 18, -3, -16, -6, -9, 13, 26, -1, -4],\n [9, -4, -4, 34, -4, -2, -14, 18, 26, 14, 16, -28],\n [14, -8, 6, -16, -10, 28, 33, 0, -1, 16, -5, -20],\n [-13, 12, 4, 4, 8, -4, -15, -34, -4, -28, -20, 22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-34, -28, 12, 2, 18, -10, -12, 13, -12, 12, 26, -8],\n [-28, 29, 0, -10, -8, 12, 3, 8, 4, 8, -24, 12],\n [12, 0, 5, -6, -10, 2, -24, -4, 6, -2, 26, -5],\n [2, -10, -6, 25, 30, 0, -14, -4, 8, -10, -2, -1],\n [18, -8, -10, 30, 32, -24, -14, 31, -6, -2, 12, -17],\n [-10, 12, 2, 0, -24, 19, -12, 18, 8, -5, 6, -11],\n [-12, 3, -24, -14, -14, -12, 16, -24, 13, -24, 2, -11],\n [13, 8, -4, -4, 31, 18, -24, 29, 17, -27, -10, 22],\n [-12, 4, 6, 8, -6, 8, 13, 17, 9, 1, 14, 6],\n [12, 8, -2, -10, -2, -5, -24, -27, 1, -14, -22, 24],\n [26, -24, 26, -2, 12, 6, 2, -10, 14, -22, 19, -24],\n [-8, 12, -5, -1, -17, -11, -11, 22, 6, 24, -24, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[20, 22, -14, -21, -16, -12, -2, -16, -25, -12, -11, 1],\n [22, -10, 4, -14, 10, 24, -2, -20, -20, 8, -5, -4],\n [-14, 4, 3, -24, -7, 20, 20, -12, -6, 13, -16, 10],\n [-21, -14, -24, 12, -2, 10, 8, 23, -7, -11, 8, -14],\n [-16, 10, -7, -2, -20, -10, 10, 21, 16, -24, -1, -28],\n [-12, 24, 20, 10, -10, -24, -18, -19, -4, 2, -13, -18],\n [-2, -2, 20, 8, 10, -18, -22, -34, -8, -11, -6, 2],\n [-16, -20, -12, 23, 21, -19, -34, -3, 22, 28, 12, -20],\n [-25, -20, -6, -7, 16, -4, -8, 22, 23, 6, -10, -6],\n [-12, 8, 13, -11, -24, 2, -11, 28, 6, -16, -4, -23],\n [-11, -5, -16, 8, -1, -13, -6, 12, -10, -4, -11, 11],\n [1, -4, 10, -14, -28, -18, 2, -20, -6, -23, 11, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-244", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[29, -6, -14, -4, -5, 14, -12, -7, 2, -22, 0, 10],\n [-6, -19, 4, 4, -24, -16, -20, 4, 23, -7, 28, 12],\n [-14, 4, 34, -6, -3, -4, -4, 12, -2, 12, 6, -25],\n [-4, 4, -6, -1, -14, 14, -24, -20, -3, -6, 14, -20],\n [-5, -24, -3, -14, -7, -21, -25, -1, -8, -20, 6, -28],\n [14, -16, -4, 14, -21, 10, 11, 15, -21, 24, 2, 6],\n [-12, -20, -4, -24, -25, 11, -18, 28, 30, -12, 0, -8],\n [-7, 4, 12, -20, -1, 15, 28, -12, 6, 1, 2, 25],\n [2, 23, -2, -3, -8, -21, 30, 6, -25, -30, -18, 26],\n [-22, -7, 12, -6, -20, 24, -12, 1, -30, 17, 11, 8],\n [0, 28, 6, 14, 6, 2, 0, 2, -18, 11, 16, 6],\n [10, 12, -25, -20, -28, 6, -8, 25, 26, 8, 6, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1631", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[12, -19, -31, 34, 28, 30, 35, -32, -8, 2, 30, 31],\n [0, 11, -11, 30, 31, 33, 4, 14, 4, 1, 33, -19],\n [0, 0, 6, -5, -3, 7, 31, 2, 5, 27, 4, -6],\n [0, 0, 0, 7, 25, -4, -32, 9, -16, 35, 29, 24],\n [0, 0, 0, 0, -10, 26, 8, -5, -10, -31, 34, -1],\n [0, 0, 0, 0, 0, -18, 14, -16, 20, -34, -10, -13],\n [0, 0, 0, 0, 0, 0, -19, 2, -22, -22, -24, 33],\n [0, 0, 0, 0, 0, 0, 0, 30, -13, 32, -16, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 27, -4, 30, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -34, -9, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1036", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-17, -8, 4, 21, 15, -14, 32, -28, 24, 29, 0, 35],\n [-7, 29, 20, -32, 14, 3, -1, -11, 8, 11, 4, -5],\n [33, 7, 19, -20, 32, 33, 6, 5, 14, -30, 17, -19],\n [21, 31, -20, 16, -2, -16, 20, 15, 17, 13, -32, -18],\n [0, -1, -6, 27, -15, 16, 33, 5, 18, -6, 20, 5],\n [-22, -15, -11, 14, 17, 12, 34, 12, -32, -12, -5, -7],\n [-31, 31, 17, 28, -1, -24, 11, 19, 33, 2, -7, -24],\n [-17, -27, -7, -33, -6, 22, 17, -32, 21, 18, -8, -20],\n [-23, 20, 17, 12, -11, 30, -6, -33, -13, -7, 5, -25],\n [-15, -12, 29, -35, 18, -2, 32, -7, -33, -25, -28, 26],\n [-3, -28, -11, -10, -10, -19, -7, 7, -31, 14, 20, 27],\n [21, 9, 1, 0, -3, -30, 35, 9, -29, 29, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2057", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[25, -17, -4, -6, 29, -4, 21, -16, -6, 23, 26, 31],\n [0, 30, 18, -26, 2, -5, -7, -11, -4, -19, 9, 13],\n [0, 0, -16, 26, -23, 7, -15, -30, 35, 17, 16, 33],\n [0, 0, 0, -6, 7, 23, 2, -2, 10, -4, -20, 3],\n [0, 0, 0, 0, -2, 14, -25, 7, -26, -28, -17, 29],\n [0, 0, 0, 0, 0, 12, 18, -20, -6, -8, -20, 15],\n [0, 0, 0, 0, 0, 0, 8, 31, 7, -30, 28, -23],\n [0, 0, 0, 0, 0, 0, 0, -30, 1, 21, 17, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 25, -6, 7, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 21, -9, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83041", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-23, 12, 13, 22, 34, 25, -10, 3, 22, -9, 4, -5],\n [-33, -21, 18, 34, -25, -6, -1, 7, 25, 4, 6, 6],\n [-33, -15, 17, 8, 10, 1, 2, 2, -25, 9, 28, 8],\n [26, 25, -24, -27, 31, -34, -28, 7, -18, 16, 3, -5],\n [-22, 28, 8, 24, -34, -4, 0, 19, 27, 33, 4, -12],\n [22, -8, 26, -11, -29, 2, 35, 9, -4, -4, -35, 9],\n [28, 32, -29, 2, 34, 17, -6, -14, 22, 19, 10, -10],\n [28, -27, -21, -17, -20, -11, 15, 10, -29, -2, 22, -13],\n [-13, -19, -23, -9, 30, -6, -32, 31, -22, -25, 4, -33],\n [-35, -27, -35, -20, 10, -26, -3, 5, 15, -14, -20, 26],\n [17, -22, 23, -10, 8, -16, -31, 29, -25, 11, -26, 25],\n [9, 11, -2, -23, -13, 0, 27, 11, 30, -22, 17, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "484", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[13, -20, 32, 7, 29, -27, -15, 7, 30, -32, -29, 22],\n [0, -16, -1, 23, 9, -22, -14, 12, -6, -7, 0, 6],\n [0, 0, -4, -23, -23, 18, -22, -30, -20, 5, 16, -20],\n [0, 0, 0, 29, -26, 23, -1, -5, -25, -27, 30, 8],\n [0, 0, 0, 0, 12, 34, 10, -3, 16, 19, 15, 4],\n [0, 0, 0, 0, 0, 1, -31, -14, -24, 24, 8, -14],\n [0, 0, 0, 0, 0, 0, -33, -26, 27, 27, 26, -27],\n [0, 0, 0, 0, 0, 0, 0, -16, 31, 32, -19, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 17, 24, -7, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -23, -33, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3698397", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[9, 0, 28, -1, -9, 32, -19, 34, -25, -31, 22, 21],\n [0, -35, -20, -10, 13, 6, 34, 30, 17, -27, 33, 4],\n [0, 0, 20, -31, 33, 16, -3, -14, -21, 29, 35, -13],\n [0, 0, 0, -24, -34, -4, 14, 25, -25, 32, -2, -28],\n [0, 0, 0, 0, -27, 21, 18, -7, -17, 10, 26, 24],\n [0, 0, 0, 0, 0, 6, -14, 3, -9, 10, -8, 16],\n [0, 0, 0, 0, 0, 0, 28, 35, 21, -1, 1, 14],\n [0, 0, 0, 0, 0, 0, 0, -12, -13, 23, 19, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, -6, -18, -31, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -21, -29, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-170", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (10, 12) of the inverse. Round your answer to the nearest integer:\n[[-3, 4, 5, 6, -27, -18, -21, -32, -2, 26, 2, 35],\n [-13, -16, 20, 17, -34, -15, 6, 21, 13, -26, 25, -15],\n [24, -23, 12, 4, 27, -27, 21, 15, 4, 28, 34, 28],\n [-11, -8, -26, -8, 0, -25, -15, -10, -18, 32, 5, -21],\n [-13, 5, -30, 35, 24, 16, -27, -6, 8, 26, 7, -8],\n [-28, 15, -6, -25, -16, -5, -2, -24, 12, -8, 31, 27],\n [12, 6, 16, -31, -24, 23, 29, 16, 7, 27, 14, 3],\n [6, -19, 7, 13, -31, -35, 31, -12, -7, -21, -32, 8],\n [29, -5, -16, -26, -25, -8, 2, -12, 3, 15, 14, -29],\n [32, 17, 1, 18, 19, -5, 29, 23, 11, 13, -18, -33],\n [-18, 22, 35, -11, -18, 16, 7, 31, -29, 8, 8, 15],\n [-15, 1, -8, -4, 21, 5, 18, -9, 4, 5, 34, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-18, 20, -21, -1, -9, -33, -15, 3, -4, 14, -27, 14],\n [-35, -32, -32, -2, -9, -21, -4, 5, 35, 25, 27, 25],\n [-22, -13, 29, -4, 5, -10, 12, -20, -5, 30, -4, -26],\n [-11, 9, -12, -33, 26, 31, 19, -26, 19, -14, -22, -28],\n [-21, -21, 16, 34, 18, 6, -17, 4, 33, -9, 7, 16],\n [10, -22, 28, 25, 22, 13, -7, -10, -9, 31, 31, -1],\n [24, 25, 34, -33, -3, 6, -23, -7, -27, -4, -14, 22],\n [21, -26, -11, 26, 27, -33, 11, 19, -10, -23, -29, -2],\n [-14, -13, 12, -22, 16, 3, 5, 0, -30, -13, -26, 24],\n [-6, 34, -31, 21, 7, 16, -30, -34, -19, -24, 8, 18],\n [-29, -4, -7, 10, 17, -11, 17, -7, -30, 2, -33, -1],\n [19, 11, -3, -33, 33, 23, -18, 30, -11, -16, 35, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-7, -18, -9, 6, 30, -10, -13, -31, -25, -17, -24, -34],\n [0, -14, -10, -3, -12, 33, -15, 10, -18, -31, -28, 21],\n [0, 0, 30, 1, -7, 33, -4, 12, -34, 33, 15, -1],\n [0, 0, 0, -19, 9, -35, -33, 34, 16, 17, -33, 11],\n [0, 0, 0, 0, 20, 34, -16, 11, 18, 5, 30, -5],\n [0, 0, 0, 0, 0, 1, 5, -11, -7, -5, -34, -24],\n [0, 0, 0, 0, 0, 0, -7, 2, 5, -3, -23, -30],\n [0, 0, 0, 0, 0, 0, 0, -35, 10, 26, -34, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, -25, -8, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -14, -33, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-66363", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[7, 16, -22, -28, -1, -18, 19, 16, 13, -28, 1, 30],\n [0, -9, -16, 2, -24, 6, 14, -5, 29, 17, 4, 3],\n [0, 0, 4, -6, -34, -8, 11, -4, -4, -9, 18, 20],\n [0, 0, 0, -6, 19, 28, -3, 10, -3, 32, 28, -6],\n [0, 0, 0, 0, 31, -21, -26, 25, -13, -25, -20, 13],\n [0, 0, 0, 0, 0, -26, 10, 13, -27, 3, -34, 32],\n [0, 0, 0, 0, 0, 0, -34, -31, -4, -17, -32, 10],\n [0, 0, 0, 0, 0, 0, 0, 25, 15, 23, 2, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 24, 25, 16, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -34, -29, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88367", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-29, -21, 31, -18, 2, -10, 2, 23, 16, -3, -15, -19],\n [0, 23, -34, 28, -11, 5, -17, 2, -11, 3, -32, -33],\n [0, 0, -9, -35, 8, 16, -11, 29, -25, 32, -21, 21],\n [0, 0, 0, -6, -26, 18, 22, -7, -35, 22, -15, -21],\n [0, 0, 0, 0, -32, 22, 34, -24, -19, -35, -22, -34],\n [0, 0, 0, 0, 0, 16, 12, 3, 34, 24, -6, -9],\n [0, 0, 0, 0, 0, 0, 16, -30, -26, 2, -24, 10],\n [0, 0, 0, 0, 0, 0, 0, -1, -13, -15, 1, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 11, 0, -8, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 22, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71609", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[20, 23, 4, -18, 15, 25, -13, 0, 2, 20, 3, 33],\n [0, -15, 26, -13, -15, -20, 26, 29, -31, 10, 28, 5],\n [0, 0, 32, 15, 18, 32, 6, 10, -11, 31, -1, -14],\n [0, 0, 0, 25, 1, 9, -21, 21, -22, 16, 0, -9],\n [0, 0, 0, 0, -17, 5, 4, 22, 3, -29, 0, -16],\n [0, 0, 0, 0, 0, -30, -18, 17, -14, 32, -1, -27],\n [0, 0, 0, 0, 0, 0, -21, -8, -33, -7, 16, 18],\n [0, 0, 0, 0, 0, 0, 0, 35, 12, -5, -32, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 12, 22, 27, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 22, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23909", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[6, 6, -7, -20, 31, 24, -32, -20, 5, -30, 6, 21],\n [0, -13, 6, -24, 28, 22, 15, -7, -17, 9, 18, 30],\n [0, 0, -24, 35, -22, 6, 12, -12, 29, -19, 2, -8],\n [0, 0, 0, -32, -3, -26, 0, -5, -32, -28, -9, 0],\n [0, 0, 0, 0, 5, -10, -32, -35, -16, 9, 33, 16],\n [0, 0, 0, 0, 0, -9, 16, 27, 9, 22, 2, -1],\n [0, 0, 0, 0, 0, 0, -3, 26, 27, 20, 3, 24],\n [0, 0, 0, 0, 0, 0, 0, 29, 9, 19, 30, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, -16, -4, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -31, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-6, 4, 23, 27, 12, 32, -29, 11, 7, -20, -14, 27],\n [0, 9, 5, -11, 14, 31, 16, -5, 1, -14, -9, -34],\n [0, 0, -19, 20, -5, 7, 17, -31, -34, 23, -32, -2],\n [0, 0, 0, 11, -31, 25, 20, -1, -23, -10, 28, -25],\n [0, 0, 0, 0, -26, -20, -24, 35, 14, -21, 23, 34],\n [0, 0, 0, 0, 0, -8, 15, -3, -35, 33, -35, 19],\n [0, 0, 0, 0, 0, 0, -35, 11, -15, 3, -33, -20],\n [0, 0, 0, 0, 0, 0, 0, -34, -26, 24, -17, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, -5, 30, 18, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -22, -8, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-187275", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-16, -9, 22, 8, 29, 10, 18, 3, -29, 18, 7, -16],\n [0, 7, -9, -11, 0, 30, -27, 17, -15, 14, -20, 30],\n [0, 0, -7, 10, 35, 13, -21, -19, -27, -4, 30, 23],\n [0, 0, 0, -6, -25, -10, -34, -2, 5, -5, 27, 19],\n [0, 0, 0, 0, -10, -18, -2, -8, 13, 28, 35, 27],\n [0, 0, 0, 0, 0, 13, 23, -14, 25, -6, 33, 24],\n [0, 0, 0, 0, 0, 0, -33, -33, -5, 11, -28, -19],\n [0, 0, 0, 0, 0, 0, 0, -8, 10, 8, -11, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 18, 29, -30, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 17, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9756", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (11, 6) of the inverse. Round your answer to the nearest integer:\n[[23, -33, 3, 15, -28, 10, 30, -30, 22, 5, 18, 5],\n [12, 34, -9, 11, -13, -22, 25, 31, -11, 29, -12, 17],\n [14, -35, 3, 8, -31, 32, 29, -21, 14, -30, 30, 33],\n [3, -7, 10, -5, -12, -21, -16, -32, 22, 25, -26, 5],\n [17, 35, 12, -21, -29, 35, 7, -32, 15, 35, 23, 5],\n [25, -6, -18, -6, -29, 16, 12, -13, 1, 35, 17, 9],\n [13, 13, 11, -11, -9, -24, -13, -19, 8, 35, -12, 35],\n [24, 17, -20, -11, 30, 14, 33, 4, -30, 28, -8, -27],\n [-30, -19, 4, 9, 7, 10, 27, -35, 23, 27, -18, 29],\n [-16, 20, 18, 12, 18, -20, -16, 11, -29, -13, -3, 4],\n [-31, 9, 5, -28, 14, -5, -32, 30, 20, -31, 18, -35],\n [25, -29, -6, -21, -32, 27, 34, 2, 11, 24, -34, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-28, 4, -24, 13, 8, 11, -16, -14, 14, -2, -3, 0],\n [4, -23, 4, 0, -16, 14, 0, 6, 4, -2, 30, -17],\n [-24, 4, 33, -9, -30, -24, 1, 10, 17, 16, -12, -12],\n [13, 0, -9, 35, -8, -16, -7, 0, 26, 18, 0, -12],\n [8, -16, -30, -8, 20, 17, -26, 6, -16, -16, -4, -6],\n [11, 14, -24, -16, 17, -13, -2, 4, -12, 28, 18, 10],\n [-16, 0, 1, -7, -26, -2, 8, 6, -2, 2, -10, 22],\n [-14, 6, 10, 0, 6, 4, 6, -3, 24, -16, 12, -26],\n [14, 4, 17, 26, -16, -12, -2, 24, 27, -14, -2, 2],\n [-2, -2, 16, 18, -16, 28, 2, -16, -14, 32, -12, -16],\n [-3, 30, -12, 0, -4, 18, -10, 12, -2, -12, 31, 2],\n [0, -17, -12, -12, -6, 10, 22, -26, 2, -16, 2, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "197", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-25, -16, -26, -16, -8, 4, 14, 32, 6, 0, -2, 4],\n [-16, 0, 16, 9, -5, 16, 7, 20, -10, 4, 6, 1],\n [-26, 16, -2, 15, -10, -16, 6, -24, 11, -9, -16, 13],\n [-16, 9, 15, -16, -10, 2, -7, 12, -8, 0, -6, -9],\n [-8, -5, -10, -10, -11, 3, 8, -22, 0, -5, -18, -11],\n [4, 16, -16, 2, 3, -26, 2, 10, -30, 0, -31, 2],\n [14, 7, 6, -7, 8, 2, -19, 15, -4, -31, 31, -25],\n [32, 20, -24, 12, -22, 10, 15, -6, -9, 13, -12, 4],\n [6, -10, 11, -8, 0, -30, -4, -9, -27, -5, 4, 24],\n [0, 4, -9, 0, -5, 0, -31, 13, -5, -26, 12, 0],\n [-2, 6, -16, -6, -18, -31, 31, -12, 4, 12, -33, 9],\n [4, 1, 13, -9, -11, 2, -25, 4, 24, 0, 9, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-362", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-2, 31, -32, 8, -21, -28, -31, 30, 10, 29, 30, -10],\n [0, 15, 5, 15, -17, -33, 2, 34, 9, 35, 5, -11],\n [0, 0, 18, -23, 4, -15, 5, 25, -3, -7, 19, -4],\n [0, 0, 0, -5, -22, 27, 16, 18, 14, 18, -1, -6],\n [0, 0, 0, 0, -16, 35, -20, 16, 29, 34, -35, -20],\n [0, 0, 0, 0, 0, 16, 14, -19, -33, 26, -15, -3],\n [0, 0, 0, 0, 0, 0, 8, 21, 4, 20, 27, 3],\n [0, 0, 0, 0, 0, 0, 0, -11, 34, -33, -15, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 8, 32, 30, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -30, -20, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3249090", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (11, 5) rounded to the nearest integer?\n[[14, -28, -24, 15, 30, 5, -14, -27, -25, -23, 20, -8],\n [28, 28, 34, 19, 1, -3, -11, -13, 24, 20, 27, -28],\n [-19, 21, 26, -25, 31, 4, 4, 20, 17, -8, 6, 10],\n [-18, -13, -10, -7, 16, 10, -35, 27, -20, -11, 26, -20],\n [33, 34, -2, 17, -13, 7, 8, -4, -13, -16, -17, -7],\n [-18, 33, -24, -26, 1, 19, -32, 27, -24, -18, -28, -4],\n [13, 27, 23, 31, 3, 14, 35, -10, -13, 27, 30, 3],\n [30, 10, -21, -20, -20, 3, -25, 0, -18, -13, 13, 6],\n [8, -35, -29, 12, -20, 12, 7, 15, 30, -5, 3, -27],\n [5, 27, -22, 22, 28, -8, -32, -2, -32, 34, 22, -32],\n [14, -31, 9, -1, -9, -34, 18, 12, 13, -35, -3, -1],\n [18, 20, -21, 33, -32, 28, -14, -12, 11, -30, -9, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[3, 0, 19, -2, 28, -9, 22, 20, 0, -20, -17, -5],\n [0, 24, -24, 3, -8, -4, 18, -19, 2, 12, 8, 18],\n [19, -24, 15, -12, -12, -12, 24, -1, 15, -2, 28, 8],\n [-2, 3, -12, -34, -23, 17, 4, -10, -4, -10, -2, 8],\n [28, -8, -12, -23, 3, -9, 6, 4, 7, 18, 32, 19],\n [-9, -4, -12, 17, -9, 4, -14, -12, 7, -23, -1, -1],\n [22, 18, 24, 4, 6, -14, 3, 4, -2, 3, 12, 2],\n [20, -19, -1, -10, 4, -12, 4, -7, 3, -14, -2, 16],\n [0, 2, 15, -4, 7, 7, -2, 3, 30, 2, -2, 10],\n [-20, 12, -2, -10, 18, -23, 3, -14, 2, -22, 0, -10],\n [-17, 8, 28, -2, 32, -1, 12, -2, -2, 0, -29, -18],\n [-5, 18, 8, 8, 19, -1, 2, 16, 10, -10, -18, -27]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-20, 12, -26, -30, 18, 15, -15, -14, -14, -8, 14, 4],\n [12, 6, 6, 10, 6, -4, 20, -1, 14, -11, 7, 7],\n [-26, 6, 0, -18, 28, -16, -8, 0, 4, -15, -6, 6],\n [-30, 10, -18, 5, 16, 10, -7, 17, 26, 4, 2, 0],\n [18, 6, 28, 16, -10, 6, 18, 0, 1, -11, 0, 0],\n [15, -4, -16, 10, 6, 30, 20, 0, 14, -14, -5, 25],\n [-15, 20, -8, -7, 18, 20, -6, -11, 22, -8, 4, 18],\n [-14, -1, 0, 17, 0, 0, -11, 3, 2, -2, -16, 0],\n [-14, 14, 4, 26, 1, 14, 22, 2, 27, -17, 8, 16],\n [-8, -11, -15, 4, -11, -14, -8, -2, -17, -33, -10, 8],\n [14, 7, -6, 2, 0, -5, 4, -16, 8, -10, -8, 14],\n [4, 7, 6, 0, 0, 25, 18, 0, 16, 8, 14, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2883", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-30, -10, 14, -15, 8, 20, 4, -14, -10, 1, 10, 0],\n [-10, -34, 8, -3, 0, -8, -16, 1, 5, -10, 18, 21],\n [14, 8, 33, 11, -30, 11, -11, 18, -34, -8, -2, 4],\n [-15, -3, 11, 12, 5, -4, 8, 2, 8, -22, -20, 18],\n [8, 0, -30, 5, -1, 16, -7, 22, 2, 0, 8, 11],\n [20, -8, 11, -4, 16, -2, -2, 22, -6, 14, -12, 0],\n [4, -16, -11, 8, -7, -2, -15, -1, 2, -15, -18, -9],\n [-14, 1, 18, 2, 22, 22, -1, 17, 21, 20, 2, 7],\n [-10, 5, -34, 8, 2, -6, 2, 21, 16, 11, -12, 29],\n [1, -10, -8, -22, 0, 14, -15, 20, 11, 25, -1, -12],\n [10, 18, -2, -20, 8, -12, -18, 2, -12, -1, 27, -16],\n [0, 21, 4, 18, 11, 0, -9, 7, 29, -12, -16, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-85", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (10, 11) rounded to the nearest integer?\n[[-23, -2, 4, 18, 7, 22, -22, 0, -30, 14, 8, -7],\n [-2, 16, 12, 6, 7, -10, -18, 2, -16, -14, 9, -14],\n [4, 12, -32, -14, -21, 22, -6, -16, 6, -4, 0, -12],\n [18, 6, -14, -26, -31, 32, -13, -2, 0, 24, -2, -9],\n [7, 7, -21, -31, -22, -19, -16, -5, -28, -12, -2, 8],\n [22, -10, 22, 32, -19, 15, 2, -12, 24, 30, -18, -16],\n [-22, -18, -6, -13, -16, 2, 9, 8, 2, 30, -11, -8],\n [0, 2, -16, -2, -5, -12, 8, -3, 2, -18, 6, 2],\n [-30, -16, 6, 0, -28, 24, 2, 2, 7, 28, -14, 26],\n [14, -14, -4, 24, -12, 30, 30, -18, 28, 33, 11, -2],\n [8, 9, 0, -2, -2, -18, -11, 6, -14, 11, 23, -6],\n [-7, -14, -12, -9, 8, -16, -8, 2, 26, -2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-9, 12, -5, 12, -13, -2, 2, -4, 0, -10, -4, -6],\n [12, 15, 19, -1, 10, -28, 3, -9, 14, -4, 16, 24],\n [-5, 19, -26, 0, 19, -8, 3, 4, -6, 28, 3, 21],\n [12, -1, 0, 13, -4, 4, 7, -6, -16, -12, 10, 2],\n [-13, 10, 19, -4, 34, -6, 30, 14, -4, -13, -26, 24],\n [-2, -28, -8, 4, -6, -18, -8, 18, 20, -16, 20, 10],\n [2, 3, 3, 7, 30, -8, 6, -22, 9, -12, 20, -19],\n [-4, -9, 4, -6, 14, 18, -22, 20, 0, 1, -22, -2],\n [0, 14, -6, -16, -4, 20, 9, 0, 1, 22, 4, 19],\n [-10, -4, 28, -12, -13, -16, -12, 1, 22, -32, 1, 1],\n [-4, 16, 3, 10, -26, 20, 20, -22, 4, 1, 22, 8],\n [-6, 24, 21, 2, 24, 10, -19, -2, 19, 1, 8, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[34, 8, -8, -12, 14, 27, 23, 24, 6, 26, -26, -14],\n [8, 16, -10, 33, 11, 22, 21, 9, 24, 16, -2, -19],\n [-8, -10, 11, 16, 4, 13, 10, -22, -6, 10, -18, 9],\n [-12, 33, 16, 13, 3, -29, 8, -16, 0, 5, -16, -8],\n [14, 11, 4, 3, 11, 6, 6, -32, 4, 10, 15, 11],\n [27, 22, 13, -29, 6, 29, 8, -10, -6, -22, -14, 2],\n [23, 21, 10, 8, 6, 8, 5, 11, -7, 2, 0, 6],\n [24, 9, -22, -16, -32, -10, 11, 17, -7, -26, -16, -2],\n [6, 24, -6, 0, 4, -6, -7, -7, 2, -10, 4, 0],\n [26, 16, 10, 5, 10, -22, 2, -26, -10, -9, 18, -4],\n [-26, -2, -18, -16, 15, -14, 0, -16, 4, 18, 23, -8],\n [-14, -19, 9, -8, 11, 2, 6, -2, 0, -4, -8, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4831", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[15, 25, -5, -4, 9, -9, -14, -21, -28, 32, -28, -20],\n [12, -2, 21, -31, 8, 35, 1, -8, 32, 2, 10, -10],\n [17, 27, 27, 2, -21, -27, -14, 34, 20, 1, 21, 24],\n [-24, -29, 30, 5, -12, -11, 26, 8, -34, 6, -3, -19],\n [27, -14, -35, 34, 18, -22, 17, -30, 28, -3, 8, -2],\n [-2, -12, -34, -28, -11, -4, 20, -29, 12, 18, 27, -34],\n [-1, -14, 28, 23, 13, 16, -15, -24, -25, 18, 34, -22],\n [-3, -10, -22, 12, 29, 10, 19, 32, -24, 18, 28, 11],\n [1, 5, -9, 6, 32, -7, 0, 21, -24, 9, -16, 9],\n [-13, 26, -2, -15, 15, -27, -26, 16, 9, 16, -6, 28],\n [-34, 13, 9, -19, -8, 9, -19, 23, -22, -26, -18, -1],\n [12, 22, -18, 16, -6, 1, 4, -30, -1, -10, -6, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-45", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[19, -31, 18, 6, -4, -10, 8, -11, 14, 6, 16, 18],\n [-31, -24, -16, -14, 14, -12, -1, 18, -8, 2, 10, -28],\n [18, -16, 15, 9, -12, -34, -31, -21, -22, -5, 32, 20],\n [6, -14, 9, 21, -1, -26, 22, 12, 14, 14, -22, 35],\n [-4, 14, -12, -1, 14, 3, 12, -32, 12, 4, -4, -14],\n [-10, -12, -34, -26, 3, -3, -28, 32, 0, -16, 18, 14],\n [8, -1, -31, 22, 12, -28, 5, -4, -16, 20, 16, 6],\n [-11, 18, -21, 12, -32, 32, -4, -7, 7, 25, 28, 9],\n [14, -8, -22, 14, 12, 0, -16, 7, -30, 8, 12, -2],\n [6, 2, -5, 14, 4, -16, 20, 25, 8, 16, -10, -3],\n [16, 10, 32, -22, -4, 18, 16, 28, 12, -10, 1, 6],\n [18, -28, 20, 35, -14, 14, 6, 9, -2, -3, 6, -28]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "526", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 7, 17, -30, -12, -22, 16, 34, -32, 22, 1, 12],\n [0, 30, -23, 30, 24, 5, -4, 16, -31, 31, 30, 16],\n [0, 0, 2, 34, -28, 23, 19, -34, -10, 27, -19, 23],\n [0, 0, 0, 14, -10, -19, 10, 32, 14, 7, 12, 32],\n [0, 0, 0, 0, -18, 22, 28, 35, 21, -19, 23, 31],\n [0, 0, 0, 0, 0, -29, 19, -24, -19, -28, 6, 1],\n [0, 0, 0, 0, 0, 0, -32, -7, -20, -28, 3, 22],\n [0, 0, 0, 0, 0, 0, 0, -12, -30, -3, 12, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, -13, 29, 27, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27, -10, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-52187", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-6, 24, -6, 2, 29, 11, 3, 13, 22, -19, -30, -21],\n [31, -8, 8, -18, -4, 33, 8, 34, 27, 22, 11, -19],\n [3, 23, -29, 27, 21, -2, 17, 30, 12, 24, 7, -32],\n [16, -4, 15, -26, -24, 3, 32, -26, -26, -13, -23, 12],\n [8, 28, 4, -30, 7, -4, 13, -17, 16, 16, -2, 23],\n [-31, 30, 5, -2, 18, -16, 18, 30, -18, 8, 12, -1],\n [3, -33, -17, -18, -31, 19, -23, -2, -18, 32, 7, 29],\n [5, 2, 2, -23, -14, -7, -27, 32, -19, 1, 28, 31],\n [-32, 4, -20, -25, -10, 29, -34, 9, 7, -33, -2, 29],\n [28, -29, -1, -14, 12, -4, -10, -30, 10, 19, 19, 21],\n [27, -35, -15, -16, -7, 7, 9, 29, -33, -16, 1, 2],\n [9, 6, 10, 24, -23, -5, 32, 26, 13, -18, 17, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3600", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (4, 12) rounded to the nearest integer?\n[[15, 3, 26, -2, -3, 16, -12, -22, 12, 4, 5, 4],\n [3, -19, 12, 0, 14, -30, 5, -5, 17, 12, 6, -11],\n [26, 12, -4, -17, 7, 10, 5, -1, 8, -4, -2, -6],\n [-2, 0, -17, -32, -5, 3, 32, -13, -16, 2, -16, 19],\n [-3, 14, 7, -5, -35, -28, 20, -8, -4, -5, -6, -16],\n [16, -30, 10, 3, -28, 6, 19, -6, -4, -8, 12, 14],\n [-12, 5, 5, 32, 20, 19, 27, -21, -10, 23, 20, 14],\n [-22, -5, -1, -13, -8, -6, -21, 11, -3, -18, 5, 32],\n [12, 17, 8, -16, -4, -4, -10, -3, 31, -8, -12, 10],\n [4, 12, -4, 2, -5, -8, 23, -18, -8, -2, 6, -13],\n [5, 6, -2, -16, -6, 12, 20, 5, -12, 6, 32, -15],\n [4, -11, -6, 19, -16, 14, 14, 32, 10, -13, -15, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-12, -4, 11, -20, -15, 31, -5, -22, -30, 33, -7, 19],\n [0, 23, 0, 23, 28, 7, 6, 24, 26, 28, 22, -34],\n [0, 0, 20, 0, 33, -23, 3, -30, -17, -11, -33, 17],\n [0, 0, 0, -28, 21, 19, -35, 4, -13, 18, 6, 14],\n [0, 0, 0, 0, -6, -20, -6, 28, -25, -2, 19, -32],\n [0, 0, 0, 0, 0, 34, -24, 9, -28, -27, -35, -31],\n [0, 0, 0, 0, 0, 0, 4, 8, -24, -14, -9, 31],\n [0, 0, 0, 0, 0, 0, 0, -16, 20, -6, 5, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 33, 25, -32, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 18, -19, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-230001", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[23, 32, 7, -24, 17, -22, 16, 25, 5, -15, 12, 20],\n [-1, 8, 3, -21, -24, -28, 31, -35, 6, -5, -6, 7],\n [-10, -24, 23, 33, -25, 11, -13, 7, 3, 19, -18, 6],\n [-10, -18, 5, 6, -3, 7, -22, 19, 22, -26, -8, -22],\n [-10, -19, -2, -22, -10, -2, -12, 34, -16, 3, 9, -2],\n [-14, 35, -3, -30, -20, -13, -18, -22, 14, 25, 0, -21],\n [-31, 17, 12, -25, -34, -12, 32, -24, 23, 31, -4, 0],\n [-15, 34, 30, -27, 8, 23, -12, 27, 5, -34, -8, -20],\n [23, -35, -35, -5, -14, 23, -8, -9, -35, -34, 30, 13],\n [-17, -8, 34, 3, -17, 28, 22, -19, 34, 5, -31, -13],\n [33, -26, 32, -24, -26, 24, -6, -12, 33, -23, -27, -18],\n [-1, -32, 5, -10, 8, 6, -26, -35, 18, -20, 10, -23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-410", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[28, 19, 27, -18, 25, -16, 29, 28, 28, -23, 32, 34],\n [21, 9, 2, 18, 0, 31, -25, -9, -19, -3, -31, 26],\n [29, 35, 31, 8, -22, 21, 12, -19, 8, -32, -6, 19],\n [-6, -18, 8, 26, -5, -20, -13, -22, -34, -24, 22, 20],\n [-12, 1, -7, 6, -18, -33, -23, -7, 30, 23, 12, -32],\n [15, -31, 3, 5, -31, -28, 20, -11, 16, 16, -29, 25],\n [11, 30, 23, -31, 8, 6, 25, 27, 14, 2, 18, 8],\n [-12, 27, 3, -24, 27, -27, -14, 0, -8, 20, -7, -31],\n [-32, 15, -21, 24, -10, -13, -7, 21, 26, 23, 12, -1],\n [10, -3, 35, -26, 12, 8, 34, 27, 13, 5, 3, -13],\n [-23, 17, 34, 21, 31, 12, -16, 26, 9, 27, -28, -10],\n [2, 5, -34, -29, -11, 15, 14, 28, -24, 17, -26, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 8) of the inverse of matrix 1/839 * A where A =\n[[19, 11, -14, 21, 6, -2, 24, -2, 12, 3, -2, 17],\n [11, -35, 20, -1, -8, 24, -30, -16, 7, 16, -12, -2],\n [-14, 20, -30, -3, -4, 5, -4, 2, -22, -4, 11, 8],\n [21, -1, -3, 26, -14, 29, 4, -18, 26, 18, 22, 22],\n [6, -8, -4, -14, -30, 16, 10, 12, 10, 12, 1, -2],\n [-2, 24, 5, 29, 16, 31, 17, -12, 12, -4, 13, 16],\n [24, -30, -4, 4, 10, 17, -16, 1, 20, 2, -14, 9],\n [-2, -16, 2, -18, 12, -12, 1, -12, -9, -6, 8, 2],\n [12, 7, -22, 26, 10, 12, 20, -9, -33, -2, -5, 30],\n [3, 16, -4, 18, 12, -4, 2, -6, -2, 30, 8, -4],\n [-2, -12, 11, 22, 1, 13, -14, 8, -5, 8, 20, -14],\n [17, -2, 8, 22, -2, 16, 9, 2, 30, -4, -14, -35]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (6, 6) rounded to the nearest integer?\n[[29, 0, -7, 14, 2, -18, -15, -4, 0, -16, 2, 13],\n [0, -31, -12, 3, 1, 16, 4, 27, 1, 7, -12, 21],\n [-7, -12, 3, 15, -2, -6, 6, 9, 21, 6, 12, -10],\n [14, 3, 15, 17, -12, 6, 12, 17, 9, -16, 12, 28],\n [2, 1, -2, -12, 26, 4, 24, 16, 12, 2, 4, 2],\n [-18, 16, -6, 6, 4, 22, 8, -16, -6, -6, 8, -23],\n [-15, 4, 6, 12, 24, 8, -10, -2, -14, 6, -14, -10],\n [-4, 27, 9, 17, 16, -16, -2, 18, -28, -6, -5, 21],\n [0, 1, 21, 9, 12, -6, -14, -28, 22, 6, -11, -19],\n [-16, 7, 6, -16, 2, -6, 6, -6, 6, -30, -7, -14],\n [2, -12, 12, 12, 4, 8, -14, -5, -11, -7, -35, 18],\n [13, 21, -10, 28, 2, -23, -10, 21, -19, -14, 18, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-26, 6, -20, -33, -12, 4, 12, 22, 2, 10, 24, 0],\n [6, -25, -14, 22, 28, 4, 7, 0, 4, -6, 14, 10],\n [-20, -14, -13, -22, -11, -7, 2, -12, -22, 10, 6, 6],\n [-33, 22, -22, -19, -25, -2, -5, -19, -4, 0, 4, 14],\n [-12, 28, -11, -25, 22, 16, -12, 1, -16, 0, -8, 14],\n [4, 4, -7, -2, 16, 18, -20, -24, -5, 6, 7, 8],\n [12, 7, 2, -5, -12, -20, -12, -4, -18, 6, -9, -12],\n [22, 0, -12, -19, 1, -24, -4, -29, -29, -13, -18, -4],\n [2, 4, -22, -4, -16, -5, -18, -29, -14, 7, 8, -22],\n [10, -6, 10, 0, 0, 6, 6, -13, 7, -25, -34, -4],\n [24, 14, 6, 4, -8, 7, -9, -18, 8, -34, -8, -26],\n [0, 10, 6, 14, 14, 8, -12, -4, -22, -4, -26, 29]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-61", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[29, 31, 7, 5, -23, -32, -13, 34, -2, 5, -18, -3],\n [-11, 16, -19, 15, -33, 19, 20, -1, 32, 23, 23, -23],\n [26, 11, -33, -15, 29, -18, -23, 35, 9, 26, -6, -22],\n [17, -26, -5, -30, -17, -24, 28, 19, 31, -27, -30, -35],\n [6, 19, 13, -6, -1, 27, -14, 7, -8, -18, -4, 33],\n [18, -2, -5, -32, -22, -21, 24, -16, -16, 13, 32, -18],\n [-12, -9, -3, 28, -11, 33, -18, 9, -16, -1, -30, -27],\n [16, -8, -17, 27, -29, 1, 0, -19, 1, 24, 13, 20],\n [-2, -6, -9, 15, -27, -16, 11, -17, 32, -24, -31, 33],\n [-11, -5, 10, -2, 5, 32, 2, 10, 33, -9, 7, 35],\n [9, -18, -4, -34, 5, -16, 22, 2, -35, 33, 18, -22],\n [-11, -27, 25, 16, -28, -20, -28, -13, -2, -18, 8, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-133", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-21, 0, 0, 15, -19, 5, 14, 10, -4, -28, -3, 4],\n [0, 7, 16, 12, -5, -18, 25, 20, 2, 22, 26, -14],\n [0, 16, 6, -18, 7, 0, 28, -4, 21, 10, -2, 26],\n [15, 12, -18, -23, -2, -20, -3, -2, 8, -10, -4, 20],\n [-19, -5, 7, -2, -34, 20, 13, 11, 8, -1, 14, -16],\n [5, -18, 0, -20, 20, 19, -6, -27, -8, -24, 6, 6],\n [14, 25, 28, -3, 13, -6, 27, -8, -6, -6, 6, 2],\n [10, 20, -4, -2, 11, -27, -8, -22, -12, 3, -8, 6],\n [-4, 2, 21, 8, 8, -8, -6, -12, 0, 4, -23, 14],\n [-28, 22, 10, -10, -1, -24, -6, 3, 4, 24, 24, 9],\n [-3, 26, -2, -4, 14, 6, 6, -8, -23, 24, 19, -24],\n [4, -14, 26, 20, -16, 6, 2, 6, 14, 9, -24, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-317", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-30, -17, -7, 28, -22, -6, 35, -15, 29, -32, 10, -28],\n [-18, 24, 9, -5, -8, 28, 1, 31, 32, -1, 0, 21],\n [34, -32, 13, 3, -18, 24, -26, -13, 32, 23, -29, -23],\n [-33, 4, -25, 15, -13, -4, 5, 6, 2, 31, 6, 7],\n [-3, 1, 21, 28, 28, 24, 16, 32, -9, 23, -17, -33],\n [3, 30, 20, -30, -8, 12, 12, 31, 18, -20, -1, -6],\n [12, 33, -28, 15, -26, -8, 0, 24, -26, -22, 27, 11],\n [33, 20, -30, -17, 16, 26, 13, -25, 10, 33, 9, 22],\n [-4, -26, -23, -23, 0, -17, -29, -21, 10, 12, 30, -32],\n [-33, -33, 33, -8, -13, -6, 26, 15, 5, 28, 7, 22],\n [23, 4, 10, 26, 13, -13, 8, 8, -17, 8, -25, 24],\n [2, -33, -20, -27, 5, 2, 33, 29, -1, -1, 12, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "788", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 10) of the inverse of matrix 1/839 * A where A =\n[[-9, 0, 5, 6, -24, -14, 9, -16, 14, 3, -14, 2],\n [0, 21, 6, 25, 0, -15, 2, 9, -28, -20, 6, -2],\n [5, 6, 24, 3, -10, -28, 2, -18, -4, -31, 0, 13],\n [6, 25, 3, 11, -4, 16, 1, 2, -16, 18, 12, 12],\n [-24, 0, -10, -4, 33, 18, -3, -19, -30, -6, -4, -20],\n [-14, -15, -28, 16, 18, -3, 20, -6, 11, 0, -8, -20],\n [9, 2, 2, 1, -3, 20, -27, -8, -14, -12, 0, 13],\n [-16, 9, -18, 2, -19, -6, -8, -27, -2, -6, 4, 3],\n [14, -28, -4, -16, -30, 11, -14, -2, -13, -31, -17, -6],\n [3, -20, -31, 18, -6, 0, -12, -6, -31, 26, -4, -2],\n [-14, 6, 0, 12, -4, -8, 0, 4, -17, -4, 9, 16],\n [2, -2, 13, 12, -20, -20, 13, 3, -6, -2, 16, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-11, 14, 9, -6, 12, 15, 19, 19, 10, -5, -2, 32],\n [-3, 20, 22, 21, -19, -25, 35, -19, -26, -10, -30, -20],\n [-32, 26, 28, 20, -13, -3, -5, -29, -31, 1, -35, 34],\n [9, 11, 32, -6, 24, -12, -5, -8, 9, -32, 25, 3],\n [-12, 35, 10, 17, 12, -27, -14, -34, -20, -31, -24, 16],\n [-10, -21, 31, 23, 3, 27, -11, 5, -8, -15, 25, 21],\n [-25, -17, -35, -4, -2, -19, 19, -17, 6, 23, 2, -5],\n [30, 33, 14, -6, -1, 23, -19, 30, -15, 16, 29, -22],\n [-20, 19, -27, -28, -2, -3, -29, -15, -31, 35, -24, 23],\n [22, 1, 9, -11, -9, 15, 6, 35, 6, 24, 22, -14],\n [22, -25, -30, -14, -24, -9, -35, 28, 3, 24, 34, 18],\n [-11, -16, 0, -13, -35, -9, 16, -34, -15, -27, 12, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31884", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 35, 9, -34, 31, 7, -18, 3, -30, 6, 16, -9],\n [-21, -17, 26, 28, 15, 11, 21, -16, -16, 28, 2, 2],\n [29, -31, 28, -9, -16, 24, 4, -30, 0, 29, -25, 13],\n [-8, -14, 11, 30, -11, 31, -4, -19, 4, -6, 23, -8],\n [11, -13, 21, -35, -7, 14, 28, 1, 25, -29, 28, -18],\n [-7, 24, 18, -15, -15, 22, 13, 0, -19, 17, -21, 4],\n [15, 29, -23, 2, -10, -21, -31, -34, 29, 24, 20, 2],\n [21, 15, 5, 34, 16, -35, -18, -9, 6, -30, -12, 9],\n [35, -29, -20, 22, 21, 6, -22, 20, -24, -21, -28, 22],\n [17, -27, 10, -29, 8, -22, -30, -1, 34, 25, -12, -34],\n [15, -5, -9, -5, 34, 7, 16, -22, 23, -16, 16, 4],\n [32, 8, -30, 21, 22, -6, 16, -25, 11, -31, -33, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-34, -2, 23, 18, 20, -1, 2, 21, -20, 2, 13, 16],\n [-2, -19, 9, 12, 2, -22, -26, -24, 25, 6, -27, 18],\n [23, 9, -10, -18, -3, 4, -22, -6, 9, 14, -25, -14],\n [18, 12, -18, -27, 14, -6, 14, 8, 16, 0, -18, 4],\n [20, 2, -3, 14, -14, -5, -27, -1, -7, -19, -14, -27],\n [-1, -22, 4, -6, -5, -34, -16, -6, 20, -19, 30, -12],\n [2, -26, -22, 14, -27, -16, -21, 16, -6, -12, -14, -22],\n [21, -24, -6, 8, -1, -6, 16, -2, -28, -24, 16, 24],\n [-20, 25, 9, 16, -7, 20, -6, -28, 30, -3, 9, 18],\n [2, 6, 14, 0, -19, -19, -12, -24, -3, -23, 4, -4],\n [13, -27, -25, -18, -14, 30, -14, 16, 9, 4, -4, 24],\n [16, 18, -14, 4, -27, -12, -22, 24, 18, -4, 24, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-233", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, 4, -10, -22, -17, 10, 8, -12, -12, -24, -23, 26],\n [4, -16, -6, 0, 3, -12, -4, -20, 21, 1, 2, -18],\n [-10, -6, -7, 0, 25, 26, 11, 18, 0, -3, 10, 26],\n [-22, 0, 0, -21, -28, -2, 3, -2, 14, 20, 24, -7],\n [-17, 3, 25, -28, -14, 18, 2, 16, 9, -14, -18, -18],\n [10, -12, 26, -2, 18, 1, 24, -24, -20, -24, -8, 27],\n [8, -4, 11, 3, 2, 24, 34, 2, -6, 5, -4, 18],\n [-12, -20, 18, -2, 16, -24, 2, -1, 9, 22, 12, -10],\n [-12, 21, 0, 14, 9, -20, -6, 9, 17, -34, 2, -12],\n [-24, 1, -3, 20, -14, -24, 5, 22, -34, 29, -2, -6],\n [-23, 2, 10, 24, -18, -8, -4, 12, 2, -2, -24, 10],\n [26, -18, 26, -7, -18, 27, 18, -10, -12, -6, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-103", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, 9, -16, 7, 14, 7, -12, 24, -4, -31, -34, -10],\n [0, 14, 3, -25, 27, 32, -18, -8, 6, 24, -14, 4],\n [0, 0, 35, 27, -16, 35, 35, -10, 5, -33, 7, -19],\n [0, 0, 0, 24, 32, 20, 28, -28, 33, -3, -11, 35],\n [0, 0, 0, 0, -3, -7, 3, 21, 28, 30, -27, -7],\n [0, 0, 0, 0, 0, 18, -30, 9, 4, -13, 6, 2],\n [0, 0, 0, 0, 0, 0, 18, 24, 6, 25, -4, 17],\n [0, 0, 0, 0, 0, 0, 0, 6, -23, -22, 22, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, -22, 2, -20, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 24, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "317", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[5, -20, 23, -27, 33, -26, -29, 30, -16, 27, -32, -8],\n [0, -34, 5, -8, -35, -9, 31, 3, 4, -8, -12, 15],\n [0, 0, 16, -30, 23, -24, 27, 0, -27, 31, -7, 35],\n [0, 0, 0, -14, 30, -15, 35, 5, 5, 13, -32, 29],\n [0, 0, 0, 0, 31, 17, -1, -32, 32, -25, 8, 24],\n [0, 0, 0, 0, 0, 1, 22, 7, -21, 31, -34, 35],\n [0, 0, 0, 0, 0, 0, -34, -26, 7, 7, 31, -13],\n [0, 0, 0, 0, 0, 0, 0, -28, 22, 4, -35, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, -26, -33, -2, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -11, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-231394", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (5, 8) rounded to the nearest integer?\n[[23, 18, 30, -6, -13, -27, 19, -35, 20, 3, -18, 6],\n [29, -3, -6, -31, 14, 29, -26, 24, -9, -8, 9, 16],\n [30, 26, 24, 4, -21, -29, 3, 15, -29, -24, -22, -2],\n [3, 28, -24, -2, -9, -14, -18, 10, 8, -18, 1, -29],\n [32, 24, 12, 15, 16, 16, 18, 5, 6, -14, 3, -13],\n [12, -3, 5, -6, 11, 21, 21, 26, 21, 32, -11, 4],\n [-19, 12, 3, -21, -19, -1, -3, -18, -6, 1, -29, -8],\n [-18, 11, -13, -16, -5, -22, -13, -34, -7, 14, 23, -3],\n [12, 8, -24, 6, -1, 5, 19, -23, 3, 30, -1, -3],\n [0, -23, 20, 10, 10, 8, 10, 33, -5, -12, -4, 31],\n [-20, 21, -12, -2, 16, 12, 17, 19, 2, -34, 33, 17],\n [14, -7, 19, 25, 14, -20, 34, 8, -20, -8, 21, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-25, -29, 34, 4, 12, -6, 32, 0, -3, 8, -7, -3],\n [-29, -18, 12, -2, 12, -10, 16, 14, 25, -10, -2, 24],\n [34, 12, -32, -15, 3, 0, -8, 14, 3, 14, -18, 19],\n [4, -2, -15, -19, 6, -7, -24, -12, 2, -22, 8, 4],\n [12, 12, 3, 6, 2, 0, -11, -6, -28, -7, 15, -6],\n [-6, -10, 0, -7, 0, 7, 7, 4, 8, 1, -14, -6],\n [32, 16, -8, -24, -11, 7, -25, -28, -18, -30, -19, -30],\n [0, 14, 14, -12, -6, 4, -28, 27, 14, -18, -1, 12],\n [-3, 25, 3, 2, -28, 8, -18, 14, -11, 22, -6, -17],\n [8, -10, 14, -22, -7, 1, -30, -18, 22, -2, -8, 12],\n [-7, -2, -18, 8, 15, -14, -19, -1, -6, -8, -33, 2],\n [-3, 24, 19, 4, -6, -6, -30, 12, -17, 12, 2, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-458", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-5, 0, -4, 27, -10, 29, -34, 34, 9, -11, 4, -18],\n [-24, -12, 7, -4, 11, 9, -1, -27, -26, 29, 23, 21],\n [-26, -17, 14, 32, -31, -7, -31, 24, 29, -8, -35, -7],\n [15, 0, -4, 28, -22, -4, -27, -25, 12, 15, -32, 5],\n [-11, -19, 11, -28, 22, -35, -34, -26, -9, -23, 27, -25],\n [-22, -10, 33, 3, -8, -19, 1, -9, 31, 32, 11, -2],\n [-18, -1, -18, 34, -2, -3, 7, -9, 12, 33, 35, -14],\n [-2, 7, -20, -22, 3, 35, -24, 19, -30, 4, -23, 33],\n [-12, 23, 10, 8, -25, 25, 0, -26, -35, 27, -24, -31],\n [0, -19, 22, -14, -5, -10, -23, 27, 31, 27, -25, 33],\n [28, 32, -4, -26, 18, 19, 26, 19, -1, 31, 29, -19],\n [6, 23, 34, -25, -8, 3, 18, -25, 22, 4, -32, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "457", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, 34, -5, -34, 7, 5, 24, 10, 4, 23, 9, 6],\n [-15, -33, 30, -25, -12, 14, -15, -11, -32, 7, 11, -13],\n [24, -15, 30, 15, -21, 22, -10, 23, 9, 30, -1, 28],\n [-9, -5, -24, 9, -4, 18, 30, -4, -21, 19, 5, 4],\n [13, 2, 20, -2, -35, -26, 4, -20, 10, -12, -22, 3],\n [-18, 5, 20, 0, -12, -7, -14, -25, 5, 13, -25, 16],\n [31, -28, -5, -30, 35, -23, -30, 31, -9, 9, -10, -32],\n [1, -15, -8, -4, 17, -3, -10, -19, 20, -6, -31, -30],\n [26, -26, 34, -26, 8, 20, -32, -23, -17, 34, 26, -27],\n [10, 20, 4, 31, 26, 10, -30, -7, -17, -21, 21, 2],\n [-15, 15, 3, -16, -34, -4, -32, -29, -33, -11, -27, -10],\n [28, -18, -34, -35, 12, 27, 0, 27, -10, -30, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-35, 2, 12, 12, -8, 10, 0, -8, 2, 3, -4, 4],\n [2, -32, -2, 17, -11, 21, 5, -20, -15, 8, 14, -26],\n [12, -2, -34, 28, -30, 6, -2, 14, -9, -26, 10, -26],\n [12, 17, 28, -18, -7, -1, -7, -8, -6, -4, -2, 7],\n [-8, -11, -30, -7, 23, -20, 14, -6, -7, 12, 11, -14],\n [10, 21, 6, -1, -20, 21, 4, 0, 2, -7, 12, -24],\n [0, 5, -2, -7, 14, 4, 27, -2, -2, 16, -18, 3],\n [-8, -20, 14, -8, -6, 0, -2, 35, 6, 2, 7, 2],\n [2, -15, -9, -6, -7, 2, -2, 6, 26, 1, 12, 10],\n [3, 8, -26, -4, 12, -7, 16, 2, 1, 24, -1, -5],\n [-4, 14, 10, -2, 11, 12, -18, 7, 12, -1, -27, -25],\n [4, -26, -26, 7, -14, -24, 3, 2, 10, -5, -25, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-849", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[13, -1, -7, 5, -30, -26, -13, 10, -24, 19, -23, -29],\n [-24, 25, -11, -34, -10, 15, 33, 26, 3, -25, 28, 6],\n [-26, -17, -32, -33, -22, -26, -30, -5, -5, 12, -27, -10],\n [-34, -32, -30, -6, 19, -8, 25, 19, 0, -31, -7, -24],\n [-14, 23, 3, -34, -22, -26, 12, 28, -33, 24, 32, -15],\n [-17, -16, 22, 6, -26, -13, -24, -27, -7, -16, 29, -33],\n [-28, 3, 28, -5, -14, -31, 22, 27, 25, 16, -3, -14],\n [15, -25, 22, 14, 34, -19, 10, 8, 21, -31, 3, 22],\n [-27, -13, 11, 0, -5, -13, 20, 35, 10, 22, 0, 32],\n [24, -22, -11, 35, 8, 10, -23, 26, -17, -24, 12, -3],\n [1, -30, 7, 14, 10, -8, 31, -25, -16, -6, 0, 32],\n [0, 22, -8, 3, 30, 7, -31, -23, -27, 21, -9, 25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4326", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[14, -2, 29, 9, -2, -28, 12, 0, 30, -25, 16, 0],\n [-5, -12, -15, -6, 28, 3, -35, 6, -31, -24, -7, -33],\n [25, 15, 0, -34, -7, 5, -7, 28, 22, -26, -25, -29],\n [25, 30, 17, 29, -9, -29, 29, 22, -11, 12, -32, -28],\n [32, 24, -32, -28, -20, -17, -35, -2, 9, 27, -30, 0],\n [30, -28, 31, -9, -2, -8, -5, -19, 19, -27, 21, 9],\n [-30, -22, -5, 18, -25, 33, -34, -19, 0, -33, 27, 7],\n [-3, -7, -13, 23, 13, 19, -8, 35, -11, -29, -2, -14],\n [31, 14, 12, 34, 21, -11, 30, -20, 22, 5, 15, -15],\n [20, 11, 7, -5, -21, 12, 26, 34, -33, 2, 22, 31],\n [9, 8, -28, 30, 35, 25, -19, 35, 0, 32, -15, 10],\n [10, -20, -14, -30, 20, 9, 22, -8, -19, 0, -24, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1756", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[23, -24, 26, 4, -34, -11, -5, 11, 24, 5, 14, -13],\n [0, 35, -14, 20, -20, 22, 15, -30, -34, 26, 6, 7],\n [0, 0, -16, 20, 31, 23, 12, -1, -28, -4, 9, 31],\n [0, 0, 0, 29, -16, 35, 5, -35, -32, 35, -26, -7],\n [0, 0, 0, 0, 10, -18, -33, 34, -14, 19, 28, 5],\n [0, 0, 0, 0, 0, -18, 22, -35, -14, -13, -28, -7],\n [0, 0, 0, 0, 0, 0, 32, -31, -31, -11, -12, -35],\n [0, 0, 0, 0, 0, 0, 0, 1, -26, 31, -23, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 29, -6, -12, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -20, -32, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11259", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[4, 10, 22, 20, -24, -11, -20, 15, 17, 16, 31, -12],\n [0, -14, -5, 22, 33, -17, 17, -34, 17, 31, 11, 17],\n [0, 0, -1, -7, -19, 13, 20, -33, -14, -22, -33, 2],\n [0, 0, 0, 9, 33, 8, 11, 21, -17, -2, -33, 3],\n [0, 0, 0, 0, 9, -9, 17, -27, -35, -3, 2, 21],\n [0, 0, 0, 0, 0, 32, -19, 6, 32, -24, 9, 0],\n [0, 0, 0, 0, 0, 0, -9, 11, 30, 7, -17, 32],\n [0, 0, 0, 0, 0, 0, 0, -30, -9, -21, -5, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, -26, 13, 18, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-42571", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[24, 7, -4, 20, 10, -30, 6, 26, -6, -14, 8, -9],\n [7, 11, -30, -2, 9, 12, -8, 8, -25, -18, 12, -32],\n [-4, -30, 8, 5, 8, -10, 6, -2, -14, -12, -3, -27],\n [20, -2, 5, -6, -21, -8, 14, -4, -12, -2, 4, 4],\n [10, 9, 8, -21, 1, 29, 17, -6, -8, -23, -15, 12],\n [-30, 12, -10, -8, 29, 9, 12, 28, 22, -16, 2, 9],\n [6, -8, 6, 14, 17, 12, 23, 10, 32, 8, -8, 2],\n [26, 8, -2, -4, -6, 28, 10, 31, 0, 6, -2, -12],\n [-6, -25, -14, -12, -8, 22, 32, 0, 10, -8, 18, 4],\n [-14, -18, -12, -2, -23, -16, 8, 6, -8, -15, -6, 18],\n [8, 12, -3, 4, -15, 2, -8, -2, 18, -6, -23, -2],\n [-9, -32, -27, 4, 12, 9, 2, -12, 4, 18, -2, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (10, 1) of the inverse. Round your answer to the nearest integer:\n[[-25, -5, -2, 2, -6, 2, -16, -10, -12, -4, -4, -10],\n [-5, 30, -14, -30, 5, 16, -16, 27, -2, 8, -26, -16],\n [-2, -14, -2, 4, -16, -12, 28, 4, 5, -18, -4, 2],\n [2, -30, 4, -30, 6, -20, -16, 1, 14, -14, 2, 14],\n [-6, 5, -16, 6, 3, 2, 1, 4, -3, -2, -16, -29],\n [2, 16, -12, -20, 2, 8, 2, -1, -6, 14, -26, 2],\n [-16, -16, 28, -16, 1, 2, 8, 9, 2, 3, -8, -18],\n [-10, 27, 4, 1, 4, -1, 9, -9, -7, 0, -4, -4],\n [-12, -2, 5, 14, -3, -6, 2, -7, 11, 20, -20, -24],\n [-4, 8, -18, -14, -2, 14, 3, 0, 20, 29, -22, 0],\n [-4, -26, -4, 2, -16, -26, -8, -4, -20, -22, -2, 8],\n [-10, -16, 2, 14, -29, 2, -18, -4, -24, 0, 8, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-43", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[0, -1, 10, 9, 20, -31, 8, -8, 6, -5, -29, -29],\n [-32, -4, -8, 20, -32, -28, -22, -6, -33, -34, -26, 34],\n [35, -20, 34, -14, -1, 13, -34, 30, -17, 33, -32, 5],\n [20, 19, -5, -14, 12, -32, -15, 5, 9, -28, -27, -18],\n [-5, -1, -6, -18, 5, -12, 12, -22, -17, 24, -14, -6],\n [-21, -15, -10, -24, -29, -1, 32, -34, -16, 11, -24, 17],\n [-19, -18, -12, 1, -6, 16, -13, 1, -12, 14, -16, 11],\n [-18, -10, 35, 7, 11, 7, -4, -29, -4, 29, 22, 17],\n [-2, 33, 20, 30, -4, 14, -12, 10, -33, -26, -30, 16],\n [14, 22, 16, -23, 23, 3, 17, 22, -16, 27, -26, -10],\n [-17, 25, -2, 8, -18, -20, -10, 29, 30, -9, -32, 15],\n [-33, 30, -20, -8, 8, -18, -34, 8, -16, 20, -13, 24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52807", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[35, 9, 11, 1, -28, -31, -13, -26, -9, -35, 35, -28],\n [0, -8, -2, 7, -8, 13, 25, 1, -33, -27, -34, -13],\n [0, 0, -11, -9, -16, 0, -8, -7, 6, 22, -4, -24],\n [0, 0, 0, -25, 14, -35, -9, -4, -30, 5, 0, 3],\n [0, 0, 0, 0, 12, -30, -29, 8, 25, 18, 15, 12],\n [0, 0, 0, 0, 0, 31, -34, 8, 4, -17, 27, -12],\n [0, 0, 0, 0, 0, 0, 1, -32, 22, -26, 27, 0],\n [0, 0, 0, 0, 0, 0, 0, -34, 11, 20, -20, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 1, -24, -25, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -24, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485142", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[9, 17, 17, -19, 29, 22, 1, 6, 34, 4, -13, -13],\n [13, -29, 1, -20, 2, 4, -7, -19, -16, -11, 24, 2],\n [27, 3, 28, -15, -4, -8, -24, -13, -21, -24, -32, -1],\n [25, -9, -3, -23, 1, 8, -34, 2, 1, 23, 33, -18],\n [12, 30, 13, 22, -1, 22, -29, -27, 33, -32, -4, -31],\n [20, 20, 8, -23, -32, 16, -21, -35, 29, -25, 25, 27],\n [2, 33, 9, 34, 32, -32, 35, 12, -27, 11, 24, 16],\n [-3, 22, 12, -31, -9, 5, -35, 15, -20, -4, 11, -13],\n [-21, -10, 1, 19, -34, -17, -4, 33, 19, 20, -7, 0],\n [35, 17, 3, -25, -6, 17, -28, -16, -24, 31, 14, -24],\n [18, 18, -17, -22, 16, -14, -32, 23, -2, 28, -18, -5],\n [6, -33, 19, -26, 35, -14, -13, -23, 4, -23, 15, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3349", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-23, -7, 35, 11, -10, 34, -13, 20, -17, 14, -1, 13],\n [10, 34, 17, -5, -14, 31, -28, -17, -5, -4, 19, -5],\n [31, 15, -9, 12, 7, 15, 33, 35, 14, 25, 5, 15],\n [-12, -6, 16, 14, 21, 26, 17, 32, 33, -5, -6, -26],\n [8, -30, -9, -16, -16, -24, 13, 16, -26, -31, 28, 22],\n [-28, -6, -19, 31, -15, -20, -9, -30, 6, -20, 9, -33],\n [4, -16, -29, 23, -25, 16, -33, -15, 17, -6, -25, -11],\n [14, -27, 9, -7, 26, -21, -17, -21, 3, -1, -23, -20],\n [31, 19, 29, -1, -20, -35, 14, -22, 26, -29, -13, 27],\n [-7, -14, -30, -7, -34, 28, 0, -16, 19, 1, 16, 33],\n [34, -14, -21, 11, 35, 33, 16, 3, -34, 9, -12, 25],\n [29, 17, -15, 31, -35, 23, 11, -18, -3, -21, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (8, 5) of the inverse. Round your answer to the nearest integer:\n[[24, -3, 9, -6, -9, -20, -14, -4, -27, 0, 14, -2],\n [-3, 17, -13, 10, 14, 14, -4, 10, 3, -14, 24, 4],\n [9, -13, 3, -14, -6, -25, -18, 20, -8, 13, 2, 10],\n [-6, 10, -14, -20, -4, -12, 20, -18, -1, -26, 20, -4],\n [-9, 14, -6, -4, 34, -2, 0, -22, -4, 31, 22, -11],\n [-20, 14, -25, -12, -2, -25, 6, -10, -1, 2, 1, -26],\n [-14, -4, -18, 20, 0, 6, 18, 4, -10, 13, 30, 2],\n [-4, 10, 20, -18, -22, -10, 4, -31, -2, 0, 8, -21],\n [-27, 3, -8, -1, -4, -1, -10, -2, -1, 26, 10, 28],\n [0, -14, 13, -26, 31, 2, 13, 0, 26, 7, -18, 7],\n [14, 24, 2, 20, 22, 1, 30, 8, 10, -18, 2, 16],\n [-2, 4, 10, -4, -11, -26, 2, -21, 28, 7, 16, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-12, -7, -30, 22, 21, -33, -12, -17, -27, -6, 8, 17],\n [32, 24, -13, 25, -29, 8, 19, 3, 23, -31, 6, -22],\n [-9, -20, -34, -17, -13, 5, -22, 11, 27, -28, -9, 4],\n [-8, 32, 25, 2, -12, -8, 5, -18, 13, -10, -33, 2],\n [-22, -35, -25, 4, -32, -2, 29, 20, -26, 35, 28, -23],\n [-14, 20, 29, -23, -35, 2, 22, -11, 6, -3, 21, 1],\n [21, 26, -33, -6, 31, 27, -13, 30, 25, -34, -9, 12],\n [27, -31, -35, -14, -12, 23, 14, -13, -18, -14, 8, 8],\n [1, -29, -12, 5, 34, 35, -18, 24, 16, 13, 31, 9],\n [-27, -10, -10, -6, -9, -32, 15, 34, -26, 0, 10, -30],\n [34, -33, 14, 6, 18, 3, 19, -25, -6, 20, -7, -19],\n [-3, -15, -26, 3, 11, 16, 5, 11, 35, 7, 1, 28]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[35, 24, -11, -14, 7, 35, 34, 0, 10, -14, -1, 11],\n [0, -23, 20, 31, -23, 14, 21, -8, 29, -12, 31, -29],\n [0, 0, -21, 20, -19, -17, -27, 28, 21, 2, -28, -30],\n [0, 0, 0, -2, -24, 3, -30, -4, 24, -28, 2, -17],\n [0, 0, 0, 0, 26, 12, 3, 17, 27, -17, -3, 28],\n [0, 0, 0, 0, 0, 9, -3, 33, -5, 28, -21, 10],\n [0, 0, 0, 0, 0, 0, 18, 29, -21, 25, -22, 33],\n [0, 0, 0, 0, 0, 0, 0, 19, 13, 4, -21, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 30, -1, -26, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27, 25, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20025", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-32, 7, -22, 31, -29, -28, 8, 28, -29, 12, 26, -11],\n [0, 28, -18, -32, -19, 11, 9, 22, -33, -24, -19, -14],\n [0, 0, -20, 15, -7, 35, 5, 21, -8, -15, -32, -21],\n [0, 0, 0, -18, -15, -28, 23, -16, 31, 19, 26, -18],\n [0, 0, 0, 0, -24, 12, 27, -9, -1, -34, -28, -16],\n [0, 0, 0, 0, 0, -23, -10, -7, -18, 33, -24, -34],\n [0, 0, 0, 0, 0, 0, -3, 31, 27, 12, 30, 29],\n [0, 0, 0, 0, 0, 0, 0, -31, -6, -26, -12, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, -23, 20, 23, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 31, -3, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26353", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (11, 4) rounded to the nearest integer?\n[[-2, 22, -29, -11, 21, -24, -5, -9, -2, -2, 1, 22],\n [0, -10, 9, 9, -4, 33, 35, -13, 29, 3, 31, 9],\n [0, 0, 34, 18, -9, 0, -31, 31, 15, -4, -15, -19],\n [0, 0, 0, 23, -26, -31, 19, -10, -32, -9, 22, -33],\n [0, 0, 0, 0, 9, -23, -30, -1, 17, 32, 6, -32],\n [0, 0, 0, 0, 0, 15, -19, 0, 13, -20, 8, -14],\n [0, 0, 0, 0, 0, 0, 6, -15, -34, -31, -19, -12],\n [0, 0, 0, 0, 0, 0, 0, 25, -28, -24, -22, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 14, 6, 35, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 0, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (4, 11) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -27, -5, -34, -12, 7, 34, 7, 15, 10, -35, 31],\n [-35, 27, 26, 25, 4, -7, -1, -25, -25, 27, 33, 20],\n [-29, 15, 3, 6, 17, -15, -6, -35, -12, -30, -30, 33],\n [26, -1, -1, 12, 7, -1, -31, -5, -5, -28, -30, 17],\n [8, 13, -28, 28, -32, -4, 17, 31, 27, 24, -3, -14],\n [-5, -12, -33, -3, -10, 15, -6, -1, -11, -8, -10, -28],\n [-21, 13, -28, 19, 22, -33, -27, -22, -16, -32, -12, -8],\n [-5, 31, 28, -19, -30, 24, -25, 2, -2, 11, -4, 21],\n [10, -1, -14, -20, -31, -10, -12, 31, -4, -13, 13, 26],\n [30, -25, -18, -26, 24, -28, 35, 12, 5, -28, 1, 1],\n [28, 23, 9, -20, -10, -5, -9, 7, -21, 22, 13, -11],\n [32, 0, 11, 23, 16, 4, 7, 20, -33, 35, -24, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[7, 34, -12, 25, 26, 4, 8, -6, 22, -4, 7, -16],\n [34, -15, 29, -5, 24, 14, -27, -25, -2, -10, 10, -18],\n [-12, 29, 22, -10, 12, -15, 14, -28, 16, -8, -8, -11],\n [25, -5, -10, -19, 6, 20, -2, -4, 8, -28, -2, 29],\n [26, 24, 12, 6, 20, 11, -7, -22, -2, -12, -22, 3],\n [4, 14, -15, 20, 11, -13, -4, -5, -18, 0, 6, -8],\n [8, -27, 14, -2, -7, -4, -2, -3, 10, 10, 16, -18],\n [-6, -25, -28, -4, -22, -5, -3, 19, -4, 14, 10, -11],\n [22, -2, 16, 8, -2, -18, 10, -4, -19, 1, -8, -29],\n [-4, -10, -8, -28, -12, 0, 10, 14, 1, 26, -8, -6],\n [7, 10, -8, -2, -22, 6, 16, 10, -8, -8, 7, 30],\n [-16, -18, -11, 29, 3, -8, -18, -11, -29, -6, 30, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1791", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[32, 8, 24, -35, -17, -3, 0, -12, -11, -25, -27, -30],\n [22, -7, -25, -13, -10, -35, 11, 5, -13, -31, 14, -27],\n [-32, 35, 29, 21, -11, 22, -30, -22, 27, 29, 16, 29],\n [-28, -28, -22, -12, 28, -11, -30, -35, -3, -22, 27, 20],\n [26, -8, -7, -13, 8, 2, 13, 7, -26, -9, -28, 32],\n [-6, -23, 22, -33, -31, -14, 22, 30, 4, -31, -20, -21],\n [-18, 11, -32, 17, 22, 22, 23, -2, -6, 18, 32, 32],\n [-10, -33, 21, 1, 2, 5, -32, -10, 3, 6, -25, -25],\n [18, 2, -16, -10, -22, 14, -11, 19, 15, -26, -22, -31],\n [21, -14, -7, -29, -18, -5, 7, -1, 35, -32, 15, -6],\n [17, -22, 0, -24, -2, -10, -30, 17, -21, -17, 11, 25],\n [16, -18, 24, 11, 21, -3, -4, -32, 5, -17, -29, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1286", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (5, 8) of the inverse. Round your answer to the nearest integer:\n[[15, 20, 35, 15, -28, -23, -4, -2, -18, 19, 7, -12],\n [0, -18, -22, 17, -17, 21, 28, -34, 21, -2, 13, 18],\n [0, 0, -1, -7, -30, 1, 22, 28, -5, 14, 24, -22],\n [0, 0, 0, 33, 2, 26, 17, -18, 16, -12, -29, -22],\n [0, 0, 0, 0, -7, -14, -34, 0, 2, -18, 15, -21],\n [0, 0, 0, 0, 0, 10, -32, -29, -26, -21, -10, 4],\n [0, 0, 0, 0, 0, 0, 18, 2, -21, 28, -28, 10],\n [0, 0, 0, 0, 0, 0, 0, 2, -15, 9, 22, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, -9, -34, 24, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 25, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1911", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[32, 10, 0, 22, 1, -2, 14, 27, 4, 6, -24, 8],\n [10, 29, -4, 5, -4, 2, -3, 18, 0, -4, 20, -16],\n [0, -4, -28, -6, 4, -4, -3, 20, -16, -7, 2, -29],\n [22, 5, -6, 12, -11, -32, -2, 33, -2, -7, 0, 12],\n [1, -4, 4, -11, 9, 7, -6, 26, 2, 0, 5, -10],\n [-2, 2, -4, -32, 7, -22, 4, 9, -14, 7, -30, -8],\n [14, -3, -3, -2, -6, 4, -33, 16, -28, -5, 12, -11],\n [27, 18, 20, 33, 26, 9, 16, -13, -22, 0, -6, -6],\n [4, 0, -16, -2, 2, -14, -28, -22, 22, 0, -1, -16],\n [6, -4, -7, -7, 0, 7, -5, 0, 0, 13, -10, -12],\n [-24, 20, 2, 0, 5, -30, 12, -6, -1, -10, 35, -18],\n [8, -16, -29, 12, -10, -8, -11, -6, -16, -12, -18, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (9, 8) rounded to the nearest integer?\n[[-20, -18, 30, 11, 4, -14, -2, 11, 7, 5, -13, -20],\n [-18, 11, -21, -5, 10, 19, -26, 14, 10, 6, -16, -18],\n [30, -21, -25, 6, -1, 8, -28, 22, 20, 0, 12, 1],\n [11, -5, 6, -31, 5, -12, 2, 0, 7, -12, 2, 8],\n [4, 10, -1, 5, 19, -2, -20, 2, 12, 14, 16, 29],\n [-14, 19, 8, -12, -2, 3, 24, 6, -2, 4, -22, -12],\n [-2, -26, -28, 2, -20, 24, 9, 22, -2, 22, -8, -23],\n [11, 14, 22, 0, 2, 6, 22, 32, 15, -16, 0, 3],\n [7, 10, 20, 7, 12, -2, -2, 15, -8, 19, 12, 2],\n [5, 6, 0, -12, 14, 4, 22, -16, 19, 10, -20, -2],\n [-13, -16, 12, 2, 16, -22, -8, 0, 12, -20, 21, 4],\n [-20, -18, 1, 8, 29, -12, -23, 3, 2, -2, 4, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 7) of the inverse of matrix 1/839 * A where A =\n[[10, 27, 0, 10, 1, -18, 7, -7, -18, -21, 23, -8],\n [17, -21, 7, -3, -34, 23, -28, -3, -1, -18, -15, 28],\n [-8, 9, -16, -32, 0, 16, 3, 35, -24, 19, 12, -27],\n [-24, 33, 21, -8, -19, -14, -1, 23, -17, 14, -10, 24],\n [8, 20, 7, -13, -14, 11, 19, -25, 19, -10, -35, 26],\n [-15, -28, -16, 9, 29, 24, 31, 20, -5, -14, 26, 20],\n [-28, 26, -12, -14, -21, -8, -14, -5, 26, 33, 3, 4],\n [33, 19, 35, 28, -28, 35, 8, 2, -15, -32, -4, 19],\n [24, 23, 31, -31, 1, -9, -23, -30, 29, -6, 16, 5],\n [-21, -31, -21, -35, -21, 24, 12, 18, 19, -9, -6, 24],\n [30, 10, 16, -1, 6, 20, 9, 16, -13, -7, -7, 21],\n [-17, -28, 14, -29, -25, 31, 30, -8, 20, -8, 4, -34]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[25, -11, 18, -19, 12, -24, 25, -34, 29, 16, -2, 9],\n [0, 16, 31, 20, 22, 14, -11, -24, 29, 20, 14, -8],\n [0, 0, 28, 18, 0, 8, 8, 33, 17, -23, 8, -32],\n [0, 0, 0, -25, 18, 26, 23, 25, 4, -32, -9, -20],\n [0, 0, 0, 0, -30, 12, 33, -30, 25, 30, 17, -8],\n [0, 0, 0, 0, 0, 32, 10, -26, 1, -15, -15, -26],\n [0, 0, 0, 0, 0, 0, 18, 0, 2, -33, 0, -14],\n [0, 0, 0, 0, 0, 0, 0, -12, -30, -28, -11, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, -31, 26, -4, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 20, -1, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "204", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[32, -22, -27, -20, -23, 0, 8, -22, -19, 29, 18, -34],\n [-19, -13, -35, -24, -23, -24, 21, -18, -21, 3, 33, -3],\n [12, -31, -28, -17, 16, -24, -28, 19, -2, 29, 11, -1],\n [-4, 15, -30, -27, 4, 12, -10, 1, 16, -24, 2, 32],\n [-20, 25, -12, -19, -32, 14, -33, -28, -24, -1, 30, 17],\n [-3, -18, 22, 9, -21, -21, 9, 32, 33, 31, 26, 8],\n [-16, 3, 3, -35, 31, 11, 18, -16, -27, -8, 28, -1],\n [4, -34, -33, -22, 32, 11, 18, 22, 26, 15, 12, -9],\n [19, 13, -12, -26, -29, -19, -14, 23, 8, -25, 6, -13],\n [24, 26, 18, -23, 32, -9, 4, -26, -21, 9, 17, -29],\n [-6, -6, -9, 13, 21, 28, 27, 12, 5, -6, -33, 1],\n [-6, 18, -29, -28, 27, 27, 28, -6, -26, 33, 13, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4758", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[33, 16, -2, 12, -12, -23, 14, 29, 35, -32, 28, 3],\n [0, 22, -20, 26, -26, 26, -3, 35, 6, 8, 10, -5],\n [0, 0, -30, 14, -8, -12, 33, -8, 22, 31, -18, -32],\n [0, 0, 0, 22, -25, 29, -19, 30, -32, -4, 35, -7],\n [0, 0, 0, 0, -31, 25, -15, 22, -22, 18, 5, -20],\n [0, 0, 0, 0, 0, 25, -15, -35, -9, 15, -25, -22],\n [0, 0, 0, 0, 0, 0, -12, -10, -11, 9, -7, -25],\n [0, 0, 0, 0, 0, 0, 0, 35, 2, -5, -7, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, -13, -26, 34, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -32, -12, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-949", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[32, 9, -27, 15, -22, 33, 20, -25, -6, 3, -12, 22],\n [-6, -12, 31, -7, 6, 26, -9, -7, 30, 21, 25, -7],\n [21, 19, 8, -8, 1, -13, 33, 22, -4, 33, 0, -4],\n [23, 24, -9, -12, 31, 0, -22, 32, 8, 12, -4, -19],\n [21, 3, -4, 32, -34, 6, 2, 19, 19, -2, 10, 7],\n [-34, 0, 34, 0, -14, 33, 2, 18, -14, -5, 17, 23],\n [13, -9, 21, -30, 10, -11, -27, 28, -5, -17, 29, -19],\n [-2, 0, -23, 23, -15, 29, -30, -25, -14, -25, 1, -10],\n [21, -10, -15, 21, -10, -21, 27, -1, -25, 32, 14, -7],\n [28, 5, -10, -8, 12, 30, -13, 3, 33, -15, 13, 0],\n [1, 6, 26, -30, -28, 33, 4, -26, -5, -6, 15, 0],\n [25, -9, -1, 24, -4, -32, -9, 11, -30, -10, -12, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-64", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[8, 1, -19, -8, 13, 20, 7, -5, 0, -26, 1, 20],\n [1, 19, -5, 22, 2, -2, 24, 2, -29, -12, 6, 19],\n [-19, -5, -13, -20, -2, 22, 18, 0, -16, 2, -17, 11],\n [-8, 22, -20, -12, -32, -9, -14, -12, 25, 27, -16, -7],\n [13, 2, -2, -32, -14, 10, 10, 10, 0, -34, -22, 0],\n [20, -2, 22, -9, 10, -26, -20, -2, -11, 3, -6, 8],\n [7, 24, 18, -14, 10, -20, 18, -4, -10, -21, 13, 6],\n [-5, 2, 0, -12, 10, -2, -4, 34, 7, 15, -10, 4],\n [0, -29, -16, 25, 0, -11, -10, 7, -10, -24, -2, -6],\n [-26, -12, 2, 27, -34, 3, -21, 15, -24, -8, -27, 10],\n [1, 6, -17, -16, -22, -6, 13, -10, -2, -27, 35, -8],\n [20, 19, 11, -7, 0, 8, 6, 4, -6, 10, -8, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1143", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-2, 21, -32, 35, 33, 32, 14, 31, 32, 23, 27, 31],\n [0, -35, 32, -18, -24, 2, 6, 0, -20, 29, 31, 3],\n [0, 0, -20, -25, -8, -34, -16, 2, 20, 3, -5, -13],\n [0, 0, 0, -1, -13, -28, 18, -15, -17, -5, 14, 35],\n [0, 0, 0, 0, -2, 21, 22, -1, -15, 29, 30, 21],\n [0, 0, 0, 0, 0, -28, 11, 1, -18, 0, -34, -33],\n [0, 0, 0, 0, 0, 0, -18, -3, -29, 9, -7, 2],\n [0, 0, 0, 0, 0, 0, 0, -12, 13, -15, 21, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 8, 14, 19, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 35, -3, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1021260", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-12, -14, -26, 30, 2, 0, -20, 8, -4, 32, -22, -4],\n [-14, -10, 1, 0, -22, 12, -9, 0, 19, -10, 2, -20],\n [-26, 1, -31, 26, -10, -4, 10, -11, -12, 6, -4, -18],\n [30, 0, 26, -28, -13, -12, -12, 14, -5, 12, -16, -6],\n [2, -22, -10, -13, 11, 6, -20, 8, -22, 16, 2, 2],\n [0, 12, -4, -12, 6, 0, -15, 15, -10, -9, -4, 12],\n [-20, -9, 10, -12, -20, -15, -20, -4, -28, -19, -6, -30],\n [8, 0, -11, 14, 8, 15, -4, 8, -8, 12, 18, 12],\n [-4, 19, -12, -5, -22, -10, -28, -8, -7, -10, -4, -8],\n [32, -10, 6, 12, 16, -9, -19, 12, -10, 9, -1, 28],\n [-22, 2, -4, -16, 2, -4, -6, 18, -4, -1, -33, 20],\n [-4, -20, -18, -6, 2, 12, -30, 12, -8, 28, 20, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-64", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-2, 18, -8, 0, 19, -12, -25, -5, -15, -4, 20, -12],\n [18, -19, 21, -4, 2, -6, 9, 16, -1, -6, -9, 24],\n [-8, 21, 2, -8, 15, -7, -26, -23, -5, -13, -3, 2],\n [0, -4, -8, -28, -19, -26, -16, -14, 20, 14, 1, -16],\n [19, 2, 15, -19, -17, -8, -4, 13, 0, -2, -20, 11],\n [-12, -6, -7, -26, -8, 9, -12, -18, 2, 22, 6, 18],\n [-25, 9, -26, -16, -4, -12, 34, 10, 32, 0, 12, -28],\n [-5, 16, -23, -14, 13, -18, 10, -28, -2, -21, -26, -6],\n [-15, -1, -5, 20, 0, 2, 32, -2, -9, 12, 0, -2],\n [-4, -6, -13, 14, -2, 22, 0, -21, 12, -34, -12, 10],\n [20, -9, -3, 1, -20, 6, 12, -26, 0, -12, -23, -14],\n [-12, 24, 2, -16, 11, 18, -28, -6, -2, 10, -14, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-489", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-23, 27, -21, 4, 2, 19, 8, 30, 30, 7, 2, -7],\n [20, -30, -27, -14, 10, -5, -15, 2, 16, -17, -26, 10],\n [30, 2, 26, 10, -1, 7, -6, 27, -6, -7, 30, -14],\n [-1, 6, -12, -10, -5, -34, 3, -24, 8, 7, 31, 2],\n [30, 4, -14, 27, 23, -17, -16, 7, 22, 18, 4, -9],\n [-23, 11, -13, 23, -29, 14, 30, -33, 3, -29, 32, 19],\n [-28, -4, -17, -24, 21, -26, -15, -16, -32, -17, -7, 35],\n [28, -25, -3, -11, -3, -10, 0, -25, -6, 21, -26, -11],\n [32, 21, -2, 18, 15, -30, 23, 18, -19, -10, -27, -34],\n [-16, -30, 19, 12, 22, 6, -15, -30, -6, -13, 0, -33],\n [-2, -6, 6, -15, -32, 13, 12, 15, -12, 10, -9, 15],\n [-16, 35, -18, -28, -9, -22, -18, 29, -5, -16, 34, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-43", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-35, -17, 3, -9, 20, -20, -29, -16, -5, -11, -35, -19],\n [0, -12, 26, 16, 15, 30, 21, 19, 17, -17, -23, -7],\n [0, 0, -12, -30, 12, -16, 31, 19, -18, -15, 28, 1],\n [0, 0, 0, -18, -6, 20, 6, 17, 14, -32, 27, 31],\n [0, 0, 0, 0, 13, -23, -3, 11, 28, -19, -2, 32],\n [0, 0, 0, 0, 0, -35, -1, -19, 24, -35, -32, -27],\n [0, 0, 0, 0, 0, 0, 10, -9, 0, 32, -4, 30],\n [0, 0, 0, 0, 0, 0, 0, -7, 1, 33, -22, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, -16, 22, -22, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 15, -4, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2730", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-23, 5, -19, -4, -31, -27, -2, -35, 4, 18, -4, 14],\n [0, 26, -25, -13, -10, 27, 10, 33, -30, 15, 7, 6],\n [0, 0, -34, -22, -19, 4, 3, -11, 12, 13, -3, -9],\n [0, 0, 0, 2, 4, 22, 29, -25, -21, 21, -11, 3],\n [0, 0, 0, 0, -23, 33, -15, -33, -10, -3, -14, 26],\n [0, 0, 0, 0, 0, 3, 25, 12, 14, 26, 17, -15],\n [0, 0, 0, 0, 0, 0, 27, -13, 32, -10, 12, 11],\n [0, 0, 0, 0, 0, 0, 0, -26, 9, -28, -31, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 15, 12, -16, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 18, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14777", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-4, -4, 2, 26, 7, 16, -8, -24, -16, -6, 32, -14],\n [-4, 34, 28, -8, -10, -1, -18, 10, 20, 0, 17, 12],\n [2, 28, 30, 14, 1, 4, -8, -10, -12, -14, -21, 3],\n [26, -8, 14, -27, 22, -17, -32, -4, -30, -19, -6, -32],\n [7, -10, 1, 22, 8, -28, 1, 0, -12, -16, -19, 20],\n [16, -1, 4, -17, -28, 2, 20, -28, 6, -24, -8, -18],\n [-8, -18, -8, -32, 1, 20, 21, -3, -2, -10, -2, -6],\n [-24, 10, -10, -4, 0, -28, -3, 29, 8, -8, -13, 3],\n [-16, 20, -12, -30, -12, 6, -2, 8, 22, 1, -18, 20],\n [-6, 0, -14, -19, -16, -24, -10, -8, 1, -34, 19, -10],\n [32, 17, -21, -6, -19, -8, -2, -13, -18, 19, -25, 24],\n [-14, 12, 3, -32, 20, -18, -6, 3, 20, -10, 24, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-67559", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-11, 18, -12, 22, -2, 6, 18, -14, 4, -18, 22, 9],\n [18, 21, -6, -4, -24, 2, -21, -11, -2, 4, -16, -14],\n [-12, -6, 19, 12, 18, 6, 4, -8, -18, 27, -28, -26],\n [22, -4, 12, -1, 10, -25, -7, 0, 24, 2, 7, -16],\n [-2, -24, 18, 10, 15, -28, 29, 2, 30, -14, -6, -6],\n [6, 2, 6, -25, -28, 16, -4, 11, -18, -32, -4, -14],\n [18, -21, 4, -7, 29, -4, -20, -18, 14, 5, 4, 2],\n [-14, -11, -8, 0, 2, 11, -18, -7, -14, 20, 24, 12],\n [4, -2, -18, 24, 30, -18, 14, -14, -22, 20, 3, 6],\n [-18, 4, 27, 2, -14, -32, 5, 20, 20, -22, -8, 16],\n [22, -16, -28, 7, -6, -4, 4, 24, 3, -8, -33, -16],\n [9, -14, -26, -16, -6, -14, 2, 12, 6, 16, -16, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-170", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (1, 11) rounded to the nearest integer?\n[[-14, 10, -24, -4, -10, 10, 16, 6, 18, 20, 0, -8],\n [10, -24, 12, 6, -6, 18, 4, 20, 27, -8, -10, 12],\n [-24, 12, -19, 4, 16, 12, 2, 17, 18, 0, 12, -17],\n [-4, 6, 4, 6, -16, 16, -2, -20, 25, -11, 9, -1],\n [-10, -6, 16, -16, -34, 13, 23, -6, 6, -29, 6, 8],\n [10, 18, 12, 16, 13, 28, 21, 18, -24, -30, 7, -18],\n [16, 4, 2, -2, 23, 21, 20, -15, 28, 9, -16, 7],\n [6, 20, 17, -20, -6, 18, -15, 24, 4, 7, 24, -5],\n [18, 27, 18, 25, 6, -24, 28, 4, -23, -13, -6, -8],\n [20, -8, 0, -11, -29, -30, 9, 7, -13, 10, 10, -32],\n [0, -10, 12, 9, 6, 7, -16, 24, -6, 10, 35, -12],\n [-8, 12, -17, -1, 8, -18, 7, -5, -8, -32, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-17, -14, 6, -10, 10, -10, -20, 10, -34, -7, -14, -12],\n [-14, 21, -4, -2, 16, 8, -2, -4, -4, -18, 20, -34],\n [6, -4, -1, 30, 30, -8, -5, 20, -10, 2, -4, 14],\n [-10, -2, 30, -2, -8, 14, 11, 6, 22, 12, -19, -4],\n [10, 16, 30, -8, -19, -11, -14, 12, 21, -1, 3, 11],\n [-10, 8, -8, 14, -11, -2, -8, -13, -5, -3, 8, -1],\n [-20, -2, -5, 11, -14, -8, 30, -19, 14, 29, 2, 4],\n [10, -4, 20, 6, 12, -13, -19, 16, 4, -10, 20, -16],\n [-34, -4, -10, 22, 21, -5, 14, 4, -17, 1, -6, 4],\n [-7, -18, 2, 12, -1, -3, 29, -10, 1, 33, 22, 0],\n [-14, 20, -4, -19, 3, 8, 2, 20, -6, 22, 25, -6],\n [-12, -34, 14, -4, 11, -1, 4, -16, 4, 0, -6, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-15, -15, -8, -17, -22, -12, -16, -4, 16, 29, 16, 22],\n [0, 34, -21, 11, -26, -15, -17, 32, -14, 27, 2, -21],\n [0, 0, -6, -12, 10, -32, -30, 2, -10, -17, -34, 32],\n [0, 0, 0, 28, -24, -25, -28, 24, -10, -4, 3, -32],\n [0, 0, 0, 0, -7, 0, 24, -21, 15, 14, 19, -24],\n [0, 0, 0, 0, 0, -1, -23, 8, 10, 32, 17, -35],\n [0, 0, 0, 0, 0, 0, -11, -26, -31, -14, 6, -16],\n [0, 0, 0, 0, 0, 0, 0, -3, 9, -28, -30, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, -26, -15, -24, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 3, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1354", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[17, -31, 31, -16, 15, 10, 31, -33, -13, -27, -25, 11],\n [0, 8, -23, -28, 27, -14, 2, -9, -10, -13, 29, 11],\n [0, 0, -32, -5, -32, -7, 8, -33, 23, 17, -25, -30],\n [0, 0, 0, -35, 20, 7, -8, -7, -18, 26, -30, -20],\n [0, 0, 0, 0, -13, -15, 15, 2, -8, 8, 3, 6],\n [0, 0, 0, 0, 0, -4, -29, 4, -21, 23, -24, 6],\n [0, 0, 0, 0, 0, 0, 2, -29, -6, 20, 0, 6],\n [0, 0, 0, 0, 0, 0, 0, -14, 11, -30, -12, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, -20, 8, -34, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 17, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1858055", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[29, -10, 24, -18, 23, -15, 10, -24, -4, 3, 19, 19],\n [-26, -1, -30, 32, 26, -27, -7, 35, -30, 8, 28, 31],\n [8, -22, -27, -13, 21, 21, -21, 28, -29, -16, 28, -17],\n [-30, 15, 3, 29, 35, -11, -13, 22, -25, -2, -5, 2],\n [10, -24, -27, -23, 28, -16, 23, -14, 29, 24, 5, 9],\n [-32, 34, 9, 22, -13, -4, 27, -28, -11, -3, 30, -20],\n [19, 0, -29, 33, -28, -33, -1, 0, -6, -21, 32, 22],\n [-8, 6, -18, -31, -27, -27, -18, 20, -21, 26, -1, 4],\n [15, 24, 20, 5, 18, -19, -11, -27, 20, -13, -34, 9],\n [29, 2, -30, 12, 8, -29, 30, 26, -6, 16, 0, -1],\n [30, 14, -33, -32, 19, 16, 23, 35, -16, -17, -28, 31],\n [-9, -28, -18, -7, 10, 0, -33, -27, -26, 30, -35, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[12, 6, 2, -20, -9, 23, -15, 8, -8, -14, -4, 0],\n [6, 11, -22, -14, 4, 2, 9, 0, 2, 19, 2, -1],\n [2, -22, 15, 2, 7, -12, 10, -4, -10, 4, -9, -10],\n [-20, -14, 2, -7, 0, 8, 30, -11, 10, 23, -10, -4],\n [-9, 4, 7, 0, -6, 12, 8, 10, 3, -12, 6, -9],\n [23, 2, -12, 8, 12, -34, -15, 3, -24, -10, 18, 22],\n [-15, 9, 10, 30, 8, -15, 14, 0, -14, -19, -28, 2],\n [8, 0, -4, -11, 10, 3, 0, -7, 22, 23, -8, -10],\n [-8, 2, -10, 10, 3, -24, -14, 22, 33, 15, -26, -16],\n [-14, 19, 4, 23, -12, -10, -19, 23, 15, -15, 2, -25],\n [-4, 2, -9, -10, 6, 18, -28, -8, -26, 2, 27, 17],\n [0, -1, -10, -4, -9, 22, 2, -10, -16, -25, 17, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-185", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 7, -15, 12, 30, -20, 4, -15, 16, -28, 19, 22],\n [-31, 6, -6, -27, 5, 15, 21, 25, -30, -10, -30, 17],\n [25, -3, 9, 4, -12, 9, 2, -7, -28, 28, 15, -30],\n [11, 13, -4, 18, 0, -17, 1, -19, -20, 22, 8, 32],\n [13, 15, -31, 22, 10, 19, -19, -24, -12, 20, 19, -20],\n [-14, 8, 7, -15, -28, 13, -30, 11, 0, -13, -5, 26],\n [21, 34, 29, 1, 32, -19, -29, 16, -1, -34, 4, 1],\n [21, -26, 10, -31, -31, -9, -31, 25, -28, -5, -15, -15],\n [15, 23, -34, -6, 22, -16, 4, -7, -31, -26, 25, -35],\n [11, 21, -22, -11, -15, -20, -4, 9, 28, 24, -17, 11],\n [28, -6, 11, -3, -15, 27, 6, 25, 7, 32, -10, -3],\n [-3, 13, 5, 0, -14, 11, -16, -12, 7, -20, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[35, 35, 10, 11, 33, -22, 9, 16, 14, 29, 28, -13],\n [0, 34, 23, 18, 35, -10, 8, -23, 18, 4, -32, 17],\n [0, 0, 19, 30, -18, -7, 17, -3, -33, -16, -32, -28],\n [0, 0, 0, -2, 35, 13, 13, -9, 29, -3, 13, 27],\n [0, 0, 0, 0, 31, -27, -1, 35, -32, 1, -8, -27],\n [0, 0, 0, 0, 0, -19, -27, 18, -31, 27, 11, -17],\n [0, 0, 0, 0, 0, 0, 9, -1, 17, -26, 5, -19],\n [0, 0, 0, 0, 0, 0, 0, -23, -19, -4, -20, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 15, -13, -7, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 34, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38417", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[3, 14, -3, -8, 20, -11, -22, 19, -29, -32, -6, 26],\n [0, 1, 19, 29, 16, -33, -29, 34, 34, -2, -20, -28],\n [0, 0, 14, -30, -21, -25, -9, 9, 2, -32, 9, -26],\n [0, 0, 0, 20, 4, 1, 30, -16, -24, 2, -6, 11],\n [0, 0, 0, 0, 15, -24, -26, 1, 30, 31, -22, 11],\n [0, 0, 0, 0, 0, -33, -34, 5, -6, 1, -33, -27],\n [0, 0, 0, 0, 0, 0, -18, 3, 11, -9, 35, -2],\n [0, 0, 0, 0, 0, 0, 0, 28, -21, 22, 31, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, 20, -17, 2, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 26, -23, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1562", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, 29, -15, -10, -1, 22, 6, -7, -7, -27, -34, -34],\n [-18, 33, 21, 35, -13, -17, -17, 22, 13, 9, -8, 14],\n [-25, 19, -27, -22, -15, 12, 22, 33, -27, 31, -18, -24],\n [-20, 1, -16, -16, -21, -11, -19, -24, 6, 3, 20, 17],\n [35, 11, -11, 14, -3, -7, -33, 3, -32, 1, -30, -26],\n [-24, 30, -33, 29, 28, -1, -12, 11, 16, -2, -11, 33],\n [-7, 28, 17, 22, 5, 15, -18, 5, 25, -12, 11, -8],\n [0, -15, 20, 33, -10, 18, 8, -3, -10, -14, -16, -34],\n [5, 18, 21, -18, -31, 10, -15, -14, -33, -27, -34, -8],\n [-2, 17, 23, -26, -34, 12, -30, 8, 18, 35, 0, -28],\n [-26, -3, -17, -18, 15, -13, -35, 23, -33, -26, 35, 13],\n [20, -20, 3, 8, -28, -28, 9, -25, -11, -19, 19, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1550", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 0, -10, -6, -4, 11, 2, 34, -16, 7, 32, -1],\n [0, -19, 22, -20, 15, -8, 4, 11, 10, -19, 6, 16],\n [-10, 22, 15, 26, 22, 6, -8, 26, -1, -6, 0, -7],\n [-6, -20, 26, 10, 12, -28, 14, -3, 6, -22, 29, 2],\n [-4, 15, 22, 12, 14, 0, 2, -14, 26, -2, 4, -12],\n [11, -8, 6, -28, 0, -19, 20, -20, 21, 6, -6, 8],\n [2, 4, -8, 14, 2, 20, -17, 2, -22, -12, -2, 4],\n [34, 11, 26, -3, -14, -20, 2, 32, 2, 7, 9, 12],\n [-16, 10, -1, 6, 26, 21, -22, 2, 2, 10, 19, -1],\n [7, -19, -6, -22, -2, 6, -12, 7, 10, 26, 7, -21],\n [32, 6, 0, 29, 4, -6, -2, 9, 19, 7, -35, 16],\n [-1, 16, -7, 2, -12, 8, 4, 12, -1, -21, 16, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-2, -5, 25, -4, 28, -4, 5, 30, -19, 34, -3, 10],\n [-5, 12, -29, 8, -4, -2, -4, 5, 8, 12, 30, 29],\n [25, -29, -4, 15, -1, -4, -16, -2, 11, -14, 16, 26],\n [-4, 8, 15, 19, -3, -12, -10, 9, 8, -6, 4, 0],\n [28, -4, -1, -3, 31, 20, -4, 0, 3, 0, 21, -7],\n [-4, -2, -4, -12, 20, -17, 3, -12, 14, -3, -12, 14],\n [5, -4, -16, -10, -4, 3, -35, -21, -32, -11, 15, -1],\n [30, 5, -2, 9, 0, -12, -21, 10, 3, -20, 20, -2],\n [-19, 8, 11, 8, 3, 14, -32, 3, 9, -23, -29, -9],\n [34, 12, -14, -6, 0, -3, -11, -20, -23, -11, 13, 10],\n [-3, 30, 16, 4, 21, -12, 15, 20, -29, 13, -3, -11],\n [10, 29, 26, 0, -7, 14, -1, -2, -9, 10, -11, 23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "271", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, 30, -30, 20, -2, 6, -6, 7, 24, -22, -20, 12],\n [30, 18, 12, 7, -8, -2, -8, 22, -16, 16, -24, 20],\n [-30, 12, -28, 16, 24, -4, 0, 16, -16, 6, -12, -22],\n [20, 7, 16, 1, -14, -17, 7, -7, 4, 0, -8, 18],\n [-2, -8, 24, -14, -31, 22, -22, 16, 20, 27, 15, 10],\n [6, -2, -4, -17, 22, -23, 2, -13, -5, -18, 12, 6],\n [-6, -8, 0, 7, -22, 2, -28, -2, -30, -22, -25, -16],\n [7, 22, 16, -7, 16, -13, -2, -33, -1, -8, -6, 18],\n [24, -16, -16, 4, 20, -5, -30, -1, -25, -28, 0, -4],\n [-22, 16, 6, 0, 27, -18, -22, -8, -28, -20, -8, 12],\n [-20, -24, -12, -8, 15, 12, -25, -6, 0, -8, 6, 6],\n [12, 20, -22, 18, 10, 6, -16, 18, -4, 12, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-47", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -20, -17, 1, 25, -10, 28, -23, -2, -13, -16, 18],\n [22, 23, -16, 3, -4, 5, 33, 32, -15, -12, -20, -4],\n [-10, -33, -29, -20, 17, -32, 9, -4, 22, -23, -14, 8],\n [8, -6, -13, -24, -22, 0, 9, -12, -33, 15, 19, 2],\n [-16, -34, -10, -34, 31, 6, 4, -27, -34, -8, -33, -20],\n [-32, -13, -30, 19, -28, 28, 31, 5, 4, -9, 3, 17],\n [4, 16, 1, 31, -17, -2, 30, -26, 16, 6, 24, -34],\n [-35, 14, 0, -14, 0, -33, 8, -20, -25, -26, 15, 6],\n [-11, -30, 8, -28, -2, 5, -35, -33, 16, 7, 11, -17],\n [34, 11, -31, 28, 9, 28, 9, 0, -27, -13, -4, 9],\n [-8, 16, -25, -17, 28, 29, 21, 30, -32, -7, -32, -35],\n [-18, -23, 34, 13, 11, -6, -9, -8, -34, -16, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-55", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-15, -22, 27, -8, 22, -12, 32, 21, 1, -30, -14, -10],\n [-22, 30, -7, 16, -4, 2, 21, -5, -15, -24, -7, 2],\n [27, -7, -34, 7, -12, 12, -2, 24, 5, 2, 10, -4],\n [-8, 16, 7, 25, 3, 9, 10, 4, -4, 26, -14, -7],\n [22, -4, -12, 3, -17, 10, -16, -6, -28, 14, -24, 4],\n [-12, 2, 12, 9, 10, 7, 22, -8, -2, 13, -14, -29],\n [32, 21, -2, 10, -16, 22, -5, 15, -12, 2, 15, -5],\n [21, -5, 24, 4, -6, -8, 15, -32, -22, -2, 4, -20],\n [1, -15, 5, -4, -28, -2, -12, -22, -20, 21, -6, 13],\n [-30, -24, 2, 26, 14, 13, 2, -2, 21, 32, 4, -14],\n [-14, -7, 10, -14, -24, -14, 15, 4, -6, 4, 26, -1],\n [-10, 2, -4, -7, 4, -29, -5, -20, 13, -14, -1, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1816", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[6, -1, 35, 12, 18, 0, -30, 35, -24, 23, 29, 14],\n [7, 7, 13, 19, 14, -15, -23, 6, -21, 14, -35, 15],\n [-2, 6, 26, -4, 25, 18, 22, -12, -9, -15, -18, 19],\n [32, 11, 18, -18, 28, 13, -1, 3, 22, 21, -30, -16],\n [14, -27, -22, -13, 12, 20, 4, 33, 3, 7, -5, 34],\n [-33, -32, -9, -9, 11, 24, 0, 10, 25, 6, -29, -6],\n [14, 11, 4, -31, 34, 22, 8, 35, -4, 4, 21, -25],\n [4, 11, -34, 16, 13, 23, 2, -20, -9, -8, 30, 9],\n [-3, 24, 14, 10, -1, 5, 22, 19, -31, -31, -14, -2],\n [29, 23, -19, 15, 13, -27, -21, -7, 17, -11, -8, -13],\n [-33, -3, 35, 33, -19, 31, 31, -2, -28, 9, 24, 20],\n [34, -14, -3, 14, 35, 10, 16, 30, -15, -12, 12, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 1) of the inverse of matrix 1/839 * A where A =\n[[28, -17, 2, 2, 22, 13, 9, 14, -18, 4, 7, -8],\n [-17, -20, -20, -14, 17, -6, 2, -2, -16, 4, -30, -26],\n [2, -20, 29, -10, 16, 14, -10, -27, 0, -2, -25, -4],\n [2, -14, -10, -28, 3, -4, 2, -19, 18, 20, 10, 11],\n [22, 17, 16, 3, 29, 1, -18, -12, -22, -22, 24, 4],\n [13, -6, 14, -4, 1, 1, -20, 30, -14, 20, -2, 26],\n [9, 2, -10, 2, -18, -20, 19, 3, 12, -16, -10, -6],\n [14, -2, -27, -19, -12, 30, 3, -8, -2, -16, 16, -11],\n [-18, -16, 0, 18, -22, -14, 12, -2, 34, -32, -14, -6],\n [4, 4, -2, 20, -22, 20, -16, -16, -32, 7, 4, -2],\n [7, -30, -25, 10, 24, -2, -10, 16, -14, 4, 19, -5],\n [-8, -26, -4, 11, 4, 26, -6, -11, -6, -2, -5, -29]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[28, 23, 26, -26, 28, 24, -16, 13, -9, 15, 21, 1],\n [0, -7, 32, 11, 33, -15, 6, -15, -34, 33, -29, -1],\n [0, 0, 10, 19, -35, 18, -35, 27, 19, -9, -21, -27],\n [0, 0, 0, -25, -12, 18, -5, -14, -22, -31, -19, 35],\n [0, 0, 0, 0, -27, 0, 15, -4, -18, -21, -16, 22],\n [0, 0, 0, 0, 0, -8, 10, -21, 8, -13, 31, 30],\n [0, 0, 0, 0, 0, 0, 25, -11, 27, -8, 20, -10],\n [0, 0, 0, 0, 0, 0, 0, -6, -27, 6, -22, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 3, 35, 11, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 9, -14, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-86", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-19, 33, 21, -18, -20, 15, 4, 3, 20, 18, 8, 10],\n [-4, 12, 25, 30, 2, 7, -32, -31, 22, 1, -10, -27],\n [-21, -10, 27, 34, -9, 18, -5, -4, -34, -18, -8, 35],\n [-11, 3, 13, -32, 16, 32, 21, -23, 29, 27, 35, -11],\n [-13, -6, 25, -29, 18, -19, 24, 30, 2, -23, 16, 16],\n [-4, -27, -19, 4, 18, 18, -8, 14, -18, -23, -3, -21],\n [2, -30, 9, 23, 12, 5, 19, 25, -34, -34, -26, 3],\n [-34, 29, 30, 16, 8, -2, 9, -4, -31, 27, 33, 18],\n [2, -27, 25, -15, 0, -35, -14, -21, 10, 29, -30, 4],\n [-1, 25, -13, -16, -8, 1, -29, 13, -12, -23, -29, -21],\n [-13, 33, 24, -26, 15, 28, 35, 20, -4, -13, 18, 34],\n [25, -16, 17, -21, -7, 34, 29, 26, 34, -20, 18, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[24, -8, 7, -20, 16, -12, -8, -12, -6, 4, -8, -8],\n [-8, -34, 19, -22, -1, 18, 0, 9, 5, 0, -30, -4],\n [7, 19, -33, 20, -8, 14, 24, -12, 24, 18, 2, 6],\n [-20, -22, 20, 21, -10, 8, 9, -8, 12, 2, 8, -16],\n [16, -1, -8, -10, 6, 12, -4, -24, -24, 5, 26, 1],\n [-12, 18, 14, 8, 12, 34, -13, 0, 15, -6, 2, -16],\n [-8, 0, 24, 9, -4, -13, 17, 0, 14, 20, -2, 18],\n [-12, 9, -12, -8, -24, 0, 0, -5, -32, 14, -24, 4],\n [-6, 5, 24, 12, -24, 15, 14, -32, 11, -20, 6, 3],\n [4, 0, 18, 2, 5, -6, 20, 14, -20, 15, -23, -6],\n [-8, -30, 2, 8, 26, 2, -2, -24, 6, -23, -8, -3],\n [-8, -4, 6, -16, 1, -16, 18, 4, 3, -6, -3, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -23, -6, 3, -28, 2, 14, -12, -14, -26, 21, 8],\n [-23, 0, -12, -2, -18, 28, 11, -14, 9, -13, -4, -7],\n [-6, -12, 4, 12, -3, -15, 4, -8, 15, -21, -2, -16],\n [3, -2, 12, -5, -3, -16, -31, 20, -4, 8, -8, 0],\n [-28, -18, -3, -3, -12, -20, 9, -5, -26, 6, -7, 26],\n [2, 28, -15, -16, -20, -22, 5, -24, 3, -14, -9, -26],\n [14, 11, 4, -31, 9, 5, 15, 12, -7, 12, -12, 2],\n [-12, -14, -8, 20, -5, -24, 12, -10, 0, -28, 25, 5],\n [-14, 9, 15, -4, -26, 3, -7, 0, 23, 1, -22, -9],\n [-26, -13, -21, 8, 6, -14, 12, -28, 1, 8, -16, -3],\n [21, -4, -2, -8, -7, -9, -12, 25, -22, -16, -12, 10],\n [8, -7, -16, 0, 26, -26, 2, 5, -9, -3, 10, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[33, 18, -22, -21, -26, -14, -23, 29, -22, 8, 3, -1],\n [0, -9, 9, 21, -14, -2, -27, 14, 18, 22, 26, 2],\n [0, 0, -33, -25, -12, -7, 33, -28, -17, 32, 33, 12],\n [0, 0, 0, 28, -28, -31, -11, 17, 13, -15, 15, 10],\n [0, 0, 0, 0, 23, -28, 28, 18, -21, 16, 15, -32],\n [0, 0, 0, 0, 0, 20, 32, -1, -10, -18, 28, 20],\n [0, 0, 0, 0, 0, 0, 16, -10, 9, -15, 17, -7],\n [0, 0, 0, 0, 0, 0, 0, 32, -14, -7, -33, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, -11, 3, 26, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 11, -8, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15465", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-32, -34, 31, -6, -32, 12, 7, 9, -23, 11, -8, 1],\n [-8, -9, -6, -30, -27, -30, -7, 34, 30, 17, 34, -31],\n [-16, -24, -28, 22, 13, 28, 14, 3, 4, -5, -33, -6],\n [-7, 34, 20, 30, 27, -6, 17, 10, -27, -29, 27, 11],\n [8, 13, 26, 23, -23, -6, 7, 15, -28, 1, 28, 3],\n [-28, 26, 3, -22, 16, 21, -15, -13, -32, 7, -25, -17],\n [29, -34, 13, 33, -2, -32, 3, 13, -33, -10, 5, 29],\n [-20, 22, -1, -20, -3, -5, -14, 25, 28, 34, -1, 3],\n [-33, -23, -22, 5, -28, -17, -22, 14, 25, 0, 31, 9],\n [-29, -14, -27, 24, 6, 23, 4, -7, 19, 28, 6, -7],\n [-15, 27, 27, 2, 30, -24, -3, -35, 32, -8, 26, 23],\n [13, 9, -30, -16, -20, -24, 16, -16, 22, 9, -34, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-10, -4, 11, 20, -12, 16, -30, -10, -8, 25, -10, -1],\n [-4, 27, 11, 22, -22, 8, -20, 8, 3, -4, -18, 10],\n [11, 11, -24, 7, 26, 14, -12, -7, 7, 26, 7, -25],\n [20, 22, 7, -34, 6, 8, -26, -28, 17, 7, 6, -9],\n [-12, -22, 26, 6, 20, 14, 10, 12, -25, 32, 12, -6],\n [16, 8, 14, 8, 14, -25, -8, 23, -10, -1, -24, 8],\n [-30, -20, -12, -26, 10, -8, -24, 10, 10, -8, 1, -4],\n [-10, 8, -7, -28, 12, 23, 10, -35, 22, 19, -8, -28],\n [-8, 3, 7, 17, -25, -10, 10, 22, -1, 7, 3, -7],\n [25, -4, 26, 7, 32, -1, -8, 19, 7, -35, 14, 2],\n [-10, -18, 7, 6, 12, -24, 1, -8, 3, 14, -14, -7],\n [-1, 10, -25, -9, -6, 8, -4, -28, -7, 2, -7, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[34, -2, -6, -4, -22, 0, -4, -10, 16, -6, -25, 8],\n [-2, -30, -16, -8, 2, -6, 4, -4, 2, -4, -28, 6],\n [-6, -16, -1, 8, 0, -8, 0, 19, 5, -18, -13, -15],\n [-4, -8, 8, -33, -30, -18, 6, 30, 15, 20, 12, 14],\n [-22, 2, 0, -30, 6, 2, 16, 14, 16, -27, -4, -4],\n [0, -6, -8, -18, 2, 15, 5, -11, 12, 20, 2, -18],\n [-4, 4, 0, 6, 16, 5, 23, -14, -21, -16, -4, -6],\n [-10, -4, 19, 30, 14, -11, -14, 11, -5, 8, 2, 8],\n [16, 2, 5, 15, 16, 12, -21, -5, 3, 17, -10, -6],\n [-6, -4, -18, 20, -27, 20, -16, 8, 17, -15, -4, 14],\n [-25, -28, -13, 12, -4, 2, -4, 2, -10, -4, 32, 6],\n [8, 6, -15, 14, -4, -18, -6, 8, -6, 14, 6, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2496", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-14, -29, -34, 26, -31, -16, 18, 27, 0, -20, 21, 28],\n [-26, 15, -9, -29, 5, -23, 30, -33, -25, -31, 24, -34],\n [28, -23, 18, -24, -18, -18, -19, 3, -23, 9, -17, -17],\n [-15, -12, -6, 12, -1, 23, -19, 12, 19, -27, -22, -10],\n [16, 8, -25, 15, 6, 26, -1, 28, -18, -22, 13, 33],\n [-19, -15, -22, -33, -5, 11, 8, -19, 20, -9, 35, 33],\n [-34, 26, -30, 29, -18, 19, 31, 21, -17, -25, 19, 1],\n [-32, -23, 34, 22, -34, 24, -4, 27, 24, -10, -14, -32],\n [-20, 27, 6, -3, -23, 10, -23, -3, -22, -28, 10, -35],\n [23, 24, 13, 25, -13, -31, 14, 0, -16, 7, -28, 5],\n [-11, -29, 25, -3, 33, 2, -24, 8, 17, -22, 35, 16],\n [16, 10, 5, -34, 13, -8, -4, -14, 6, -7, 32, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2180", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[10, -27, 2, -10, 7, 17, -9, -25, -10, 21, -35, -25],\n [-6, -32, -3, -3, 30, -32, 15, -9, -3, -4, 31, -8],\n [21, -17, -5, 17, -4, -27, 15, -13, -11, 10, 8, 30],\n [31, -8, -12, 20, 14, -33, -13, -2, -27, 23, 30, -14],\n [-1, -5, 12, 17, -4, -24, 26, -33, -30, -24, 17, -16],\n [-30, -22, 20, 5, 13, 29, -5, -8, -24, -20, -1, 8],\n [32, -26, -33, -5, 16, 29, -31, -31, 30, -21, 29, -15],\n [35, -25, 6, 30, 25, 24, -22, -31, -5, 12, -4, 21],\n [-2, -9, -31, -19, 33, 20, 2, 18, 12, 13, 5, -14],\n [21, 30, -17, -34, -3, 23, -30, -25, -9, 9, -5, 27],\n [8, 5, 11, 33, -34, -21, -16, -33, 3, -26, 4, -23],\n [8, -4, -6, -35, 17, 8, -1, 4, 9, 24, 27, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-43", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[11, -12, 21, -18, 21, 10, 7, -20, -22, -27, 33, 25],\n [0, -17, 28, 2, -26, -20, 33, 6, 8, 17, -1, 0],\n [0, 0, -24, -1, 14, 4, -14, 11, 30, -26, 7, 33],\n [0, 0, 0, -8, 9, 31, -24, -25, -33, 25, 30, 20],\n [0, 0, 0, 0, 3, -30, 16, -11, 20, -17, -9, -31],\n [0, 0, 0, 0, 0, -3, 34, -8, 0, 13, 17, 33],\n [0, 0, 0, 0, 0, 0, 12, -14, -30, -3, 3, 7],\n [0, 0, 0, 0, 0, 0, 0, -7, -26, -26, 28, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, -6, -3, 7, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 32, -18, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32477", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-9, 3, -6, -13, -13, 11, 12, 27, -27, -13, 27, 11],\n [0, 1, 2, -35, 12, -1, 35, 17, -11, 6, -13, -27],\n [0, 0, 21, 0, -2, -23, 19, 10, 16, -8, -6, 9],\n [0, 0, 0, 11, 23, -22, 6, 25, 23, -28, 21, -14],\n [0, 0, 0, 0, 18, -13, 32, 10, 32, -8, 14, 27],\n [0, 0, 0, 0, 0, -25, -35, -18, -25, -26, 12, 25],\n [0, 0, 0, 0, 0, 0, 34, 8, 33, -33, -26, -32],\n [0, 0, 0, 0, 0, 0, 0, 9, 21, 4, 28, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 34, 31, -19, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 25, -24, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640531", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, 4, -13, -2, 22, 25, -8, 24, -4, 22, 8, -2],\n [0, -35, 19, 13, -15, 19, -9, -16, -20, 12, -4, -4],\n [0, 0, -34, 21, -14, 16, 22, -2, 35, -19, -13, -3],\n [0, 0, 0, 1, -10, -12, 18, -15, -26, 6, -7, 21],\n [0, 0, 0, 0, 8, -29, -20, -1, -29, -22, 23, 26],\n [0, 0, 0, 0, 0, -26, -17, -24, -26, 35, 20, -25],\n [0, 0, 0, 0, 0, 0, -5, 29, 3, -16, 7, 30],\n [0, 0, 0, 0, 0, 0, 0, 4, -27, 6, 6, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 25, 21, 25, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -35, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7778556", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-16, 0, 0, 0, 2, 14, -1, 22, 24, -14, -30, -4],\n [0, -30, -20, 4, -20, 9, 9, 10, 26, 19, -15, -10],\n [0, -20, -29, 3, -11, 17, 1, -13, 8, -2, -14, 19],\n [0, 4, 3, -10, 29, 28, 8, -7, -14, 10, -2, -16],\n [2, -20, -11, 29, -2, 2, 10, 12, -22, 0, -2, -2],\n [14, 9, 17, 28, 2, 25, -6, 4, 2, 18, 2, 8],\n [-1, 9, 1, 8, 10, -6, 27, 6, -24, -4, 2, 9],\n [22, 10, -13, -7, 12, 4, 6, -23, 0, -26, -16, -13],\n [24, 26, 8, -14, -22, 2, -24, 0, -22, 20, 0, -2],\n [-14, 19, -2, 10, 0, 18, -4, -26, 20, 33, 2, 3],\n [-30, -15, -14, -2, -2, 2, 2, -16, 0, 2, 0, -28],\n [-4, -10, 19, -16, -2, 8, 9, -13, -2, 3, -28, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-25, -17, -31, 34, -18, -15, -21, 23, -30, -12, 24, -8],\n [0, 10, 1, -22, 12, 35, 0, 24, 18, 27, 12, -14],\n [0, 0, -19, 27, -18, -33, 18, -22, -2, -35, 12, -26],\n [0, 0, 0, -21, 23, 28, 11, -34, -6, 2, -31, -30],\n [0, 0, 0, 0, -11, -10, 19, 10, 10, 7, 24, -3],\n [0, 0, 0, 0, 0, -3, 34, 25, -6, 1, -20, 9],\n [0, 0, 0, 0, 0, 0, 31, 3, -26, 15, -22, -30],\n [0, 0, 0, 0, 0, 0, 0, -11, 21, -4, 10, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 19, 15, 29, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -13, -5, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3648", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (7, 6) rounded to the nearest integer?\n[[-13, 13, -6, -2, -3, 20, -7, -8, 7, 10, -32, -30],\n [13, 12, -26, 6, -5, -24, -32, 5, 18, -7, 13, 18],\n [-6, -26, -10, 24, 11, -9, -3, -2, -4, 17, 0, 2],\n [-2, 6, 24, 33, 4, -6, 8, 21, 24, 12, 4, 6],\n [-3, -5, 11, 4, 31, -21, -10, 16, 31, 22, 0, 9],\n [20, -24, -9, -6, -21, -34, -13, 8, -14, -10, -26, 18],\n [-7, -32, -3, 8, -10, -13, -29, 12, 20, -18, 6, 0],\n [-8, 5, -2, 21, 16, 8, 12, 6, -18, -32, 0, 17],\n [7, 18, -4, 24, 31, -14, 20, -18, -34, -2, 0, 16],\n [10, -7, 17, 12, 22, -10, -18, -32, -2, -17, 17, 8],\n [-32, 13, 0, 4, 0, -26, 6, 0, 0, 17, -13, -6],\n [-30, 18, 2, 6, 9, 18, 0, 17, 16, 8, -6, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[8, -5, 29, -18, 0, 26, -7, -13, -33, -6, 9, 13],\n [0, 28, -31, 20, -2, 12, -10, -31, -5, -12, -14, -14],\n [0, 0, 11, 31, 3, 30, -7, -22, -32, -31, 8, -12],\n [0, 0, 0, -23, 19, -6, 13, -21, -6, -8, -32, 32],\n [0, 0, 0, 0, 27, -34, 16, 16, -21, 4, -8, 19],\n [0, 0, 0, 0, 0, -34, -24, 19, -24, -27, -4, -28],\n [0, 0, 0, 0, 0, 0, 13, -18, -13, -3, 15, 7],\n [0, 0, 0, 0, 0, 0, 0, -35, -18, 28, -4, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, -32, 30, -5, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 25, -25, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2514", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -1, 2, 2, 6, 6, 13, 21, 18, -26, 24, 4],\n [-35, 28, -24, 21, -10, 4, 7, -23, 20, -19, -12, 22],\n [25, -8, 31, 15, 3, 30, 4, -23, -17, -30, -18, -27],\n [32, 18, 14, 34, -25, 19, 6, -25, 31, -34, 30, -10],\n [1, 0, -20, 30, -15, -29, -25, 20, 8, 18, 21, 22],\n [1, 12, 26, 3, 28, 32, 32, -9, 34, 24, 8, -6],\n [22, 0, -31, -17, -24, 24, -25, 17, -16, -9, 22, -31],\n [-27, -4, 18, 9, -9, -8, -18, -5, 5, -2, -29, -31],\n [-15, -30, 9, -1, -33, -3, 2, -20, 35, -28, -33, 33],\n [-17, -29, 14, -30, -31, 25, 22, -14, 21, -4, -19, 22],\n [5, -14, 6, -28, 10, 12, -33, -6, -8, -11, 1, 15],\n [3, 31, -35, 2, 16, 27, 16, 24, -23, -19, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-25, -9, 2, -8, -10, -3, -4, 18, -11, -12, 4, -9],\n [0, 33, 33, 3, -7, -5, 29, -21, -27, -23, 9, -30],\n [0, 0, -7, 12, -24, 31, 14, -25, -31, 9, 11, -30],\n [0, 0, 0, 11, -2, -24, -9, 33, 32, -8, 35, 9],\n [0, 0, 0, 0, -21, 26, -5, -9, -34, 7, -35, -27],\n [0, 0, 0, 0, 0, 19, -26, 29, 29, 25, 33, -1],\n [0, 0, 0, 0, 0, 0, -16, 7, -15, -1, 28, -4],\n [0, 0, 0, 0, 0, 0, 0, -15, 21, -17, -8, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 13, 12, -30, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 21, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1632", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[18, 29, -14, 25, 22, 18, -17, 34, -2, 8, 31, 16],\n [-14, -7, -22, 26, -21, -22, 31, -14, -29, -29, -19, -4],\n [20, 26, 22, 22, -33, -35, 31, -16, 26, 20, 17, 29],\n [20, 9, -18, 12, 2, -14, 35, -35, 6, 33, -7, -30],\n [20, -24, 3, 35, -24, -3, 17, -17, 22, 7, 9, -17],\n [1, -25, 20, -11, 33, 9, 26, -22, -2, 24, 28, 34],\n [15, 6, -15, -31, 30, 34, 25, -28, 30, 26, -16, -32],\n [-21, 20, -16, -12, -27, -15, 5, -23, -31, 28, 10, 35],\n [34, 23, 15, -20, 15, 6, -25, 32, 16, -26, 27, 0],\n [9, -30, -30, 30, 28, 2, 33, 25, 27, 35, -16, 28],\n [1, 0, -26, -2, 9, 27, -23, -11, 8, -12, 33, 11],\n [14, 0, -3, -33, -5, 24, -7, 8, 9, 6, -15, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-8, 11, 11, -19, -7, 12, -34, -3, 27, 32, 3, -31],\n [32, 16, 16, -7, 1, -28, -16, 5, 34, 0, -4, -31],\n [-16, 32, -14, -5, 5, -31, -26, 1, 20, -12, -20, -34],\n [-21, 5, 27, 13, -10, 30, -7, 34, 24, 29, 4, -25],\n [16, 28, -33, -25, -8, 26, 12, -8, 10, 28, 19, -34],\n [-20, -25, -33, 19, 6, -7, 33, -5, -11, -30, 24, 31],\n [-14, 5, 17, 24, 3, 19, -6, 35, -34, -28, 27, 23],\n [-8, 2, -18, 26, -13, 29, 4, 24, -31, -18, 2, -7],\n [-10, 24, 0, -7, -5, 27, -23, 35, 4, 34, -34, -28],\n [7, 13, -14, -1, -17, -32, -17, -16, -32, 13, -10, -33],\n [16, 0, 5, 34, 15, -20, 11, 10, 19, 3, -30, 25],\n [-27, -25, 29, 23, 34, -29, 25, 21, -2, 9, 9, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-27, 10, 10, 0, 10, 6, -6, -25, -3, 4, 34, 7],\n [3, 3, 17, -5, 27, -11, 5, 14, 23, 13, -6, 9],\n [32, 17, -10, 35, 4, -24, -35, 34, -35, -28, -3, 32],\n [14, -30, 24, 27, 16, -33, 34, -30, 1, 15, -9, 10],\n [33, -19, -19, -13, 3, -3, 30, -26, 4, -21, 7, -24],\n [-14, -18, 30, 26, 25, 24, 3, -14, -22, -29, -1, -2],\n [31, 27, -34, 9, 27, -34, 18, 15, 5, -31, 35, -11],\n [-35, -27, 30, 31, -32, -15, 25, -10, 8, 1, -26, 11],\n [-13, 18, 23, -17, -11, 31, -23, -15, -14, 11, 27, -7],\n [13, -11, -13, 13, -13, -31, -7, -31, 3, -1, -6, 20],\n [-34, -21, 15, -13, -10, -25, -12, -27, 35, -26, 35, 21],\n [-21, -3, -25, -17, 6, 22, -18, -18, -14, 16, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-27, -6, -1, -12, 10, 8, -9, -1, -12, 14, 8, -2],\n [-6, -19, -3, 24, -30, -11, 12, -10, -19, 22, 4, 21],\n [-1, -3, 18, -4, 18, 0, -3, 0, -8, 6, -32, 0],\n [-12, 24, -4, 17, -3, 16, 13, 1, -12, -8, 12, 5],\n [10, -30, 18, -3, 23, 10, -12, 4, -20, 22, 0, 12],\n [8, -11, 0, 16, 10, -8, 4, 6, 18, 10, -17, -12],\n [-9, 12, -3, 13, -12, 4, -8, 8, 0, -6, 10, 18],\n [-1, -10, 0, 1, 4, 6, 8, -23, -8, -8, 26, 5],\n [-12, -19, -8, -12, -20, 18, 0, -8, -6, 6, 13, 14],\n [14, 22, 6, -8, 22, 10, -6, -8, 6, 25, -1, 22],\n [8, 4, -32, 12, 0, -17, 10, 26, 13, -1, -2, 2],\n [-2, 21, 0, 5, 12, -12, 18, 5, 14, 22, 2, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[34, -10, 7, 18, 4, -18, -10, -18, -25, -3, 15, -18],\n [-10, -20, 16, 13, 20, 2, -30, -8, -5, 15, -10, 4],\n [7, 16, -35, -6, -1, 6, 9, -8, -9, -6, 28, -20],\n [18, 13, -6, -2, -13, 9, -27, -12, -4, -26, 21, 12],\n [4, 20, -1, -13, 35, 20, -2, 7, -10, 2, 21, -10],\n [-18, 2, 6, 9, 20, 4, 10, -22, 19, 16, 20, -27],\n [-10, -30, 9, -27, -2, 10, -4, -14, 2, 1, -2, -13],\n [-18, -8, -8, -12, 7, -22, -14, 10, 12, -2, 14, 18],\n [-25, -5, -9, -4, -10, 19, 2, 12, 32, 16, -10, 19],\n [-3, 15, -6, -26, 2, 16, 1, -2, 16, -31, 14, 6],\n [15, -10, 28, 21, 21, 20, -2, 14, -10, 14, 18, -18],\n [-18, 4, -20, 12, -10, -27, -13, 18, 19, 6, -18, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1546", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-24, -15, -21, -24, 20, -20, -3, 7, 13, -18, -20, 4],\n [0, 26, -9, -22, 30, -9, 18, 24, 4, 9, 32, 32],\n [0, 0, 5, 25, 29, -35, -27, -21, 23, 30, -26, 13],\n [0, 0, 0, -14, 15, 6, -7, 9, -3, 3, 29, 14],\n [0, 0, 0, 0, 34, 19, 8, 14, 18, 27, -20, 11],\n [0, 0, 0, 0, 0, 29, 12, -29, -5, 27, 9, 20],\n [0, 0, 0, 0, 0, 0, -17, 24, -34, 15, -2, 15],\n [0, 0, 0, 0, 0, 0, 0, -31, -7, -17, -19, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 26, -24, -25, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 7, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3260", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-35, 12, -14, 5, -11, 10, -27, 25, 11, -33, -28, -11],\n [0, 7, 14, 27, -2, -26, -9, -23, 15, 32, -20, -24],\n [-11, 13, -20, -34, -1, -14, 12, 28, 31, -14, 11, 4],\n [17, -33, -30, -22, 22, -29, -7, -33, -23, 0, 2, 24],\n [-14, -15, -3, -32, 8, -35, 26, -14, 23, 1, -13, -3],\n [-14, 28, 26, 18, 22, -24, -18, 31, 24, -35, -16, -19],\n [13, -14, -3, -10, -9, 24, -2, 16, 19, 25, 14, 27],\n [28, -22, 15, -9, 4, 32, -27, 20, 3, -21, -18, 16],\n [25, 1, 17, -24, -11, -11, -15, -29, 13, 3, 13, -2],\n [-20, -21, 4, -29, 4, 30, 34, -14, 23, -31, -18, -25],\n [-28, -16, 23, -11, 22, -17, -34, 22, 30, -29, 15, -3],\n [-23, -26, 23, 2, -16, -22, 4, -29, 33, -30, 4, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1670", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-27, 29, -16, -30, 3, -15, 1, -24, 34, -21, -15, 10],\n [0, -26, 30, 3, -14, 6, -30, 16, 1, -30, -7, 33],\n [0, 0, 1, 10, -11, 1, -13, -10, 16, -33, -8, -2],\n [0, 0, 0, 32, 26, 2, 31, -34, 8, -4, -33, -19],\n [0, 0, 0, 0, -34, 17, -2, 4, 35, 29, 19, 15],\n [0, 0, 0, 0, 0, 10, -9, 34, -5, 5, 9, 0],\n [0, 0, 0, 0, 0, 0, -3, 13, -33, 2, 35, -21],\n [0, 0, 0, 0, 0, 0, 0, 35, 16, 10, 4, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, -32, -25, 28, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 33, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-427339", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (3, 4) rounded to the nearest integer?\n[[-31, -2, 26, -27, 18, 13, -26, -32, 11, -11, -30, -8],\n [-2, -31, 22, 1, -22, 6, -16, -4, 10, -28, 0, -12],\n [26, 22, 9, 18, -7, 22, -2, 10, -3, -4, -6, 2],\n [-27, 1, 18, -31, 10, -2, 10, -9, 5, 1, 20, 28],\n [18, -22, -7, 10, -12, -3, -11, -2, 22, -8, -12, -24],\n [13, 6, 22, -2, -3, 31, -4, -2, -10, -23, 26, -4],\n [-26, -16, -2, 10, -11, -4, 11, 4, 2, 3, -22, -10],\n [-32, -4, 10, -9, -2, -2, 4, -8, -15, -4, -8, 12],\n [11, 10, -3, 5, 22, -10, 2, -15, -12, 7, -15, -1],\n [-11, -28, -4, 1, -8, -23, 3, -4, 7, 0, 14, -8],\n [-30, 0, -6, 20, -12, 26, -22, -8, -15, 14, -29, 16],\n [-8, -12, 2, 28, -24, -4, -10, 12, -1, -8, 16, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[19, 0, -26, 34, 27, -2, -19, 25, -18, 25, 0, 17],\n [0, -13, 28, 2, 33, -6, -20, 18, 23, -30, -31, -35],\n [0, 0, 15, -17, -4, 21, -5, 22, -10, 12, 5, -11],\n [0, 0, 0, 25, -32, -5, 31, 5, -10, 32, 30, -17],\n [0, 0, 0, 0, -33, -3, -8, -14, -6, 11, 0, 23],\n [0, 0, 0, 0, 0, 7, -33, -13, -16, -21, 7, 35],\n [0, 0, 0, 0, 0, 0, -20, 7, -13, -21, 22, 4],\n [0, 0, 0, 0, 0, 0, 0, 29, -7, -5, -11, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 33, 30, -20, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 19, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "165", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[4, -12, -10, 2, -10, 22, -20, 9, 2, -2, 26, -11],\n [-12, 0, 6, 0, -3, -16, 11, 8, 12, -6, -2, -27],\n [-10, 6, -30, -12, 26, -1, 16, -7, 21, 14, -11, 8],\n [2, 0, -12, -18, -8, -8, 12, -4, -1, -10, 7, 4],\n [-10, -3, 26, -8, 5, 6, -14, -20, -6, 20, -12, 30],\n [22, -16, -1, -8, 6, 28, -6, 18, -3, 16, 3, -3],\n [-20, 11, 16, 12, -14, -6, -11, 10, -14, 18, 0, -34],\n [9, 8, -7, -4, -20, 18, 10, 30, -4, 1, -2, 22],\n [2, 12, 21, -1, -6, -3, -14, -4, -17, 2, 31, 28],\n [-2, -6, 14, -10, 20, 16, 18, 1, 2, 30, 0, -4],\n [26, -2, -11, 7, -12, 3, 0, -2, 31, 0, -31, -2],\n [-11, -27, 8, 4, 30, -3, -34, 22, 28, -4, -2, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (3, 2) rounded to the nearest integer?\n[[-23, 2, -4, -6, 11, 2, -6, -20, 26, 2, 10, -18],\n [2, 34, -19, -2, -7, -14, 16, 12, -11, 28, 8, -6],\n [-4, -19, -10, 2, 4, -1, 6, 16, 14, -2, 9, -8],\n [-6, -2, 2, 10, 8, 0, 5, -3, -22, -10, -3, 4],\n [11, -7, 4, 8, -3, 5, -8, -10, 22, 12, 2, -4],\n [2, -14, -1, 0, 5, 25, 22, 10, 10, 8, 1, -18],\n [-6, 16, 6, 5, -8, 22, -4, 13, -21, -10, 4, 6],\n [-20, 12, 16, -3, -10, 10, 13, 30, 16, -8, -5, 6],\n [26, -11, 14, -22, 22, 10, -21, 16, 13, -22, 0, 15],\n [2, 28, -2, -10, 12, 8, -10, -8, -22, -17, -2, 10],\n [10, 8, 9, -3, 2, 1, 4, -5, 0, -2, -4, 18],\n [-18, -6, -8, 4, -4, -18, 6, 6, 15, 10, 18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "654", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (5, 11) rounded to the nearest integer?\n[[7, 10, 3, 15, -10, 24, -4, 12, 9, 0, -22, -10],\n [10, 28, -4, 10, 13, -8, 6, 10, -7, -16, 14, 16],\n [3, -4, 1, 22, -8, -20, -5, -2, 5, 4, 4, 1],\n [15, 10, 22, -22, -18, -3, -2, -13, 6, 18, 5, -16],\n [-10, 13, -8, -18, 19, 28, 11, -9, 6, 2, -13, 22],\n [24, -8, -20, -3, 28, -25, -20, 27, -5, 18, -12, -4],\n [-4, 6, -5, -2, 11, -20, -35, 2, -26, -22, -14, -16],\n [12, 10, -2, -13, -9, 27, 2, -30, 6, 16, 6, -4],\n [9, -7, 5, 6, 6, -5, -26, 6, 17, 17, 10, 12],\n [0, -16, 4, 18, 2, 18, -22, 16, 17, -3, 8, -2],\n [-22, 14, 4, 5, -13, -12, -14, 6, 10, 8, -27, -4],\n [-10, 16, 1, -16, 22, -4, -16, -4, 12, -2, -4, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-104", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-22, 10, 14, -31, 7, -18, 12, 28, -10, 34, -22, 30],\n [0, -15, 19, -34, -33, -23, -15, -3, -16, -18, 2, -11],\n [0, 0, -7, 28, -4, 7, -23, -11, 13, -28, -8, -25],\n [0, 0, 0, 29, -31, -16, -31, 31, -6, -2, -35, -9],\n [0, 0, 0, 0, 10, 32, 21, -14, -7, 9, 9, 31],\n [0, 0, 0, 0, 0, 3, 26, 35, 9, 22, -35, -25],\n [0, 0, 0, 0, 0, 0, -30, 2, 22, -28, 34, 27],\n [0, 0, 0, 0, 0, 0, 0, 19, 7, -26, 13, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 28, 24, -28, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 19, -34, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "271", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-8, 0, 2, 24, 18, -24, 2, 24, 1, 4, 10, 7],\n [0, 5, -20, -4, -3, 2, -22, 20, -6, 3, -2, -11],\n [2, -20, -3, 10, 24, -14, 14, -3, -26, 0, 12, -31],\n [24, -4, 10, -33, 0, 8, 7, 14, -6, 18, 1, -16],\n [18, -3, 24, 0, 35, -24, 6, -15, -18, -23, -21, -21],\n [-24, 2, -14, 8, -24, 14, -12, 4, 14, -22, -10, -24],\n [2, -22, 14, 7, 6, -12, 3, 25, -21, -3, 14, -31],\n [24, 20, -3, 14, -15, 4, 25, -29, 14, -19, -6, -18],\n [1, -6, -26, -6, -18, 14, -21, 14, -19, 2, 0, -24],\n [4, 3, 0, 18, -23, -22, -3, -19, 2, 2, 4, 28],\n [10, -2, 12, 1, -21, -10, 14, -6, 0, 4, 13, 4],\n [7, -11, -31, -16, -21, -24, -31, -18, -24, 28, 4, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5378", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 0, 8, 12, -18, -1, 4, -20, 18, 6, 4, 14],\n [0, -35, 0, -6, 10, -16, 6, -4, 0, -16, 14, -12],\n [8, 0, 18, 22, -30, 12, 34, 8, -16, -33, 1, 14],\n [12, -6, 22, -4, -6, -31, -7, 1, 0, -22, 17, 8],\n [-18, 10, -30, -6, -17, 9, -18, -34, 6, 22, 4, 10],\n [-1, -16, 12, -31, 9, -1, -1, -4, -3, 20, 4, -14],\n [4, 6, 34, -7, -18, -1, -16, -18, -1, 4, 6, -8],\n [-20, -4, 8, 1, -34, -4, -18, 33, -27, -7, -17, 4],\n [18, 0, -16, 0, 6, -3, -1, -27, -13, -10, 20, 21],\n [6, -16, -33, -22, 22, 20, 4, -7, -10, -20, -24, 7],\n [4, 14, 1, 17, 4, 4, 6, -17, 20, -24, 5, -6],\n [14, -12, 14, 8, 10, -14, -8, 4, 21, 7, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5346", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 10) of the inverse of matrix 1/839 * A where A =\n[[-5, -13, 2, 6, -9, 0, 12, 4, -10, -13, 8, -16],\n [-13, 5, -3, -19, -25, 25, 16, 30, 12, 6, -4, 1],\n [2, -3, 35, 26, 4, 9, 12, -14, -17, -28, 5, 5],\n [6, -19, 26, -5, -22, -12, 9, 18, 7, 5, 4, 4],\n [-9, -25, 4, -22, 22, -5, 7, 15, 22, -13, 6, 2],\n [0, 25, 9, -12, -5, 11, 2, -5, 19, 8, -19, 0],\n [12, 16, 12, 9, 7, 2, 33, -10, -2, 28, -8, 6],\n [4, 30, -14, 18, 15, -5, -10, 7, 26, -10, 2, 12],\n [-10, 12, -17, 7, 22, 19, -2, 26, -11, 0, -24, 4],\n [-13, 6, -28, 5, -13, 8, 28, -10, 0, -8, 16, -12],\n [8, -4, 5, 4, 6, -19, -8, 2, -24, 16, 27, 2],\n [-16, 1, 5, 4, 2, 0, 6, 12, 4, -12, 2, -22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-53", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-31, -23, -12, -1, 32, -10, 2, -2, -2, -17, -33, 0],\n [0, -10, -33, 13, -27, 10, 30, -22, -33, -34, -3, -26],\n [0, 0, 2, -15, -1, 31, -14, -16, 32, -28, 15, -10],\n [0, 0, 0, 11, 7, -27, -1, -17, 12, -8, -33, -18],\n [0, 0, 0, 0, 22, 21, -12, -14, 15, 2, 25, 13],\n [0, 0, 0, 0, 0, -28, -16, -20, -23, 26, 30, 17],\n [0, 0, 0, 0, 0, 0, -26, -5, 6, 33, 23, 2],\n [0, 0, 0, 0, 0, 0, 0, -29, 14, -18, -28, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 16, -10, -11, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -33, -30, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "284", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[31, -29, 31, 10, 22, -8, -5, 16, -27, -28, -18, 13],\n [0, -34, -7, 19, 17, -10, 15, -30, -24, -2, 34, 28],\n [0, 0, -28, 1, 10, -5, -25, 0, 32, -19, -20, -6],\n [0, 0, 0, 1, -10, -15, -17, -25, -17, 33, -34, -11],\n [0, 0, 0, 0, -30, 7, 34, -19, 6, -17, 19, -7],\n [0, 0, 0, 0, 0, 7, 14, -32, 0, -31, -17, 6],\n [0, 0, 0, 0, 0, 0, -4, 0, 21, 8, -2, 15],\n [0, 0, 0, 0, 0, 0, 0, 29, 35, -6, 31, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, -26, -10, -19, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 29, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10297", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (11, 12) of the inverse. Round your answer to the nearest integer:\n[[-14, -33, -17, 7, 31, -31, -7, -31, 9, 18, -12, -15],\n [-4, -31, 26, -18, -1, -31, -27, -32, -3, -14, 23, -25],\n [33, -26, -33, -21, 1, 4, -19, -16, -32, -2, -2, 31],\n [-8, 0, -1, 5, 23, -19, -6, 18, 16, -13, -17, 1],\n [23, 0, 32, -10, -9, 26, 26, 16, 8, -3, 27, 33],\n [-2, -9, 0, -32, 17, 35, 1, 14, 34, -10, -11, -3],\n [31, 1, 2, -9, -23, -13, 31, 19, 1, -24, 18, -16],\n [-18, -29, -34, 18, -28, -3, 10, 6, 27, -3, 33, 34],\n [-32, 22, -7, -15, -10, 5, -2, 8, -35, -4, -4, 15],\n [-12, 8, 1, 30, -22, -19, -21, 25, 13, -28, -33, -9],\n [-27, -21, -4, -25, -33, -10, -29, 19, 3, -32, -6, 2],\n [15, 0, 24, 15, 13, -21, -8, -11, 0, -32, -15, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[33, -26, 14, -26, -20, 2, 31, -16, 33, 34, -11, 18],\n [0, 29, 18, 31, -15, -31, 22, -32, -17, 19, 25, -12],\n [0, 0, -12, 18, -15, -17, 17, 14, -13, 1, -8, 35],\n [0, 0, 0, -1, -35, 31, 34, -32, -35, -15, 16, 17],\n [0, 0, 0, 0, -13, -30, 11, 22, -31, -27, -33, 25],\n [0, 0, 0, 0, 0, 5, -25, 5, 11, 13, 29, -1],\n [0, 0, 0, 0, 0, 0, -32, 4, 7, 22, 26, -29],\n [0, 0, 0, 0, 0, 0, 0, -3, -29, 19, 11, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 28, 24, 6, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -15, -12, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5435253", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (6, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 28, -19, 15, 20, 12, 26, 20, -25, -16, 32, -2],\n [6, 5, 26, -19, -24, 32, 5, -22, -32, -22, -27, 7],\n [-16, -35, -19, -16, 23, -23, 11, 14, 4, -29, 19, 15],\n [-34, -22, -19, -35, -35, -10, 10, -23, -2, 26, 15, 5],\n [19, -8, 25, -29, -34, -34, -8, 18, 22, 11, 25, 4],\n [-18, -22, -11, -26, 12, 12, 25, 17, -27, -25, -9, 23],\n [22, -23, 29, -25, 21, 31, 30, -12, 13, 4, 34, -34],\n [18, -21, 12, 18, 10, 21, 19, 24, -6, -8, 16, 5],\n [-15, 6, -23, 9, 18, -17, -9, 4, -29, -11, 13, 0],\n [35, -12, 25, 33, 16, 0, 15, -3, 17, 2, 8, -31],\n [-5, -27, -4, 5, -31, 15, 18, -8, 7, -24, 33, -19],\n [-28, -18, -26, 3, 5, 8, 33, 7, 11, 12, -17, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-33, 20, 7, -35, 0, -30, 10, -13, -16, 17, 2, -1],\n [0, 14, 11, 0, -20, 13, 29, 27, 16, 24, -19, 31],\n [0, 0, -5, 23, 18, 17, -10, -23, 21, -17, -9, -23],\n [0, 0, 0, -17, -33, 31, -10, -30, -23, -9, -26, -20],\n [0, 0, 0, 0, -18, 22, -34, 10, -19, 28, 29, 18],\n [0, 0, 0, 0, 0, 22, 13, -20, -6, 32, 35, 1],\n [0, 0, 0, 0, 0, 0, -2, 21, 26, 3, 31, 26],\n [0, 0, 0, 0, 0, 0, 0, -15, 18, 35, 7, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, -21, 10, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1365", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-8, -17, -6, -15, -15, 12, 19, -6, 6, 1, 5, 10],\n [0, -35, 18, -1, -20, -31, -5, 1, -11, 26, -11, 31],\n [0, 0, 28, -34, 28, 33, -16, -25, -5, -1, 8, 19],\n [0, 0, 0, -16, -27, -27, 22, 35, -3, -35, -33, 3],\n [0, 0, 0, 0, -7, 33, 16, -30, -12, 4, -3, -27],\n [0, 0, 0, 0, 0, -17, 2, -30, 16, -2, -25, 7],\n [0, 0, 0, 0, 0, 0, 29, 12, 16, 3, 18, -11],\n [0, 0, 0, 0, 0, 0, 0, 14, -28, -5, -12, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, -13, 26, 34, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -28, -28, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17155", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[33, -12, -12, 20, -14, 0, -11, 8, 14, 28, 18, -16],\n [-12, -29, 4, 22, -34, 24, -8, -1, -18, 2, -8, 22],\n [-12, 4, 6, -2, 10, -14, -15, -20, 5, -6, -10, 13],\n [20, 22, -2, -13, -7, 4, 6, 8, -6, 3, -6, 18],\n [-14, -34, 10, -7, 35, 3, -19, -30, 4, 3, -15, -16],\n [0, 24, -14, 4, 3, 35, 23, -15, -4, -12, 12, 11],\n [-11, -8, -15, 6, -19, 23, 3, 24, 0, -14, -4, -18],\n [8, -1, -20, 8, -30, -15, 24, -2, -8, -16, -4, 20],\n [14, -18, 5, -6, 4, -4, 0, -8, -19, 26, 14, 10],\n [28, 2, -6, 3, 3, -12, -14, -16, 26, 2, -12, 5],\n [18, -8, -10, -6, -15, 12, -4, -4, 14, -12, 22, 13],\n [-16, 22, 13, 18, -16, 11, -18, 20, 10, 5, 13, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "939", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 13, -33, 6, 27, -7, -34, -22, -24, -12, -8, -18],\n [0, -6, -2, 22, -8, 17, -20, -10, 29, 21, -5, -9],\n [0, 0, -10, -30, -29, -23, 13, -26, 7, 13, -18, -25],\n [0, 0, 0, 18, -11, -30, -25, -3, 33, 10, 19, 34],\n [0, 0, 0, 0, 10, 8, -23, 35, 12, -19, -22, -6],\n [0, 0, 0, 0, 0, -13, 16, 18, 11, 13, 20, -28],\n [0, 0, 0, 0, 0, 0, -19, -33, -17, 1, -15, 15],\n [0, 0, 0, 0, 0, 0, 0, -10, 24, -14, -12, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 17, -23, -35, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -2, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-157", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-6, 33, -29, -12, 12, 7, 0, -35, -29, 8, 25, -10],\n [-6, -35, 27, -21, 27, 19, 21, -16, -14, 14, 0, 1],\n [10, -9, -17, -20, 18, -2, 15, 0, 17, 26, -5, -32],\n [-24, 17, 25, -17, 20, -27, -11, 18, 11, 5, 15, 14],\n [-29, -9, 12, 19, 27, -30, -1, -4, -30, 27, -18, -5],\n [16, -20, 20, 31, 26, 16, -31, 17, -19, -5, -20, 21],\n [-15, 5, 3, 1, 5, 17, -4, -11, 17, 28, -3, 2],\n [-28, -35, 23, -1, -20, -22, -31, -15, 22, 21, -25, 35],\n [-28, -22, 13, -3, -12, 35, 2, 14, 28, -34, 3, -22],\n [-24, 15, -26, 8, 4, 24, 34, -5, 1, 22, 7, 35],\n [2, -28, -2, -19, -19, 17, -21, 28, 21, -16, 25, -11],\n [-9, 11, -8, -30, 5, 23, 25, 13, -31, -25, 4, 34]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 34, -16, -32, -23, 13, -27, 23, -33, -25, -31, -1],\n [0, 34, -30, 6, 7, -22, -11, -18, -12, 27, -35, -21],\n [0, 0, 16, -34, 0, -13, -12, -4, 15, 10, -23, -22],\n [0, 0, 0, -24, -33, 17, 7, -31, 11, -9, 16, 20],\n [0, 0, 0, 0, 9, -26, -10, -28, -4, -15, 9, 19],\n [0, 0, 0, 0, 0, -5, -33, 33, 23, -3, 0, -33],\n [0, 0, 0, 0, 0, 0, -7, -26, -9, 27, 26, -18],\n [0, 0, 0, 0, 0, 0, 0, 21, -29, -16, 20, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 3, 23, 30, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 15, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "987939", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[20, 8, 28, -12, 5, -8, 26, -21, 26, -26, -7, -5],\n [27, -18, -29, -9, -27, -16, 14, 25, 31, -19, -15, -4],\n [12, 2, -8, 24, 34, 22, 34, 17, -26, -34, -11, 2],\n [-35, -23, 35, -35, -5, 31, 20, -17, -32, -8, 8, -6],\n [0, 17, 23, 32, -32, -25, 17, 18, 9, -19, 28, 22],\n [-23, 15, 16, -21, -32, -27, 31, 21, -7, 11, -31, 34],\n [28, 23, -1, -31, 14, 24, -21, -12, -15, -34, 9, -26],\n [9, 1, -13, 9, 5, 29, 25, -30, 29, -18, 4, 2],\n [9, -19, -23, -26, -5, 14, -13, 9, 2, -25, -28, -23],\n [-2, 29, -26, 0, -32, -15, 25, 2, 3, 18, 26, -17],\n [-34, -14, 21, -33, -13, -32, -8, 34, 34, 5, 1, -29],\n [-35, -2, 16, -26, 24, -30, 32, 12, 9, -24, 34, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "945", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 3) of the inverse of matrix 1/839 * A where A =\n[[-6, -22, 9, 10, 31, -20, -26, 32, 16, 14, 32, -34],\n [0, 14, -35, 1, -13, 13, 28, -19, 35, -21, 15, -9],\n [0, 0, 27, 17, 6, 34, -1, -19, 8, 7, 8, 2],\n [0, 0, 0, 24, -34, 29, -33, -22, 9, -2, 0, -21],\n [0, 0, 0, 0, -1, 10, 11, -18, -11, -1, 15, 19],\n [0, 0, 0, 0, 0, 21, -14, 9, -24, -31, -10, -16],\n [0, 0, 0, 0, 0, 0, 9, 29, -31, -5, -13, -15],\n [0, 0, 0, 0, 0, 0, 0, 14, -34, -10, 33, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, -1, 11, 15, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -13, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[3, -2, 2, 15, -19, -13, 14, 12, -4, 16, -9, -14],\n [-2, -33, -13, -14, 6, 2, -21, 23, -10, -17, 14, -16],\n [2, -13, -4, -1, 20, -20, 7, 11, 4, -8, 0, -10],\n [15, -14, -1, 35, 6, 28, 11, -13, 18, 6, 8, 8],\n [-19, 6, 20, 6, -20, 10, -24, -14, -17, 0, 14, -14],\n [-13, 2, -20, 28, 10, 14, 10, -7, 8, 14, 14, -20],\n [14, -21, 7, 11, -24, 10, 34, 10, 24, 21, 4, -6],\n [12, 23, 11, -13, -14, -7, 10, 2, 2, -1, 8, 22],\n [-4, -10, 4, 18, -17, 8, 24, 2, 27, -20, -8, -18],\n [16, -17, -8, 6, 0, 14, 21, -1, -20, 27, 24, -24],\n [-9, 14, 0, 8, 14, 14, 4, 8, -8, 24, -29, 25],\n [-14, -16, -10, 8, -14, -20, -6, 22, -18, -24, 25, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[23, 31, -33, -6, 28, 34, -34, -16, -7, -27, -32, 4],\n [19, -23, -30, -10, 5, 6, 25, 26, 32, -15, -5, 7],\n [-15, -7, 19, 22, -12, 9, -27, 30, -34, 1, 1, 33],\n [10, -30, 12, -28, -4, 31, 32, -8, 4, -20, 21, 19],\n [3, 19, -6, 6, -31, 9, 28, -4, -24, 30, 16, 35],\n [-4, -1, -30, -14, 11, -23, -13, 8, -27, 23, -6, 8],\n [13, -20, 17, -34, 31, 6, 28, -28, -15, 24, -2, -32],\n [26, -34, 14, -10, 1, 19, -18, -12, -6, -19, 6, -24],\n [-9, 19, -32, -1, 29, -7, 0, -2, 0, 19, -32, -25],\n [23, -33, -24, -15, -14, -18, -30, 29, 19, 4, 16, 8],\n [26, -7, -17, -8, -17, -5, 18, 26, -22, 14, 23, 34],\n [22, -27, 21, 5, -9, 22, 32, 22, -12, 26, 31, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-313", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[15, 31, 21, -16, 9, -30, -3, 7, 14, -9, -6, -18],\n [-6, -21, 26, -15, -24, 13, -35, 19, -11, 11, 3, -9],\n [14, 19, -8, 21, -20, 20, -1, -8, 10, 31, -20, 13],\n [32, -14, -18, -14, -20, 20, -33, 17, -1, -15, 29, 21],\n [11, -2, 12, 3, -6, 14, -20, -33, 25, -34, -10, -18],\n [30, 4, -33, -19, -12, -34, 34, 4, -10, 21, 13, 21],\n [20, 34, -15, -20, -30, -2, 23, 31, 5, -17, -7, -4],\n [-26, 28, -16, -8, -9, -11, -7, -21, 9, 9, -6, 2],\n [24, -4, 14, 35, -1, -31, -5, 17, -35, 33, 32, 29],\n [-21, 16, 2, -12, -13, 11, -29, -5, -29, -32, 18, 16],\n [12, 30, 18, 18, 9, 4, -1, -12, -1, 1, -2, -12],\n [-32, 14, -12, 0, -1, -7, 0, 32, -25, 19, 13, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120701", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[19, 20, -32, -11, -34, -17, -28, 28, -30, -22, 34, 35],\n [0, -6, -28, -22, 12, -8, -30, -6, -32, 31, -26, -9],\n [0, 0, -23, 19, 7, 32, 7, 4, -5, -33, -19, 3],\n [0, 0, 0, -14, -28, 32, 35, -18, -30, -32, 5, 15],\n [0, 0, 0, 0, 9, 3, 18, -18, -23, -22, 5, 4],\n [0, 0, 0, 0, 0, -12, 13, 6, 14, -15, -8, 19],\n [0, 0, 0, 0, 0, 0, -17, 25, -19, 13, -33, -2],\n [0, 0, 0, 0, 0, 0, 0, -21, 9, -27, -1, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 35, -17, -25, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -35, -32, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-297", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-8, -14, 30, 6, 24, -9, -2, -16, 5, 2, 4, -19],\n [-14, -11, -1, -16, 4, -8, -20, 4, -12, 14, 2, 10],\n [30, -1, -11, -6, -12, 4, -1, -6, 8, -10, 16, -6],\n [6, -16, -6, -18, 12, 0, -12, 18, -14, 14, 24, 18],\n [24, 4, -12, 12, 30, 6, 2, -27, 7, 6, -24, -11],\n [-9, -8, 4, 0, 6, 17, -8, -2, 14, 11, 22, -4],\n [-2, -20, -1, -12, 2, -8, -35, 14, 20, -3, 0, 4],\n [-16, 4, -6, 18, -27, -2, 14, -6, 8, 4, -7, -2],\n [5, -12, 8, -14, 7, 14, 20, 8, -35, -3, 6, -16],\n [2, 14, -10, 14, 6, 11, -3, 4, -3, 17, -8, -12],\n [4, 2, 16, 24, -24, 22, 0, -7, 6, -8, 13, 14],\n [-19, 10, -6, 18, -11, -4, 4, -2, -16, -12, 14, -28]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-119", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-1, 27, -5, 6, 30, 5, -35, -3, 1, 21, -25, 11],\n [0, -32, 19, -24, 30, 1, -13, 19, -17, 31, -13, -32],\n [0, 0, -1, -9, 7, 31, 33, 28, 16, -19, -3, 16],\n [0, 0, 0, 32, 14, 22, -6, 34, -34, -2, 16, -20],\n [0, 0, 0, 0, -23, 4, -4, 31, -22, 22, 10, 23],\n [0, 0, 0, 0, 0, -32, 18, -32, -19, 35, 19, 12],\n [0, 0, 0, 0, 0, 0, 17, -10, 24, -34, -33, 20],\n [0, 0, 0, 0, 0, 0, 0, 24, 8, -3, 30, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, -8, 17, 35, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 32, -24, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "328352", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[6, 1, -22, 26, 1, -2, -6, 12, -11, -22, 14, -4],\n [1, -18, 10, 8, 4, -8, -1, -4, -12, 26, 18, 7],\n [-22, 10, -9, 5, 10, -19, 6, -16, -2, -1, 30, -16],\n [26, 8, 5, -20, -15, 5, 12, 10, -26, 14, -2, 18],\n [1, 4, 10, -15, -3, -16, -2, -20, 2, 6, -32, -28],\n [-2, -8, -19, 5, -16, -18, 7, 32, 14, -14, -30, -14],\n [-6, -1, 6, 12, -2, 7, 25, 14, -16, 16, 2, -1],\n [12, -4, -16, 10, -20, 32, 14, -33, -16, 12, -14, -22],\n [-11, -12, -2, -26, 2, 14, -16, -16, -8, 25, 16, 18],\n [-22, 26, -1, 14, 6, -14, 16, 12, 25, 9, -26, -30],\n [14, 18, 30, -2, -32, -30, 2, -14, 16, -26, -8, -23],\n [-4, 7, -16, 18, -28, -14, -1, -22, 18, -30, -23, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[18, 34, 27, -2, 7, -31, -17, 18, -22, -26, 13, -25],\n [0, 30, -26, -15, -35, 10, -16, -15, 1, -22, 22, 21],\n [0, 0, 34, -12, 24, -13, 11, 2, 16, -23, -28, -4],\n [0, 0, 0, -24, 8, 32, 23, -26, 12, -8, -31, 8],\n [0, 0, 0, 0, -34, -13, -25, -34, -23, 9, -26, -15],\n [0, 0, 0, 0, 0, 30, 13, -16, -15, 0, 2, 20],\n [0, 0, 0, 0, 0, 0, 7, 16, 26, -19, 10, 5],\n [0, 0, 0, 0, 0, 0, 0, -30, 22, 27, -35, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 21, -14, 30, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 28, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "825", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-31, -19, -11, 25, 1, 30, -23, 4, 6, 34, -11, 6],\n [0, 7, 32, -8, -12, 5, 25, -31, -25, -28, -15, 28],\n [0, 0, -27, 2, 7, -26, -24, -18, -24, -5, -25, -9],\n [0, 0, 0, 11, -11, 28, 34, -8, -16, 5, -32, 33],\n [0, 0, 0, 0, -10, -19, 20, -28, 28, 33, -26, 14],\n [0, 0, 0, 0, 0, -31, -24, -28, 23, 29, 24, 19],\n [0, 0, 0, 0, 0, 0, 1, 8, 29, -30, 2, 7],\n [0, 0, 0, 0, 0, 0, 0, -33, 15, 25, 4, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, -9, 16, 1, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 31, -10, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "182396", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (9, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, 25, 22, -1, -5, 21, -26, -18, 20, 0, 15, 25],\n [-17, -25, -31, 9, 9, 12, -22, -8, -27, 23, 2, -11],\n [12, -17, -34, -30, -6, 25, -34, 15, -23, 13, -28, -27],\n [-13, -20, -20, -24, -25, -23, -1, 7, -6, 24, 31, -7],\n [-11, 30, -31, -31, 13, -10, 35, -6, -8, -22, -18, 21],\n [-11, 34, -31, 17, 3, 21, -25, 33, -11, -6, -34, 0],\n [1, -34, 11, 23, -32, 31, 10, 0, 29, 20, -1, -13],\n [8, -35, 30, -24, -23, -9, -16, -30, -28, -15, -15, 9],\n [34, 8, 23, -6, -26, -35, -26, -11, -22, -33, 32, 4],\n [-3, -29, -33, 1, -10, -11, 4, 7, 8, 35, -7, 21],\n [-27, -14, 34, -30, -9, 16, 34, 13, -13, -15, -28, 18],\n [-22, -5, 15, 26, -18, 11, 16, 1, -6, -6, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-9, -20, -4, -7, 16, -21, 8, -13, 12, -13, 35, -22],\n [0, 34, 7, 9, -14, 25, -18, 8, -18, 21, -21, 22],\n [0, 0, -15, 7, 9, -2, 35, -24, -29, 33, -8, -11],\n [0, 0, 0, 10, 11, -4, -24, -17, 11, 2, -26, -26],\n [0, 0, 0, 0, 2, -9, -4, 35, 12, -10, 22, -12],\n [0, 0, 0, 0, 0, 34, 29, -23, -30, -24, -27, 23],\n [0, 0, 0, 0, 0, 0, -35, -25, 31, -14, -29, 13],\n [0, 0, 0, 0, 0, 0, 0, 31, -26, 30, -4, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, -11, -23, 5, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -19, -9, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2629", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-1, 28, -24, 17, 8, 10, -25, 34, 10, 23, 23, -2],\n [0, 16, 12, -17, -32, -4, -8, 22, 5, -3, -22, 17],\n [0, 0, -11, 16, 4, 34, 26, -27, 33, -15, 17, 34],\n [0, 0, 0, -8, -33, 4, -32, 34, -24, 26, 35, 12],\n [0, 0, 0, 0, -23, 16, 27, 5, -13, 11, 29, -5],\n [0, 0, 0, 0, 0, -8, 29, 11, 35, -4, -12, -22],\n [0, 0, 0, 0, 0, 0, -18, 27, 32, 14, 32, -20],\n [0, 0, 0, 0, 0, 0, 0, 26, 7, 21, -5, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, -7, -20, 23, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 25, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1587", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-13, -28, 14, -20, 7, 10, 13, -21, 13, -15, -30, 19],\n [-21, -25, 3, 15, 1, 13, 21, 29, -19, 27, -22, 2],\n [-11, 1, 20, -29, -25, -1, 0, 34, 16, 33, 6, 35],\n [-21, -15, -35, 32, -25, -26, 9, 20, -17, 6, 5, -16],\n [-9, -24, 28, 2, 30, 22, -25, -6, 28, 12, 4, 32],\n [-15, -31, 0, -29, 24, 20, -5, -11, 20, -2, 8, -29],\n [15, -11, -8, 6, -9, 1, 19, 2, 20, -2, -7, 12],\n [10, 1, -33, 14, -15, 12, 22, -5, -29, 21, 0, -12],\n [-12, 20, 25, 34, -8, -4, 9, 33, 32, -18, -34, -33],\n [-7, 12, 29, 6, -30, 23, -17, 16, 25, -34, -13, -17],\n [34, 14, 25, -17, -14, -33, -31, 31, 24, 3, -8, -35],\n [-14, 9, 15, 15, -8, -6, -28, 5, -11, 23, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4930", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[35, 10, 2, -3, -14, -9, 27, -9, -15, 17, -1, 11],\n [14, -26, -8, 1, 5, 25, 15, -28, 22, 25, -3, -17],\n [-6, -22, 0, -29, -2, 14, -4, 6, -3, -22, -8, 3],\n [-5, -12, -32, -27, 34, -12, 29, -19, 1, 14, 9, -16],\n [23, 23, -25, 19, 29, 22, 8, -22, 16, -2, 27, -9],\n [-24, 2, 20, 29, 4, -15, -4, -24, -10, 0, -20, -2],\n [-12, 3, 28, -7, -5, 27, 7, -17, -26, 20, 24, 7],\n [12, 4, -2, -35, -17, -35, -11, 32, -8, 9, -12, 8],\n [-34, -13, 26, -21, -4, -32, -5, 23, 35, -35, 33, -22],\n [-13, 35, -20, -27, -5, 25, 9, -29, 21, 28, -34, -30],\n [25, -2, -19, -10, -16, 5, 22, 18, -7, 12, -14, 35],\n [-31, 16, -35, 9, 4, 28, -25, 16, -29, 15, -15, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-210", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 21, 5, 3, -16, -14, -7, 10, 32, -33, -31, 20],\n [31, -4, 5, -7, 30, -25, 23, -32, 18, 31, -34, 12],\n [32, 8, 26, -17, 8, -5, 26, -21, -7, 31, 11, -29],\n [32, -35, 35, -14, 21, 22, -9, 2, -23, -21, 12, -21],\n [4, -6, -13, -27, -4, -1, 13, 9, -20, -4, -11, 1],\n [1, -1, 9, -28, 11, 0, -26, -35, 32, -21, -33, -4],\n [-16, 20, 6, 24, 20, 11, -12, 5, -32, 15, -35, -22],\n [-26, 0, 6, 12, -18, 24, -8, 17, -27, -12, -16, 33],\n [-9, 4, 35, 18, -21, 15, 33, 4, 33, 7, 28, -29],\n [-34, -6, 16, -3, -27, -25, -26, 18, -16, -31, -12, -4],\n [-5, 8, -17, -12, -24, 14, -11, 15, -22, -7, -11, 23],\n [21, -24, 14, -24, 12, 14, -17, 17, -1, -9, 31, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-10, 14, -34, -29, -9, 13, 10, -10, 29, -34, 28, 28],\n [0, -27, -21, 1, -30, 7, 9, 35, -8, 16, -1, 30],\n [0, 0, 26, -35, 17, -6, 24, -26, -14, -7, 33, -28],\n [0, 0, 0, -17, -17, -6, 0, 6, 20, -27, -29, -18],\n [0, 0, 0, 0, -14, 34, -4, 31, -20, -34, 31, 5],\n [0, 0, 0, 0, 0, 3, 0, -26, -32, -34, -8, -10],\n [0, 0, 0, 0, 0, 0, 9, -23, -22, -26, -19, -19],\n [0, 0, 0, 0, 0, 0, 0, -20, -27, 32, 9, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, -10, 33, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 13, -5, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432094", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[12, -12, -19, -20, -16, 8, -5, 2, 9, 12, 11, -10],\n [-12, 16, 15, -10, -9, 1, -5, -4, -2, 32, 0, -26],\n [-19, 15, -32, 9, 6, 12, 21, 25, -16, -13, -18, 15],\n [-20, -10, 9, -11, 30, 2, 24, -4, -1, -4, 22, 24],\n [-16, -9, 6, 30, -6, -8, -3, 28, -2, 22, 26, -20],\n [8, 1, 12, 2, -8, -14, -23, 20, 28, 4, -2, 6],\n [-5, -5, 21, 24, -3, -23, -13, -14, -12, -5, -10, -4],\n [2, -4, 25, -4, 28, 20, -14, -8, -4, 10, 10, 18],\n [9, -2, -16, -1, -2, 28, -12, -4, 8, -8, 26, 12],\n [12, 32, -13, -4, 22, 4, -5, 10, -8, -9, -8, 35],\n [11, 0, -18, 22, 26, -2, -10, 10, 26, -8, -26, 0],\n [-10, -26, 15, 24, -20, 6, -4, 18, 12, 35, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[7, 14, -17, -18, -26, 14, 13, 5, -21, -13, -9, -30],\n [0, -27, 26, 31, 34, 6, 24, 12, 20, -31, 18, 2],\n [0, 0, 35, -12, -26, -15, -21, 28, -23, 35, 4, -28],\n [0, 0, 0, -14, -32, 16, -29, -35, 22, 26, 30, 19],\n [0, 0, 0, 0, -20, 10, -33, -33, 5, -7, 4, -17],\n [0, 0, 0, 0, 0, -34, 7, 21, -17, 28, 10, 5],\n [0, 0, 0, 0, 0, 0, 21, -34, 30, -15, 16, -21],\n [0, 0, 0, 0, 0, 0, 0, -18, 9, 3, -10, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, 18, 0, -21, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 14, -2, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6182", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-16, -32, 17, 35, 26, 2, 0, -2, -30, 30, -18, -9],\n [0, 15, -17, -2, -12, -11, 34, -6, 18, -11, -31, -34],\n [0, 0, 2, -19, -5, -35, -30, 34, 0, -28, -26, -12],\n [0, 0, 0, -16, -3, -22, 18, 19, 1, -30, -3, 14],\n [0, 0, 0, 0, -8, 8, -24, 21, -10, -11, -21, 17],\n [0, 0, 0, 0, 0, 28, -25, 16, 18, 33, -29, -24],\n [0, 0, 0, 0, 0, 0, -17, -33, 24, -2, -7, 21],\n [0, 0, 0, 0, 0, 0, 0, -14, 26, 24, -29, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, -32, 12, 25, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -24, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64763", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-12, 27, -14, -2, 1, 5, 7, -14, -21, -15, 16, -32],\n [0, -18, 35, -1, -29, 5, -26, 26, 29, -24, -8, 22],\n [0, 0, 29, 21, 14, 9, 26, 29, 19, 2, -32, -21],\n [0, 0, 0, -1, -32, -4, -24, 18, -6, -27, -17, -6],\n [0, 0, 0, 0, 31, 30, 7, -34, 12, 22, 4, 17],\n [0, 0, 0, 0, 0, -30, -22, -3, -17, 7, 18, 25],\n [0, 0, 0, 0, 0, 0, 9, -26, -27, 10, -19, 31],\n [0, 0, 0, 0, 0, 0, 0, -1, -35, 7, 33, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 9, 31, -10, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 31, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34146252", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -11, -32, -5, -17, -34, -32, 2, -3, -18, -4, -3],\n [-2, 15, 27, 11, 30, -23, 16, 16, 7, 25, -33, 32],\n [23, 18, 33, -34, 32, 8, 2, 24, -9, -21, 3, 2],\n [18, 27, 22, 26, -18, -7, 35, 21, -12, 2, -30, -16],\n [6, -14, -3, 10, 18, 6, 15, 32, 20, 6, -23, 18],\n [-24, -1, -27, -23, -14, 4, 0, 5, -29, 19, -23, -16],\n [22, -13, 17, 1, -16, -17, -18, 32, 25, 10, 12, -16],\n [33, -2, -29, 14, 17, -25, -28, -4, 27, 19, 23, 27],\n [-19, -10, 15, -3, -10, -14, 31, 27, -19, 5, 3, -3],\n [-4, -15, 17, 28, 30, 13, 35, -5, 5, 35, 0, 3],\n [5, 5, -31, -30, 26, -20, -17, 1, 28, 23, 33, -29],\n [6, -11, 20, 11, 14, -3, -10, -19, -15, -34, 8, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[35, -8, 14, 2, 30, -4, 10, -3, 0, -16, 1, 4],\n [-8, 9, -18, -16, -3, -12, 4, -20, 20, -20, -28, 2],\n [14, -18, -24, 4, 1, -20, -20, 10, 6, -16, -12, 4],\n [2, -16, 4, 29, -11, -21, -18, 3, 4, -12, 3, -17],\n [30, -3, 1, -11, 15, 18, 18, -8, -4, 2, -20, 9],\n [-4, -12, -20, -21, 18, 29, -14, -28, 0, 20, 14, 7],\n [10, 4, -20, -18, 18, -14, -4, -20, 18, -9, -16, -18],\n [-3, -20, 10, 3, -8, -28, -20, 35, -20, 16, -16, 6],\n [0, 20, 6, 4, -4, 0, 18, -20, 9, -24, -1, 20],\n [-16, -20, -16, -12, 2, 20, -9, 16, -24, 14, -25, -2],\n [1, -28, -12, 3, -20, 14, -16, -16, -1, -25, -1, -9],\n [4, 2, 4, -17, 9, 7, -18, 6, 20, -2, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-67", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-16, -15, 10, -18, -18, 12, -7, -7, -28, -3, -2, 2],\n [-15, 25, -34, 30, 5, -2, -16, -1, 21, -3, -12, -20],\n [10, -34, 0, 6, 12, 28, 12, 2, 4, -16, -8, 10],\n [-18, 30, 6, -2, -22, 12, 18, -30, -4, -20, 23, 20],\n [-18, 5, 12, -22, 8, -4, -12, -5, 26, 20, -14, 18],\n [12, -2, 28, 12, -4, 16, 6, -20, -6, -13, 18, 21],\n [-7, -16, 12, 18, -12, 6, -16, 16, -9, -32, 2, -2],\n [-7, -1, 2, -30, -5, -20, 16, 28, 19, 20, -2, 4],\n [-28, 21, 4, -4, 26, -6, -9, 19, 19, 18, 10, -30],\n [-3, -3, -16, -20, 20, -13, -32, 20, 18, -25, 2, 1],\n [-2, -12, -8, 23, -14, 18, 2, -2, 10, 2, 34, -4],\n [2, -20, 10, 20, 18, 21, -2, 4, -30, 1, -4, 25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "791", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[20, -22, -29, 18, 22, 25, -8, 19, 17, 8, -8, 10],\n [0, 31, -9, 3, -9, -1, 11, 16, 33, 30, 5, 14],\n [0, 0, 35, 0, 34, -12, 0, -31, -16, 17, 4, 14],\n [0, 0, 0, 1, 9, 2, -9, 29, -33, 23, -6, -20],\n [0, 0, 0, 0, 13, 27, 10, 12, -11, 7, 19, -2],\n [0, 0, 0, 0, 0, 33, -2, 23, 25, 16, 27, -10],\n [0, 0, 0, 0, 0, 0, 23, 32, 16, 32, 15, 32],\n [0, 0, 0, 0, 0, 0, 0, -17, 29, 33, 17, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 24, 23, -10, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -15, -31, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "947", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-25, -2, 12, -4, -11, -16, 10, 11, -14, -10, 13, -10],\n [-2, 25, 18, -16, -2, 5, 13, 10, -18, -17, 0, -13],\n [12, 18, -28, 13, -1, 23, 11, 0, 6, 2, -22, 12],\n [-4, -16, 13, -32, -14, 0, 6, 27, -7, 32, -10, 21],\n [-11, -2, -1, -14, 18, -12, -16, 30, -21, -20, 26, 6],\n [-16, 5, 23, 0, -12, -1, -14, 4, 1, 18, -7, 32],\n [10, 13, 11, 6, -16, -14, 21, 30, 10, 9, 0, -8],\n [11, 10, 0, 27, 30, 4, 30, -25, -14, -10, -18, -4],\n [-14, -18, 6, -7, -21, 1, 10, -14, 20, 0, -7, -2],\n [-10, -17, 2, 32, -20, 18, 9, -10, 0, 24, 4, 8],\n [13, 0, -22, -10, 26, -7, 0, -18, -7, 4, -5, 4],\n [-10, -13, 12, 21, 6, 32, -8, -4, -2, 8, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[18, 0, 17, 24, 8, -3, 8, 19, 8, 15, 15, -29],\n [-35, -23, 12, 11, 11, -26, -10, 14, 11, 8, -35, 27],\n [-19, -19, 3, 7, 5, -21, -35, 22, 18, -31, 26, 35],\n [10, 29, -8, 5, -13, -4, 22, 3, -3, 22, -4, 14],\n [15, -17, -33, -19, 7, -7, 8, 16, -8, -2, 18, -34],\n [-19, -18, -8, -8, 16, -20, -3, -31, 9, 1, 16, 28],\n [26, -31, -25, -33, 15, 24, 30, 21, -19, -33, -33, 4],\n [27, 15, -35, 15, -32, -32, 11, 3, 13, 21, 3, 32],\n [-19, -21, -8, -20, -30, -4, -11, 3, -19, 10, 17, 15],\n [-18, -16, -31, 26, -24, -6, -20, -34, -33, -28, 1, 17],\n [19, 13, 23, 24, 10, 27, -4, 30, -32, -7, 13, -13],\n [-33, 18, -15, 8, -16, 21, 33, 35, 16, -19, 30, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-121", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[35, 13, -28, -30, 4, 18, -19, 15, -34, -6, -4, 14],\n [0, -20, 19, 21, 9, 16, 35, 11, -3, -12, -1, 28],\n [0, 0, -18, 22, 12, -25, -33, 6, -18, -20, 5, 29],\n [0, 0, 0, -8, 15, -9, -27, 2, 0, 24, 21, 11],\n [0, 0, 0, 0, 23, 11, -21, -34, 25, 4, 7, 12],\n [0, 0, 0, 0, 0, 15, -7, -7, -23, 21, 10, -16],\n [0, 0, 0, 0, 0, 0, 24, -33, 27, -5, 25, 13],\n [0, 0, 0, 0, 0, 0, 0, 29, -19, -8, -27, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, -14, -27, -14, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 28, -10, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22634", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, -1, 29, 3, -18, -11, -35, 26, -27, 5, -14, 30],\n [9, 16, -16, -24, 28, -4, 26, -31, 8, -7, -3, -23],\n [14, -34, -8, -18, 30, 10, -19, -3, -3, -6, -14, 17],\n [10, 8, -2, -8, -1, 32, -27, -14, 25, -11, 5, -29],\n [23, 31, -3, 29, 24, 22, 8, 12, 1, -11, -11, 21],\n [-23, -24, 27, 26, -8, 19, 6, 25, 2, -31, 12, -1],\n [12, -22, 18, -10, 7, 6, -18, 19, 14, -15, -2, 4],\n [-6, 34, -11, 33, -7, 31, 21, 11, -19, 13, 14, -31],\n [-23, 27, 3, 32, 9, -19, 23, 23, -28, -6, -33, -19],\n [15, -12, 28, 35, 13, -16, -7, -26, -27, 35, 27, -3],\n [-12, -4, -32, 26, -14, -13, -10, 13, 8, -14, 31, 6],\n [16, -19, -22, 28, 9, 28, -6, -23, -10, -4, 10, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -8, -17, 12, -2, -20, 35, -9, 15, 18, -19, 32],\n [-35, -22, -29, 28, -28, 18, -12, 19, -35, 33, -4, -35],\n [30, 6, -27, -12, -17, 15, -34, -26, 33, -30, 26, 30],\n [-28, 32, 23, 14, 0, -28, -19, 23, -28, 7, 27, -24],\n [20, 13, 16, -25, -9, 26, -27, 0, 10, -7, 32, 5],\n [-8, 28, -12, -20, -14, 11, -19, -35, -5, -24, -16, -17],\n [-31, -21, -11, -1, 19, 27, 11, 31, 28, -14, 33, -34],\n [-11, 25, -31, -8, 30, -21, 19, 2, -13, -22, -4, 8],\n [34, 22, -32, 26, 24, 23, -7, -17, -19, -32, 8, -32],\n [23, -24, 11, -29, -24, 35, 18, 22, 27, -21, 1, 20],\n [-5, -21, -34, -23, -31, 12, -3, -4, 17, -15, 30, 25],\n [18, 5, 2, -3, -28, 0, -3, -7, 21, 25, 19, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -10, -34, 19, -18, 14, 9, -21, -29, -9, 4, -19],\n [0, -20, 27, 24, 16, 13, 13, -10, 15, 7, 34, 35],\n [0, 0, 28, -34, 0, -33, 18, -15, 31, -27, -24, 1],\n [0, 0, 0, 27, -10, 10, 17, 24, -4, 26, 11, 25],\n [0, 0, 0, 0, 5, 32, 1, -25, 0, -21, 31, -6],\n [0, 0, 0, 0, 0, -33, -27, -4, 9, 21, -15, -13],\n [0, 0, 0, 0, 0, 0, -14, 3, 19, -29, 26, 3],\n [0, 0, 0, 0, 0, 0, 0, -31, 20, -29, 17, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 11, 17, -15, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -32, -21, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184896", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, 0, 0, -15, 4, 12, -4, 0, -22, -12, -25, -20],\n [0, 23, -16, 12, 15, 16, 15, -22, -1, -12, 1, -14],\n [0, -16, -18, -12, 20, -17, 5, 35, -4, 12, 9, 24],\n [-15, 12, -12, 15, -2, -12, -19, -8, 24, 22, -29, -7],\n [4, 15, 20, -2, 1, 6, -1, -1, -6, 4, -5, 3],\n [12, 16, -17, -12, 6, 24, -22, 12, 15, -16, 7, 8],\n [-4, 15, 5, -19, -1, -22, -2, 4, -7, 8, 19, -10],\n [0, -22, 35, -8, -1, 12, 4, 6, 16, 8, -16, -11],\n [-22, -1, -4, 24, -6, 15, -7, 16, 8, -8, -12, 25],\n [-12, -12, 12, 22, 4, -16, 8, 8, -8, 11, -21, -2],\n [-25, 1, 9, -29, -5, 7, 19, -16, -12, -21, 18, -14],\n [-20, -14, 24, -7, 3, 8, -10, -11, 25, -2, -14, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5835", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -27, 12, 0, -27, -12, -34, -12, 6, 26, 2, 6],\n [-27, 15, 18, 12, -21, -2, -2, 18, 30, -6, -8, -16],\n [12, 18, -2, 10, -11, 16, 22, 14, 28, 20, 3, -16],\n [0, 12, 10, 14, 22, 8, -3, 10, -16, -6, 18, 12],\n [-27, -21, -11, 22, -7, -18, -11, -22, 16, 0, 3, 12],\n [-12, -2, 16, 8, -18, 31, 22, 12, 9, 3, 4, 14],\n [-34, -2, 22, -3, -11, 22, 5, -4, 25, 16, -12, 2],\n [-12, 18, 14, 10, -22, 12, -4, -13, 12, -6, -9, 11],\n [6, 30, 28, -16, 16, 9, 25, 12, 25, -4, 18, -2],\n [26, -6, 20, -6, 0, 3, 16, -6, -4, -20, -6, -10],\n [2, -8, 3, 18, 3, 4, -12, -9, 18, -6, -7, 2],\n [6, -16, -16, 12, 12, 14, 2, 11, -2, -10, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1442", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, -21, -25, -20, -14, 26, -12, 0, -18, -16, -28, -21],\n [0, -12, 11, -18, -4, 6, 1, -3, -35, -9, -19, 10],\n [0, 0, 20, -24, -10, -12, 24, 22, 27, -28, -10, 22],\n [0, 0, 0, 23, -15, -23, -33, -4, -15, -22, -28, -29],\n [0, 0, 0, 0, 30, -18, -20, -24, 24, 18, 4, 7],\n [0, 0, 0, 0, 0, 5, -20, 0, -19, 18, -29, 5],\n [0, 0, 0, 0, 0, 0, -9, 13, 30, 34, -5, -11],\n [0, 0, 0, 0, 0, 0, 0, -29, -18, 9, -12, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 13, -20, -12, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 8, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-806", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 35, 10, -20, 22, -22, 7, -11, -21, -6, 8, -27],\n [-25, 30, -14, -16, -7, 27, 5, 12, -9, -5, -11, 13],\n [34, 28, 20, -29, 34, -1, -15, 11, 24, -19, -19, 35],\n [-11, -2, -10, -30, -26, -33, 23, 33, 12, -13, -31, 20],\n [2, -29, -19, -27, 10, 1, -29, -19, 5, 28, 21, 9],\n [-28, -26, 18, 30, 8, 12, 35, -34, -30, 9, -26, -27],\n [-4, -34, -15, -33, -13, 1, 0, -22, -21, -1, -14, 11],\n [0, -21, 22, -5, 5, -10, -6, -24, -5, -34, -16, 22],\n [-16, -2, 24, -2, 1, 31, -17, 16, 8, -9, 2, -15],\n [2, -23, -15, 6, 12, 10, 21, 16, -14, -19, -10, 3],\n [35, 27, 15, -6, 5, -3, 14, 27, 3, -8, -18, 23],\n [30, 7, -23, -35, -4, -26, -21, -19, 27, 18, -13, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1365", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[14, 23, 0, -30, 30, -4, 17, 33, -34, 7, 4, 32],\n [-32, 10, -16, -22, -22, 13, -33, -15, 25, -34, -15, -26],\n [-17, 17, 13, -28, 21, -12, 11, -15, -28, -17, -6, -10],\n [-16, 9, 28, -6, 17, 14, 26, 6, -8, 22, -5, 23],\n [-24, 9, 30, 32, -4, 5, 19, 33, -31, 27, -32, 5],\n [-24, 1, 19, 9, -8, 23, -29, 24, 17, 4, 16, -25],\n [14, 14, 12, 18, -30, 14, -33, 5, -8, -4, 3, 35],\n [27, -17, -35, -3, -3, -25, 24, -8, 26, 11, -19, -27],\n [-28, 23, 33, 9, -3, 2, 27, -24, 31, -7, -14, -2],\n [34, 3, -20, -5, 13, 8, 10, -35, 8, 10, 17, -3],\n [9, 28, -33, -12, -5, 35, 4, 14, -21, -15, -15, 24],\n [29, -15, 19, 33, -10, 19, 10, 26, 34, 18, -32, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[18, 17, 8, 0, -2, 16, -30, 2, -3, 19, -13, 8],\n [0, 28, 12, 23, 23, 7, 7, -23, 7, -23, -1, -25],\n [0, 0, 14, 13, -23, 3, 19, -29, 7, 6, 22, -24],\n [0, 0, 0, -33, 26, -5, 1, -12, 32, 28, -20, -18],\n [0, 0, 0, 0, 17, -9, 0, 32, -23, 15, 12, 24],\n [0, 0, 0, 0, 0, -11, -2, 34, 20, 29, 24, 12],\n [0, 0, 0, 0, 0, 0, 28, 2, 2, 16, 11, 29],\n [0, 0, 0, 0, 0, 0, 0, -25, 0, 20, 6, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, -32, -5, -12, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 24, -12, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, -23, -34, -5, -8, 23, -25, -1, 13, 8, 22, 15],\n [-19, -32, -3, 26, 7, 6, 15, 2, 7, 12, 6, 21],\n [18, -19, 15, -27, -28, 27, 20, 34, -27, -31, 28, 16],\n [-1, 24, 3, -30, -15, 0, -18, -35, -19, 33, -30, 22],\n [9, 12, 14, 20, -27, 26, -5, 29, 25, -26, 17, 28],\n [28, 14, 29, -22, -13, -8, 22, 4, 28, -34, 7, -24],\n [-1, 33, 27, 5, 28, -18, 34, -25, 29, -13, -32, -29],\n [5, 13, -19, 19, -9, -24, 11, -2, -28, -13, -10, -2],\n [-4, -30, 29, 23, 14, 32, -28, 4, 10, -3, 22, -33],\n [-9, 29, 21, -1, 16, 15, -19, 16, 12, 22, -10, -9],\n [-12, -25, -28, 12, -4, -7, -31, 13, -23, 6, -26, -10],\n [-10, -13, 8, 3, 7, 16, 22, -4, -18, 6, -34, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-3, 10, 23, 21, 26, 27, -5, 3, -14, -19, -33, -4],\n [-3, 28, -26, -31, 32, 2, 5, 25, -21, 16, -28, 20],\n [-6, -2, 23, 20, -23, 15, 23, 26, -7, 26, -29, 8],\n [-30, 26, 32, 34, -19, 13, -12, -24, 21, -7, 26, -9],\n [-31, 4, 11, -27, -20, -23, 18, -21, -11, -20, 8, 11],\n [-3, -10, 4, 35, 9, 7, -13, 11, 8, 6, -24, 0],\n [-23, 29, -9, -16, -18, 28, -27, -11, -35, 23, 0, -18],\n [11, -3, -14, 29, -25, -10, 34, 27, 2, 13, -19, 21],\n [-22, -28, 20, -13, 8, 30, -33, 17, -23, 33, -35, -15],\n [20, -34, -5, -23, -22, 21, -23, -22, -9, 34, 24, 34],\n [-21, 20, 26, -23, -29, -15, -22, -33, 27, 7, -24, 19],\n [23, -16, 33, 9, 19, 23, 24, 25, 6, 8, -30, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "633", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-14, 29, -16, 11, 12, -12, 3, 19, 19, 34, 27, -17],\n [0, -10, 11, -22, -33, 33, -22, -28, -21, 9, 9, -33],\n [0, 0, -32, 14, -30, 8, -31, 21, 13, 33, -8, 3],\n [0, 0, 0, 33, 18, 1, -3, 13, -35, 11, 1, -27],\n [0, 0, 0, 0, -33, -18, 1, -16, 0, -32, -19, 21],\n [0, 0, 0, 0, 0, -15, -35, 0, -30, -18, -25, 33],\n [0, 0, 0, 0, 0, 0, 24, -2, 23, -30, -4, -8],\n [0, 0, 0, 0, 0, 0, 0, 26, -5, 11, 1, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 28, 35, -20, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 7, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14763", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-8, 4, 6, 7, 0, 14, -4, 4, -25, -5, 10, -7],\n [4, 15, 18, -3, 25, -16, -13, -4, -10, 5, -10, 7],\n [6, 18, -21, -28, -6, -18, 6, 6, -10, 2, 6, -7],\n [7, -3, -28, 18, -4, -19, 6, 4, 21, -8, -6, 0],\n [0, 25, -6, -4, -6, -14, -2, -4, -14, -18, -21, -6],\n [14, -16, -18, -19, -14, 20, 18, -18, -3, 24, -6, 5],\n [-4, -13, 6, 6, -2, 18, -26, -22, -23, 0, -16, -31],\n [4, -4, 6, 4, -4, -18, -22, 30, -5, 1, 30, 4],\n [-25, -10, -10, 21, -14, -3, -23, -5, 12, 0, 4, 3],\n [-5, 5, 2, -8, -18, 24, 0, 1, 0, 0, -14, 16],\n [10, -10, 6, -6, -21, -6, -16, 30, 4, -14, 0, 8],\n [-7, 7, -7, 0, -6, 5, -31, 4, 3, 16, 8, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "225", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (4, 10) of the inverse. Round your answer to the nearest integer:\n[[-27, -32, -13, -18, 16, -10, -14, -1, -21, 17, -26, 31],\n [-32, -29, -9, -24, 26, -12, 28, -20, 18, 18, -28, -14],\n [-13, -9, -34, -30, -26, 4, 16, -2, 5, 7, -16, 5],\n [-18, -24, -30, -34, 0, -14, 2, 12, 7, -18, 14, 0],\n [16, 26, -26, 0, 24, 29, -1, -4, 10, 28, 4, -10],\n [-10, -12, 4, -14, 29, -1, -6, 24, 6, -8, -1, -19],\n [-14, 28, 16, 2, -1, -6, 32, 5, -28, -1, 2, -20],\n [-1, -20, -2, 12, -4, 24, 5, 6, 2, 0, -3, 8],\n [-21, 18, 5, 7, 10, 6, -28, 2, 11, 6, 2, 6],\n [17, 18, 7, -18, 28, -8, -1, 0, 6, 9, 0, 6],\n [-26, -28, -16, 14, 4, -1, 2, -3, 2, 0, 32, -10],\n [31, -14, 5, 0, -10, -19, -20, 8, 6, 6, -10, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-52", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (5, 8) of the inverse. Round your answer to the nearest integer:\n[[18, -28, -26, -15, -1, -32, 17, -11, -16, 35, 35, -14],\n [0, -30, 15, -9, -18, -24, -8, -17, 7, -21, 33, 0],\n [0, 0, -6, 3, 10, 22, -6, 20, 18, 1, -14, -12],\n [0, 0, 0, 26, -24, -6, -23, -30, 31, -25, 24, -26],\n [0, 0, 0, 0, -21, 3, -31, -5, -8, 2, 16, -21],\n [0, 0, 0, 0, 0, -16, -27, -31, -25, -34, 16, -16],\n [0, 0, 0, 0, 0, 0, -10, -27, 4, -15, -24, 1],\n [0, 0, 0, 0, 0, 0, 0, 31, 1, -32, -21, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 24, 16, 34, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -16, -20, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, 20, 34, -6, 19, -8, 15, -9, 16, -2, -4, 8],\n [-32, 12, -20, 24, 11, -21, 20, -20, -35, -11, 28, 7],\n [-22, 12, 32, -22, -21, -19, 16, -26, -19, -28, -34, 20],\n [29, 19, 33, 0, -27, -22, -14, -20, 5, 31, -8, -7],\n [29, -8, -4, 16, -25, -10, -5, -16, 33, 5, 31, 8],\n [24, -29, 18, 27, -23, -3, -29, -6, -25, 34, -15, -4],\n [-31, -1, 11, -24, 1, 8, -14, -25, 19, -26, 6, 19],\n [14, -4, 32, -18, 29, -11, -5, -17, -18, 32, -3, 34],\n [-29, -35, 23, -2, 16, -25, -28, 17, -21, -8, -22, 22],\n [21, 16, 1, -34, -2, -2, 22, 25, 18, 31, -6, 23],\n [22, -12, -21, -14, -4, 6, 23, 19, -31, 5, 21, 17],\n [2, -35, 24, 10, -32, -21, -24, -35, -6, -30, 14, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-30, 16, -10, -14, -16, -20, 21, -4, -16, -12, 17, 4],\n [16, -27, 3, -17, -16, -2, 14, 6, 22, 28, 22, -4],\n [-10, 3, -14, -12, 26, 4, 0, 16, 30, -12, 0, -6],\n [-14, -17, -12, -27, -14, 15, 0, 11, -16, -18, -26, 10],\n [-16, -16, 26, -14, 16, -31, 2, 1, -23, -10, -26, -1],\n [-20, -2, 4, 15, -31, 3, 7, -2, 4, 18, -14, 10],\n [21, 14, 0, 0, 2, 7, -3, -8, -6, -23, -12, -19],\n [-4, 6, 16, 11, 1, -2, -8, 27, 6, 24, 10, 12],\n [-16, 22, 30, -16, -23, 4, -6, 6, -4, 2, -12, 4],\n [-12, 28, -12, -18, -10, 18, -23, 24, 2, -8, -4, -8],\n [17, 22, 0, -26, -26, -14, -12, 10, -12, -4, 16, 12],\n [4, -4, -6, 10, -1, 10, -19, 12, 4, -8, 12, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-35", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[11, 2, -18, -34, 18, -6, -32, -29, 21, -6, 8, -7],\n [0, 12, -17, 27, -34, -22, -1, -15, -19, -4, -13, -30],\n [0, 0, 34, -32, 22, -5, -14, -9, -20, -30, -29, -22],\n [0, 0, 0, -7, -32, 4, 5, -14, -32, -13, -32, 32],\n [0, 0, 0, 0, 2, -10, 5, 13, 5, 23, -32, -23],\n [0, 0, 0, 0, 0, 13, -22, 1, -6, -22, -9, 26],\n [0, 0, 0, 0, 0, 0, 11, -13, 23, -16, 9, 8],\n [0, 0, 0, 0, 0, 0, 0, 10, -12, 33, 0, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 22, 25, 19, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -17, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-92651", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[20, -17, 34, -8, -14, -8, -3, 9, 12, 27, -10, -35],\n [26, -33, -31, 9, -24, 12, -22, 17, 9, -4, -6, -24],\n [8, -11, 6, -15, 25, 30, -15, -10, -4, -19, -32, 3],\n [-21, -3, 25, -22, 11, -34, 30, 12, 28, 30, 12, -18],\n [15, -32, -3, -13, 17, -23, 35, 22, 27, 29, 6, 4],\n [-15, -3, 34, 6, 1, -35, -10, 3, 11, 20, 22, -8],\n [21, 35, 9, 29, -32, 25, 25, 7, -17, -35, -17, 15],\n [28, 27, -7, -17, 7, 34, 3, -13, -35, 25, -11, -32],\n [-35, 4, -15, 7, -26, 30, -19, -23, -26, 16, -26, 11],\n [-27, 10, 32, 18, 32, -32, -35, 23, -11, -27, -11, 35],\n [-10, 20, 13, 29, 25, -27, -26, -25, 0, 20, -4, -1],\n [-32, 26, 27, -28, 33, 25, 27, 25, 1, -32, 20, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-15, 22, -20, 17, -18, 21, 2, -4, -17, 12, -10, 9],\n [9, -21, -18, -5, -21, -21, 29, 10, -20, 19, -6, 5],\n [31, -19, -10, 28, 22, -33, -8, -32, 4, 21, 29, 11],\n [-2, 9, -4, 8, -25, 0, -23, 21, -11, 34, 1, -32],\n [-10, -23, 15, 11, -3, 6, -5, 4, -20, 20, 0, 20],\n [12, 22, -21, -21, -15, 28, -29, 16, -17, 10, 2, -23],\n [8, -14, 35, -1, -33, -20, 9, -20, 30, 2, -12, 14],\n [21, 20, 30, 26, -22, 30, 24, -15, -1, -6, 3, -11],\n [8, 23, -30, -33, 0, -35, -2, 29, -10, -18, 0, -30],\n [8, 4, -6, -5, 22, 19, 0, -6, 12, -19, -9, 27],\n [-22, -10, 7, -35, -12, -16, -28, -6, -18, -23, 12, 24],\n [-10, -27, 17, 35, -27, -10, -3, -3, 16, 4, -32, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2609", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 12) of the inverse of matrix 1/839 * A where A =\n[[18, 32, 13, -30, -3, -31, -18, -33, -34, 29, -1, 15],\n [0, -1, 8, -7, 0, 6, -29, -23, -14, 21, 9, 18],\n [0, 0, -2, 8, 33, 17, 26, -3, 33, -35, -1, -11],\n [0, 0, 0, -16, 4, 31, -21, -8, -1, -29, 18, 6],\n [0, 0, 0, 0, 30, -30, -34, 3, -30, -22, -18, 34],\n [0, 0, 0, 0, 0, -27, -27, 21, -1, -10, 5, 31],\n [0, 0, 0, 0, 0, 0, -15, 35, -30, 19, 4, 34],\n [0, 0, 0, 0, 0, 0, 0, -9, -1, -20, -16, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 13, -13, 1, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 13, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1521", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (9, 5) rounded to the nearest integer?\n[[-6, -25, -10, 2, -6, -24, -6, 2, 8, 13, -10, 4],\n [-25, 21, -18, -10, -30, 1, -20, -20, 18, -2, -6, -6],\n [-10, -18, -20, -5, 20, -12, 20, -10, 2, 2, 22, 2],\n [2, -10, -5, 26, 22, -5, -12, -25, -27, -13, 4, -2],\n [-6, -30, 20, 22, -12, -4, 2, 28, 17, -32, -6, 12],\n [-24, 1, -12, -5, -4, 9, -13, 5, -22, 28, 20, -7],\n [-6, -20, 20, -12, 2, -13, -13, -22, 18, 4, 8, 18],\n [2, -20, -10, -25, 28, 5, -22, 15, 0, 5, -30, 12],\n [8, 18, 2, -27, 17, -22, 18, 0, -20, 0, 8, 18],\n [13, -2, 2, -13, -32, 28, 4, 5, 0, -13, -26, -26],\n [-10, -6, 22, 4, -6, 20, 8, -30, 8, -26, -9, 24],\n [4, -6, 2, -2, 12, -7, 18, 12, 18, -26, 24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-37", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (7, 2) of the inverse. Round your answer to the nearest integer:\n[[-16, -31, 5, -23, -33, -21, 20, 7, 31, 10, 12, 0],\n [0, 19, 19, 18, 29, 15, -4, -16, 0, -4, 21, -7],\n [0, 0, 16, -21, 15, -5, -20, 0, 3, -25, -16, 20],\n [0, 0, 0, -1, -28, 35, 1, 14, -20, -27, 24, 15],\n [0, 0, 0, 0, -15, -31, -30, 7, -10, 18, -33, -25],\n [0, 0, 0, 0, 0, 29, 34, -2, -20, -22, 25, 17],\n [0, 0, 0, 0, 0, 0, 26, 3, -23, -23, -20, 18],\n [0, 0, 0, 0, 0, 0, 0, -21, 16, -1, 2, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 29, 6, -1, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (12, 4) rounded to the nearest integer?\n[[-22, 32, 30, 23, -21, -5, -7, 11, 21, 22, -5, 17],\n [0, -34, 24, 12, 12, 25, -32, -10, -14, 7, -16, 12],\n [0, 0, 25, 27, -17, -23, -34, 15, -35, 5, -26, -33],\n [0, 0, 0, 3, 11, 24, -28, 1, 27, -9, -33, 3],\n [0, 0, 0, 0, -16, 30, -24, -23, 3, 3, 9, 5],\n [0, 0, 0, 0, 0, -2, -17, -18, 10, 5, 13, 16],\n [0, 0, 0, 0, 0, 0, -24, 16, -3, -12, 12, -5],\n [0, 0, 0, 0, 0, 0, 0, 11, 20, -22, -15, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, -1, -24, -17, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -23, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-33, -2, 18, 4, -2, 2, -13, 16, 12, 13, -11, -6],\n [-2, -4, -26, -24, 14, -13, -3, -3, 14, -22, -8, 2],\n [18, -26, -34, 0, 16, 18, -26, -24, -12, 23, 2, -11],\n [4, -24, 0, 10, -17, -6, -23, -1, 21, -30, 18, 10],\n [-2, 14, 16, -17, 29, 21, 21, 18, 11, 22, -3, 2],\n [2, -13, 18, -6, 21, -28, -7, 2, -8, -20, -2, -8],\n [-13, -3, -26, -23, 21, -7, -17, 13, -1, 3, -1, -8],\n [16, -3, -24, -1, 18, 2, 13, -32, -22, 26, 3, 2],\n [12, 14, -12, 21, 11, -8, -1, -22, 20, -4, -14, 0],\n [13, -22, 23, -30, 22, -20, 3, 26, -4, 30, -9, 6],\n [-11, -8, 2, 18, -3, -2, -1, 3, -14, -9, -13, 2],\n [-6, 2, -11, 10, 2, -8, -8, 2, 0, 6, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1738", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, 6, -17, 4, 18, -4, 0, 0, 12, -20, -14, 10],\n [6, 17, -2, -17, 16, 5, -15, -18, 19, -8, -11, 10],\n [-17, -2, -13, 0, -4, 15, 22, 12, -22, 8, -14, -11],\n [4, -17, 0, -9, 26, 16, -24, 7, 10, -3, -29, -6],\n [18, 16, -4, 26, -17, -4, -12, 21, 6, -16, 18, -26],\n [-4, 5, 15, 16, -4, -32, 9, -8, 26, 21, 22, -13],\n [0, -15, 22, -24, -12, 9, -29, -8, 8, -1, -13, -20],\n [0, -18, 12, 7, 21, -8, -8, 35, 0, 16, -1, 26],\n [12, 19, -22, 10, 6, 26, 8, 0, 29, -22, 1, -7],\n [-20, -8, 8, -3, -16, 21, -1, 16, -22, -19, 2, 25],\n [-14, -11, -14, -29, 18, 22, -13, -1, 1, 2, 28, 4],\n [10, 10, -11, -6, -26, -13, -20, 26, -7, 25, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-20, 34, -23, 12, 4, 22, -28, -11, 16, -13, 3, -2],\n [34, -25, 20, 2, 0, 22, -8, -12, -12, -18, -8, -2],\n [-23, 20, 12, 10, -8, -5, 11, -26, -24, -14, -4, 3],\n [12, 2, 10, -21, -22, 20, -18, -30, 10, 11, 0, 16],\n [4, 0, -8, -22, -9, -25, -34, -4, -19, 12, 6, -16],\n [22, 22, -5, 20, -25, -19, -10, 29, -13, 0, -18, 4],\n [-28, -8, 11, -18, -34, -10, -7, -14, -22, -12, 16, 3],\n [-11, -12, -26, -30, -4, 29, -14, -7, 18, -15, 0, -2],\n [16, -12, -24, 10, -19, -13, -22, 18, 11, 13, 6, -3],\n [-13, -18, -14, 11, 12, 0, -12, -15, 13, -16, 4, 6],\n [3, -8, -4, 0, 6, -18, 16, 0, 6, 4, 22, 18],\n [-2, -2, 3, 16, -16, 4, 3, -2, -3, 6, 18, 20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-79", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[27, -22, -3, -14, 8, 6, 22, -9, -4, 19, 4, -6],\n [-22, -3, -4, -16, 12, -13, -3, 11, -8, 9, -24, -19],\n [-3, -4, 18, -2, -12, 3, 23, 17, -2, -10, 18, 20],\n [-14, -16, -2, -24, 2, -8, 18, -3, -4, -1, 0, -13],\n [8, 12, -12, 2, -7, -7, -15, 4, 6, -10, 13, 4],\n [6, -13, 3, -8, -7, 24, -24, -6, -9, -5, 28, 8],\n [22, -3, 23, 18, -15, -24, -21, -31, -3, 8, -28, -28],\n [-9, 11, 17, -3, 4, -6, -31, 28, 2, -30, 0, -10],\n [-4, -8, -2, -4, 6, -9, -3, 2, 26, -16, 6, 0],\n [19, 9, -10, -1, -10, -5, 8, -30, -16, 16, -12, -16],\n [4, -24, 18, 0, 13, 28, -28, 0, 6, -12, -23, 21],\n [-6, -19, 20, -13, 4, 8, -28, -10, 0, -16, 21, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "520", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-22, -13, 28, -19, -12, 18, -20, 32, -4, -2, 18, -32],\n [-13, -23, 18, -11, 28, 4, 11, -20, 4, 24, -25, -7],\n [28, 18, 22, 0, 0, 6, 22, 8, 9, -30, -26, 3],\n [-19, -11, 0, -18, 2, 8, -16, 28, 4, -4, -20, -8],\n [-12, 28, 0, 2, 35, -9, -12, 8, 26, -8, -6, 14],\n [18, 4, 6, 8, -9, -27, -29, -1, -14, -16, 0, 1],\n [-20, 11, 22, -16, -12, -29, -13, 10, 14, -12, 3, -29],\n [32, -20, 8, 28, 8, -1, 10, -21, 18, 6, 22, -9],\n [-4, 4, 9, 4, 26, -14, 14, 18, -11, 15, -2, 20],\n [-2, 24, -30, -4, -8, -16, -12, 6, 15, -13, 0, 26],\n [18, -25, -26, -20, -6, 0, 3, 22, -2, 0, 8, 4],\n [-32, -7, 3, -8, 14, 1, -29, -9, 20, 26, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2979", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[35, 34, 17, -22, -15, -22, 17, 31, 12, 20, 3, 5],\n [12, -8, -34, -14, 35, 25, 0, 30, 13, -33, -13, 23],\n [-8, -3, 32, 35, -25, -28, -16, 26, 7, 34, -29, -26],\n [4, -32, -17, 2, -14, -35, 17, -15, -29, -29, -13, 24],\n [-18, 35, 30, 17, -17, 28, -22, -11, -3, 12, 3, -31],\n [-15, 23, -22, 27, 18, 9, 14, 5, -35, -34, -23, -17],\n [15, -34, -26, 33, -6, 29, 8, 6, -33, -6, 1, -8],\n [15, -23, 4, -10, -6, -12, 2, 33, -20, 19, 13, 16],\n [13, 28, 12, 2, -19, 5, 18, 4, -5, -10, -18, -1],\n [20, -6, 9, 16, 32, 19, -26, 18, -2, 27, -5, 28],\n [14, -8, 1, -4, -1, 21, 25, -4, -28, -1, -13, 2],\n [-17, 18, 9, 0, 13, 24, 20, 28, 26, 23, -35, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-497", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-17, 22, 21, 6, -30, -14, 17, 21, 15, -31, -14, -29],\n [28, 21, -10, -11, 33, -4, -28, -27, 18, -16, 32, 31],\n [8, 5, 6, -25, 7, -28, 10, -2, 32, -21, -18, -25],\n [-17, -11, -14, 26, 1, -26, 16, 32, -8, -6, 10, 4],\n [-15, -21, -33, 33, -28, -27, -34, 1, -24, -17, -9, -12],\n [30, -20, -34, -15, -26, 22, -19, -29, 10, 14, -26, -20],\n [-35, -27, -23, 25, 12, -20, 5, -6, 19, -25, 16, 12],\n [-29, 18, -35, -4, 26, -21, 25, 20, -2, -16, -12, -8],\n [-25, -6, 2, -35, 33, -3, 29, 8, 28, -27, -4, 18],\n [-10, 26, 6, 12, -30, -6, -13, -11, -23, -11, -19, -9],\n [-25, -30, 1, 1, 23, -26, -35, 16, -18, -31, 12, -3],\n [21, -11, 8, 30, 32, -11, 9, -13, 5, -3, -8, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-159", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 20, -21, -21, 1, -17, 23, 15, -1, 0, 17, -24],\n [0, 35, -3, 19, 14, -7, 22, -10, -13, -19, -31, 23],\n [0, 0, -31, 22, -10, 7, 23, 22, -34, 8, -10, 8],\n [0, 0, 0, -30, -13, 7, 8, 30, 9, -17, -32, 21],\n [0, 0, 0, 0, -18, 4, 30, 29, -12, 17, 6, 17],\n [0, 0, 0, 0, 0, 25, -24, 13, -14, 32, 35, -13],\n [0, 0, 0, 0, 0, 0, -10, 5, -14, 25, 10, 22],\n [0, 0, 0, 0, 0, 0, 0, -28, -12, 32, 16, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 10, 27, -33, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -17, -32, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-517", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-31, 10, -32, -5, -32, -18, -2, 12, 27, -22, -3, 6],\n [0, 7, 21, -21, 14, 35, 27, 34, -27, -23, -18, -1],\n [0, 0, 31, 10, 1, -7, 8, 32, -22, 15, -27, 33],\n [0, 0, 0, 4, -28, -30, 17, -31, 18, -18, 35, 0],\n [0, 0, 0, 0, -33, 29, -23, -28, 8, -6, -28, 22],\n [0, 0, 0, 0, 0, 26, -17, -18, 8, -16, -34, -6],\n [0, 0, 0, 0, 0, 0, -17, -33, -32, 2, -2, 15],\n [0, 0, 0, 0, 0, 0, 0, 33, -11, 15, 17, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 22, 2, 21, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 24, -33, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11701", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-28, -10, -35, 25, 3, -27, -9, 34, -16, 29, -20, 32],\n [0, -14, 20, 21, 18, -28, -29, -35, 18, -24, -22, -17],\n [0, 0, -21, 27, -13, 7, -26, 0, 27, 13, -22, -2],\n [0, 0, 0, -1, -13, -11, 33, -30, 24, -30, -17, -17],\n [0, 0, 0, 0, -5, -13, 34, 22, 31, 35, -26, 32],\n [0, 0, 0, 0, 0, 19, 31, 3, -3, -7, -19, 1],\n [0, 0, 0, 0, 0, 0, -34, 34, 34, 29, 10, 27],\n [0, 0, 0, 0, 0, 0, 0, -22, -14, -19, -7, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, -4, -8, 15, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -30, -24, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118952", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-31, -16, 2, 3, 4, 5, -4, 0, -10, 8, 5, -9],\n [-16, 6, 6, -11, 8, 2, 1, -2, -8, 6, -10, 16],\n [2, 6, 6, 0, 26, 14, 18, -8, 16, -8, 0, 5],\n [3, -11, 0, -11, -32, 20, 6, 4, 17, -16, 2, -6],\n [4, 8, 26, -32, -13, 2, 4, -8, -23, -16, -12, 2],\n [5, 2, 14, 20, 2, 10, -29, 4, 0, -2, -5, 6],\n [-4, 1, 18, 6, 4, -29, 29, -16, 9, -5, -16, -14],\n [0, -2, -8, 4, -8, 4, -16, 0, 16, 5, 28, -26],\n [-10, -8, 16, 17, -23, 0, 9, 16, -14, -19, 0, -18],\n [8, 6, -8, -16, -16, -2, -5, 5, -19, 0, 10, -3],\n [5, -10, 0, 2, -12, -5, -16, 28, 0, 10, 9, 4],\n [-9, 16, 5, -6, 2, 6, -14, -26, -18, -3, 4, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (5, 6) of the inverse. Round your answer to the nearest integer:\n[[21, 1, 11, -13, -17, -8, 3, 0, -6, -30, -13, 26],\n [1, 28, -8, 27, 16, 12, 4, -10, 10, 0, -6, 4],\n [11, -8, 22, -16, -4, -23, -16, 6, 2, -18, 4, 2],\n [-13, 27, -16, 27, 23, -8, 4, 7, 20, -8, -6, 18],\n [-17, 16, -4, 23, 16, -21, 6, 14, 2, -24, -9, -5],\n [-8, 12, -23, -8, -21, 24, -6, -6, 24, -27, 4, -2],\n [3, 4, -16, 4, 6, -6, -34, -18, -4, 33, 18, -10],\n [0, -10, 6, 7, 14, -6, -18, -34, 4, -11, 10, -8],\n [-6, 10, 2, 20, 2, 24, -4, 4, -12, 29, 0, 0],\n [-30, 0, -18, -8, -24, -27, 33, -11, 29, -9, -12, -12],\n [-13, -6, 4, -6, -9, 4, 18, 10, 0, -12, -34, -32],\n [26, 4, 2, 18, -5, -2, -10, -8, 0, -12, -32, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (4, 3) rounded to the nearest integer?\n[[-13, -8, 7, 27, -19, 0, -17, -31, -13, -17, -35, -9],\n [0, -11, 18, -30, -11, 10, 23, 19, -12, -12, -33, 4],\n [0, 0, 34, 30, 33, -28, 19, 1, -22, 12, 31, -4],\n [0, 0, 0, -25, -32, -16, -31, 27, 18, 29, -23, -33],\n [0, 0, 0, 0, 16, -21, -35, 35, 9, -20, -19, -6],\n [0, 0, 0, 0, 0, 34, -10, 2, -27, 10, 8, 6],\n [0, 0, 0, 0, 0, 0, -10, 19, -21, 30, 17, -25],\n [0, 0, 0, 0, 0, 0, 0, -23, -4, 3, 27, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 7, 11, 23, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -33, -14, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[7, -17, -25, 16, -4, -7, 0, 11, 7, 16, 17, 32],\n [-31, 12, -12, -35, -34, -26, 27, 23, -30, 12, 0, 12],\n [-7, 5, -4, -31, -19, -12, -30, -8, -16, -17, -28, -18],\n [1, 25, 9, 2, -34, 19, -21, 23, -31, -16, -24, 21],\n [32, -17, -9, 17, 6, 9, 32, 32, -12, 0, -31, -9],\n [1, -9, 11, 28, -30, 20, -22, -14, 19, 16, 20, -30],\n [-16, 18, -34, -6, 18, -32, 35, 11, -17, 6, 6, 15],\n [-33, 1, -14, -3, 13, 18, 26, -1, -7, 30, 14, -22],\n [12, 8, -35, -8, -33, 35, 12, -4, -27, 21, 10, 22],\n [20, -21, 25, -20, 10, 35, -1, 30, 21, -2, -5, -24],\n [29, 11, 29, -35, 31, -22, 18, -26, 31, 14, 0, -25],\n [-33, 3, -26, 15, -4, 16, 11, -23, 31, 17, 17, -21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[17, 6, -7, 11, -6, -22, 23, 28, 8, -22, -11, 8],\n [0, -34, 7, -27, 25, 31, -12, 29, 2, 34, -31, 32],\n [0, 0, 26, -29, 15, -4, -10, 7, 26, -5, -13, 28],\n [0, 0, 0, -32, 3, 8, 5, -23, -24, -12, 12, -4],\n [0, 0, 0, 0, -5, 28, 16, -1, -20, 4, 2, 21],\n [0, 0, 0, 0, 0, -9, 27, 2, 8, -28, -13, -30],\n [0, 0, 0, 0, 0, 0, 11, 4, -17, 8, -10, 16],\n [0, 0, 0, 0, 0, 0, 0, -34, -6, -12, -13, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 35, -2, -33, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 29, -24, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-127", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (4, 7) of the inverse. Round your answer to the nearest integer:\n[[0, -18, -7, 10, 24, -7, -12, 0, -14, -17, 1, -1],\n [-18, 23, 22, 10, 22, -18, -4, -5, -4, -20, -23, -6],\n [-7, 22, -11, 10, -12, 2, -8, 2, 0, -2, 22, -8],\n [10, 10, 10, -22, 3, 22, 15, -2, 2, -14, -10, -22],\n [24, 22, -12, 3, -15, 18, -3, -22, 12, -8, -10, -12],\n [-7, -18, 2, 22, 18, 26, -10, -20, -1, -7, -18, 3],\n [-12, -4, -8, 15, -3, -10, 24, 4, -26, 3, 14, 27],\n [0, -5, 2, -2, -22, -20, 4, 34, -10, -2, -9, 18],\n [-14, -4, 0, 2, 12, -1, -26, -10, 0, -8, 20, 20],\n [-17, -20, -2, -14, -8, -7, 3, -2, -8, -19, 7, -34],\n [1, -23, 22, -10, -10, -18, 14, -9, 20, 7, 25, -7],\n [-1, -6, -8, -22, -12, 3, 27, 18, 20, -34, -7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[25, 19, 35, -7, 12, 27, -15, 21, -23, -9, 32, 28],\n [0, -29, -25, -8, -9, -14, 6, -4, -22, -10, 19, 35],\n [0, 0, -6, 30, -10, -35, -12, 19, 29, -11, 6, 8],\n [0, 0, 0, 27, -16, 4, -31, -35, -25, -32, 2, -19],\n [0, 0, 0, 0, 31, -25, -11, 6, -1, 23, 12, -33],\n [0, 0, 0, 0, 0, 17, 9, 35, 21, 34, 4, -33],\n [0, 0, 0, 0, 0, 0, 5, 27, 12, 19, -34, -13],\n [0, 0, 0, 0, 0, 0, 0, -11, 16, 15, 11, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 28, 11, -16, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -11, -13, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[0, 33, -2, 1, 15, 1, -11, -31, -28, 17, -9, 25],\n [29, 35, 9, -33, 25, 14, 12, 11, -22, -17, 26, -30],\n [-29, -23, 10, -3, 5, 33, -7, -29, 18, -25, 6, -31],\n [11, -34, 7, -32, 27, 23, -6, -34, 7, -18, -12, 1],\n [-6, 33, 23, -13, -6, 32, 5, 15, 31, -21, 20, 29],\n [19, 29, -34, -25, 6, -33, 5, 13, 1, -29, 2, 22],\n [-31, 25, 3, -8, 21, -34, 34, -8, 1, 19, -35, -33],\n [35, -22, 12, 1, -33, 13, 20, 24, -23, 17, 14, -17],\n [-10, 17, 21, 2, -27, 10, -32, 35, 14, 34, -31, 34],\n [-2, 29, -18, -9, -26, -34, 25, -14, -26, 23, -24, 27],\n [-21, 27, 29, 2, -30, -30, 2, 12, -21, -7, -34, -20],\n [22, -2, 7, -12, -11, 5, -3, 7, -19, -29, 23, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "689", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[0, -2, -24, 14, 20, 12, 3, 4, -28, -12, 1, -16],\n [-2, 24, 6, -18, -22, -19, 14, 2, 2, 12, 4, 6],\n [-24, 6, 16, 16, 6, 17, 2, -10, 19, 6, -4, -3],\n [14, -18, 16, 21, 3, -6, 8, 22, 24, 1, -20, -6],\n [20, -22, 6, 3, -10, -24, 13, 7, -29, -1, -6, -14],\n [12, -19, 17, -6, -24, 35, -22, 13, 1, 12, 2, 22],\n [3, 14, 2, 8, 13, -22, -23, 17, 9, 0, 4, -18],\n [4, 2, -10, 22, 7, 13, 17, 33, -9, 8, 10, -24],\n [-28, 2, 19, 24, -29, 1, 9, -9, 26, 16, 11, -20],\n [-12, 12, 6, 1, -1, 12, 0, 8, 16, 0, -6, -20],\n [1, 4, -4, -20, -6, 2, 4, 10, 11, -6, -33, 8],\n [-16, 6, -3, -6, -14, 22, -18, -24, -20, -20, 8, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "918", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[23, 34, -13, -19, -11, 2, -33, 31, -22, -26, 30, 35],\n [-22, -26, 13, 26, 12, -33, 11, 24, -11, -29, 3, 7],\n [10, 7, -7, 30, 33, -9, -33, 20, 28, -15, -12, -16],\n [16, -23, 34, 7, 1, -6, -21, -11, 2, 7, -6, 4],\n [23, -13, 8, -35, 5, 26, 24, -26, 30, 21, 6, 18],\n [6, 30, 34, -25, 31, -25, -32, 13, -14, 1, -26, -16],\n [14, -5, 8, -5, 5, -32, -22, 10, 18, -3, -6, -27],\n [2, 7, -29, 4, 26, 19, -1, 7, -25, -34, -31, 4],\n [10, -15, -27, 35, -9, -19, 30, -10, 9, 19, 4, -20],\n [-4, -1, 28, 28, -21, 6, 14, -4, -6, -12, 30, -15],\n [6, 22, -34, -20, -29, 19, -21, -13, 33, -35, 33, -23],\n [-10, 16, -23, 19, -7, -18, -34, -9, 14, 6, 31, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1585", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-27, -33, 2, 34, 33, -6, -22, -34, -28, -18, 35, -23],\n [10, 18, -24, 4, 2, -24, 31, -11, -1, -20, 9, -23],\n [-12, -34, -26, -17, -12, 25, -31, -2, 28, -24, 23, -15],\n [11, 17, 3, -5, 10, 21, 1, -9, -7, -18, -32, -35],\n [-12, 6, 24, -12, 20, 33, -18, 29, -26, -19, 22, -1],\n [-32, 8, 31, -8, -25, -33, -33, -11, -24, 13, 20, 17],\n [-26, -17, 11, 18, -29, 3, -4, -13, 14, -17, 31, -11],\n [-11, -30, -21, 27, -16, 7, 31, -32, -30, 23, 16, -17],\n [-10, 12, 19, 23, 2, -31, 6, -1, 33, -33, 5, -4],\n [0, -6, 3, 24, 20, 22, -10, -31, 20, -3, -27, -4],\n [-8, -13, 33, 26, 12, 30, 26, 33, 20, 0, 0, 20],\n [-29, -4, -35, 22, -16, -2, 15, 0, -10, -3, -35, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24800", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (4, 7) rounded to the nearest integer?\n[[14, -1, -1, 23, -23, -14, 20, -31, 7, 19, -21, 6],\n [-27, 35, 21, -26, 28, 5, -23, -20, 24, -5, 19, 35],\n [-2, -32, 19, 30, 23, 5, 30, 11, -9, -15, -25, -14],\n [-13, 29, 23, 34, -8, -11, -35, -4, -7, -16, 10, 21],\n [-24, 3, -28, -8, -5, -21, 24, 3, -15, -28, 6, 23],\n [-16, 25, -25, -4, -32, -7, -31, 3, -13, -20, 14, -25],\n [12, -2, -15, 27, -19, -2, 15, 31, -12, -14, -26, -31],\n [-5, -12, -25, 15, 12, -32, -28, -29, -4, -14, 0, -7],\n [32, 25, 17, -21, 12, 18, 32, 33, 28, 30, 14, 11],\n [32, -23, -22, -27, -8, 2, -24, -23, -15, 19, 2, 16],\n [-10, -14, 15, 1, 9, 1, -22, -18, -29, 24, 22, 19],\n [-2, 9, -33, 4, 17, -5, -13, 29, 19, -24, -35, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-284", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[15, 8, 14, -10, -7, -12, 24, 18, -6, -4, -30, 30],\n [8, -21, 6, -10, -5, 8, 12, -26, 4, 6, 6, 16],\n [14, 6, 27, 0, -10, -4, -4, 14, -14, 14, 8, 4],\n [-10, -10, 0, 28, -8, -6, 4, -18, -9, -10, 22, 0],\n [-7, -5, -10, -8, 21, -1, 21, 4, 0, -14, -12, -28],\n [-12, 8, -4, -6, -1, -2, -23, -12, 12, 0, 14, -16],\n [24, 12, -4, 4, 21, -23, 10, 2, -12, -4, 4, 12],\n [18, -26, 14, -18, 4, -12, 2, 25, -20, 3, -4, 22],\n [-6, 4, -14, -9, 0, 12, -12, -20, -4, 7, -14, 2],\n [-4, 6, 14, -10, -14, 0, -4, 3, 7, 2, 2, -5],\n [-30, 6, 8, 22, -12, 14, 4, -4, -14, 2, -1, -13],\n [30, 16, 4, 0, -28, -16, 12, 22, 2, -5, -13, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-710", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-33, -8, 9, -8, -26, 4, 12, -2, -14, 24, 6, -14],\n [-8, 29, 6, 14, 26, -10, -2, 21, 12, -7, -8, 10],\n [9, 6, 2, -6, 14, -2, -17, 1, 12, 10, 6, -2],\n [-8, 14, -6, 26, 20, 7, -3, 3, 2, -26, 7, -10],\n [-26, 26, 14, 20, -8, 9, 31, -2, -2, 16, 11, -20],\n [4, -10, -2, 7, 9, -5, -2, -4, -2, 0, 16, 18],\n [12, -2, -17, -3, 31, -2, 10, 25, -20, 4, -12, -22],\n [-2, 21, 1, 3, -2, -4, 25, -35, 8, -20, -6, -18],\n [-14, 12, 12, 2, -2, -2, -20, 8, -28, -24, 17, 19],\n [24, -7, 10, -26, 16, 0, 4, -20, -24, 29, 4, 12],\n [6, -8, 6, 7, 11, 16, -12, -6, 17, 4, -33, 6],\n [-14, 10, -2, -10, -20, 18, -22, -18, 19, 12, 6, 22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-942", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -24, -27, -16, -21, -28, -15, 9, 4, -30, -25, 28],\n [0, 23, -28, 19, 3, 15, 19, -33, 7, 9, -20, -31],\n [0, 0, 9, -33, -5, -12, -7, 19, -3, 15, -6, 25],\n [0, 0, 0, -30, -21, 30, -19, -17, -22, 13, 15, -2],\n [0, 0, 0, 0, -15, -9, 35, -7, -27, 8, -8, 2],\n [0, 0, 0, 0, 0, -34, -14, -10, 4, -28, 0, -10],\n [0, 0, 0, 0, 0, 0, 29, -15, -16, 13, -3, -18],\n [0, 0, 0, 0, 0, 0, 0, -2, 0, 14, -6, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 29, -15, 35, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 9, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (1, 11) of the inverse. Round your answer to the nearest integer:\n[[5, 17, 28, 4, 26, 19, -25, 16, -10, 12, 9, -3],\n [28, -27, -34, -22, 0, -1, 28, -11, -27, 7, -26, 21],\n [-3, -27, 18, -23, -12, 26, 4, 23, 20, 28, 24, -13],\n [-9, 25, 8, 21, 7, 26, -10, 28, 33, -12, -25, 31],\n [17, 7, -9, -35, 13, 12, 17, -25, -27, 25, -14, 35],\n [8, -6, 24, 19, 3, 5, -27, -35, -33, 33, -25, -32],\n [-3, -3, 9, -16, 1, -15, 22, 15, 35, -20, 0, 14],\n [12, -7, 6, 23, 19, 31, -14, -34, -28, 5, -25, -12],\n [-10, -1, -31, -21, -22, 1, -18, 31, 10, 32, 21, 4],\n [9, -20, 26, -13, 15, -35, 9, -32, 19, -26, -6, -22],\n [-6, -31, -21, -19, 12, -11, -17, 23, 17, 3, -31, 4],\n [22, -30, -17, 32, -12, -17, 23, 25, -4, 9, -1, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-34, -10, -16, -22, -16, 0, 22, -10, 23, -18, 8, -2],\n [-10, 30, 24, 30, 15, 17, 12, 17, -14, 5, 12, 12],\n [-16, 24, -6, 8, -10, 12, 12, -15, -8, 7, 18, -1],\n [-22, 30, 8, 6, 0, -20, -16, 22, 7, 22, -9, 2],\n [-16, 15, -10, 0, 16, -10, 5, -10, 4, 11, 20, -2],\n [0, 17, 12, -20, -10, -3, 4, 18, 9, 5, 6, 30],\n [22, 12, 12, -16, 5, 4, 29, 5, 6, 14, -6, -18],\n [-10, 17, -15, 22, -10, 18, 5, -6, 32, 8, -29, 30],\n [23, -14, -8, 7, 4, 9, 6, 32, 35, -8, 10, -2],\n [-18, 5, 7, 22, 11, 5, 14, 8, -8, -22, 13, 1],\n [8, 12, 18, -9, 20, 6, -6, -29, 10, 13, 7, -8],\n [-2, 12, -1, 2, -2, 30, -18, 30, -2, 1, -8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-64", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 7) of the inverse of matrix 1/839 * A where A =\n[[0, 22, 19, 10, -9, -12, -18, 4, 0, 27, 2, -12],\n [22, -3, -15, -5, 8, -8, 10, 10, 21, 2, 17, -15],\n [19, -15, 28, -4, -7, 27, 6, 22, 4, -18, -15, -6],\n [10, -5, -4, 24, -6, 18, 18, -2, 0, 14, -14, -4],\n [-9, 8, -7, -6, 16, 20, 18, 5, -22, -8, 1, -3],\n [-12, -8, 27, 18, 20, -12, 32, -4, -4, -2, -14, -12],\n [-18, 10, 6, 18, 18, 32, 35, 26, 2, 4, 18, 20],\n [4, 10, 22, -2, 5, -4, 26, -25, 2, 11, 13, 8],\n [0, 21, 4, 0, -22, -4, 2, 2, 12, 20, -4, 2],\n [27, 2, -18, 14, -8, -2, 4, 11, 20, 21, -18, -4],\n [2, 17, -15, -14, 1, -14, 18, 13, -4, -18, -18, -4],\n [-12, -15, -6, -4, -3, -12, 20, 8, 2, -4, -4, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (2, 6) rounded to the nearest integer?\n[[16, 28, 2, 8, 26, 32, 2, 14, 25, -8, 34, -5],\n [21, -26, -24, -29, -8, -16, 29, -9, -20, 0, 34, -26],\n [8, -17, 29, 26, -3, 1, -23, 1, -17, 30, -6, -4],\n [-3, 4, -21, 34, 2, -28, 3, 24, 24, 20, -18, 12],\n [-15, 20, -24, -30, -5, 35, 25, 32, 21, 25, -19, -7],\n [31, 23, -33, -9, -35, -32, -32, -3, -25, 21, -10, -10],\n [18, -9, 18, -34, -27, 28, 29, -15, -10, -21, 7, 3],\n [-20, -1, -13, -24, 20, 16, -17, 26, -28, -25, 7, 33],\n [1, -11, -12, -2, -24, 6, -24, -7, -16, -33, 25, 35],\n [-14, -19, -34, -29, -22, -32, 9, 27, -26, 9, 8, 19],\n [-18, -25, 18, -35, 17, -3, -29, -11, 33, 13, -32, -12],\n [10, 34, -24, 26, 26, 26, 22, 2, 32, -19, -26, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-3, 1, -8, 10, -34, 10, 2, 2, -15, -13, -3, 7],\n [32, 34, 28, 28, 1, -13, -2, -2, -9, -32, 33, 27],\n [-22, 30, -8, -15, -26, -10, -1, -2, -34, 7, 8, 8],\n [7, 16, -31, -17, -6, 13, 27, -7, 17, -8, 17, -19],\n [-12, 29, 0, -4, 33, -10, 20, 31, -3, 3, 22, -24],\n [7, -23, -31, 9, -31, -13, -1, 18, 13, 34, 1, -14],\n [-28, 21, 35, 24, 19, -2, 5, -8, -5, -15, 15, 0],\n [-10, -17, -30, 12, -21, 13, -18, 29, -14, 24, 0, -26],\n [-16, 34, 25, 23, -14, 32, -32, -7, 22, 22, 18, -8],\n [3, 21, 28, -6, 14, 18, -13, -18, 18, -8, -28, -4],\n [-30, 4, 15, 11, 34, 32, -29, -9, 30, 18, -22, -14],\n [33, 20, 24, 15, -20, -30, -35, -24, -12, 7, -2, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-378", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-15, 4, -3, -3, -8, 29, 10, -3, 33, 30, 0, 18],\n [0, 15, 16, -15, -6, -21, -27, -4, -13, -9, 6, -28],\n [0, 0, 8, 3, -3, 31, 19, -23, 0, -10, 2, -13],\n [0, 0, 0, 4, -11, -11, -19, -32, 5, 24, 7, 18],\n [0, 0, 0, 0, 8, -31, 25, 8, -30, -33, 29, -5],\n [0, 0, 0, 0, 0, 3, 12, -9, -20, 16, -32, 6],\n [0, 0, 0, 0, 0, 0, 13, 8, 2, 29, -26, 27],\n [0, 0, 0, 0, 0, 0, 0, -33, -33, 34, 11, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, -28, 9, -35, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -26, 34, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "818", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[9, 23, 7, 17, -9, 33, 33, 12, -11, -28, -4, 25],\n [-35, -5, 35, -21, 34, -20, 21, -25, -18, 9, -16, -22],\n [-9, -27, -23, 9, -28, 20, -29, -21, 20, 20, 1, 28],\n [-19, -15, 16, -3, -24, 10, 34, 35, 21, -16, 32, 8],\n [-6, -11, -5, -34, 18, -22, -13, 33, 16, 14, 35, -3],\n [-27, -28, -29, -15, 17, -21, 16, 33, 1, -32, 25, -14],\n [13, 0, 27, 2, 4, 28, 32, 20, -22, -34, 27, -17],\n [35, -27, -3, 25, 8, 29, 21, -12, 8, 32, -30, 31],\n [-2, -11, -9, -18, -31, 8, -31, 25, -30, 3, -28, 7],\n [5, 33, -6, 23, -13, 21, -11, 12, 34, 6, -7, 35],\n [9, 5, 27, 11, -35, -16, -17, 29, 0, -13, -7, 8],\n [-29, -5, 2, 30, -14, 18, 18, -30, 26, -7, 7, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[26, -23, 28, 11, 24, -21, -31, 33, -34, 2, 18, 3],\n [-16, -16, -7, -1, -4, -19, 15, -28, -15, -13, 15, -30],\n [16, -28, 33, -3, 26, 29, 27, -4, 19, -3, 2, -34],\n [-26, 30, -21, 25, -5, 2, -7, 7, -13, -11, -8, -35],\n [-16, -7, -28, 26, -22, 2, -33, -33, 19, -15, -1, 8],\n [8, 7, 5, -9, -8, -31, 7, 27, 3, -26, 27, -27],\n [-7, -8, -25, -21, -12, -1, 25, -16, 22, 27, 24, 3],\n [-16, 22, 28, -22, 0, -23, -35, -23, -1, -28, -18, -2],\n [16, 34, 22, -9, -18, 21, -27, 28, -13, 23, 31, -14],\n [14, -13, 16, -29, -19, -33, -29, 5, -13, 1, 32, 34],\n [28, -18, -1, -13, -29, 25, 13, 21, 32, -24, -21, -34],\n [11, 20, -22, -9, -32, 2, -34, -32, -12, -27, -17, 26]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2049", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[5, 14, 29, -24, 3, -7, 22, 31, 35, -11, 13, 27],\n [-9, 34, 34, 22, -27, -35, 29, -12, -17, -22, -22, -4],\n [-30, -13, -17, -34, 5, 17, -9, -28, 7, -3, 7, -6],\n [-2, -16, 26, -34, 32, -17, -1, -16, 5, -7, -21, -4],\n [-23, -29, 18, -20, -26, 20, 30, 2, 17, -2, -35, 23],\n [-11, -4, -5, -33, 30, 5, 26, 17, -3, -23, 3, -7],\n [-11, -17, 29, -20, 35, 24, 21, 9, 16, -30, 24, 1],\n [18, -32, 11, 1, 6, 12, 25, 26, 19, 1, -21, 23],\n [27, 30, 6, -5, -30, -17, 2, -3, 17, -6, 29, -22],\n [-26, -19, -21, -33, -14, 20, 23, -10, 14, 25, 19, 28],\n [-33, -6, 22, -23, -12, 33, -29, 15, 18, 15, -9, -24],\n [5, -3, -5, -25, 0, -30, 9, 24, 1, -6, 2, -20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1851", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[2, 6, 2, -2, -10, -6, 26, 6, -10, -2, 22, 32],\n [6, 12, -2, 6, -30, 17, 10, 6, 8, -1, -4, -12],\n [2, -2, -22, -1, 8, -18, -6, 9, 18, -3, -2, 2],\n [-2, 6, -1, -30, 0, -8, 2, 8, 2, 28, -12, -6],\n [-10, -30, 8, 0, 3, -10, -16, -28, -2, 30, 10, 8],\n [-6, 17, -18, -8, -10, -7, 10, 10, 7, 8, 6, 2],\n [26, 10, -6, 2, -16, 10, -32, 28, -21, 26, 26, 0],\n [6, 6, 9, 8, -28, 10, 28, 35, -4, -15, -18, 8],\n [-10, 8, 18, 2, -2, 7, -21, -4, -35, 4, -8, 6],\n [-2, -1, -3, 28, 30, 8, 26, -15, 4, 24, -4, -6],\n [22, -4, -2, -12, 10, 6, 26, -18, -8, -4, 29, -28],\n [32, -12, 2, -6, 8, 2, 0, 8, 6, -6, -28, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "314", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[3, 12, -31, -15, 14, -16, 35, -9, -34, 11, 4, 0],\n [35, -23, -14, -18, -30, 32, 31, 16, 34, -33, -19, 30],\n [21, -14, -25, 0, 17, 4, -1, 7, 9, 5, 28, -21],\n [8, 6, 23, -32, 35, -7, 5, -30, 3, 30, -9, -29],\n [-25, -4, 15, 4, -29, -35, -11, -30, -20, -21, -14, -18],\n [14, -26, 13, 34, -26, 3, 22, 35, 6, 9, -8, -31],\n [21, -7, 19, -13, 21, -18, -10, -31, -28, -17, -8, 32],\n [14, 29, -28, 24, 22, -9, -3, 10, 1, 33, -21, 31],\n [-8, 27, -33, 16, 8, 24, 22, -22, -30, -17, 26, -31],\n [13, 15, -10, 20, -18, 9, -27, -34, 6, 34, 32, -5],\n [-17, 35, 11, 1, -17, -11, 17, -32, 10, -5, 0, -32],\n [-34, 3, 8, -17, 5, 2, 29, -1, -25, 23, 34, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-31, -10, -4, 11, 20, 14, 22, -8, 19, 22, 4, 22],\n [10, 9, -26, 12, 26, -8, -16, 34, 5, -30, -25, -6],\n [-33, -3, 18, 11, -26, -17, -27, -29, 25, -22, -34, -14],\n [24, 9, -16, -10, 23, 32, 3, -13, -11, 17, -25, -11],\n [-5, 10, -9, 27, 11, -22, -13, -20, -16, -33, -30, -7],\n [-32, 29, -28, 12, -20, 11, -5, -7, 32, 7, -2, -30],\n [13, 24, 15, -27, -31, 28, -20, 23, 20, 29, -1, -26],\n [11, -1, 26, -3, -21, -1, -26, -16, -28, -28, -23, 23],\n [11, 24, 5, 16, 18, 0, 33, -23, -25, -28, -5, 26],\n [-24, -25, -19, -9, -23, 8, 22, -6, -23, -28, 33, 28],\n [16, -30, 35, 18, -14, 27, 1, 20, 5, 24, -16, 33],\n [9, 22, 1, 3, -33, 2, 10, 13, -2, -10, -34, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1494", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-29, 0, 4, -10, 33, -20, -27, -14, -31, 7, -6, -4],\n [0, 31, -10, -24, 1, 6, 21, -24, 10, -9, -29, 2],\n [0, 0, -9, -26, 6, 22, 5, -27, 10, 18, 23, -23],\n [0, 0, 0, 4, 8, 11, 34, 24, -1, 24, 1, -14],\n [0, 0, 0, 0, -23, 27, -4, -13, 7, -4, -8, -3],\n [0, 0, 0, 0, 0, 2, -24, 16, -15, 4, 31, 13],\n [0, 0, 0, 0, 0, 0, -7, 14, -34, 28, 30, 7],\n [0, 0, 0, 0, 0, 0, 0, -8, -35, 23, 8, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, -33, -30, -14, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 6, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "724515", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[26, -19, -16, -10, 23, -11, -18, -7, 31, -1, -21, 15],\n [-33, -15, 25, -33, 17, -1, 14, -28, 12, -33, 18, -34],\n [-3, -24, -17, -18, 14, -14, -6, -30, -35, -27, 16, -7],\n [26, -7, -31, -14, 13, -28, 32, 4, -12, -23, 14, 9],\n [-32, 27, 29, -9, 27, -25, 6, 2, 34, 26, -32, -2],\n [-10, 18, -9, 3, -15, 18, 20, 27, 6, -10, 33, -16],\n [17, 33, 32, -31, -20, -27, -11, 21, 2, -28, 29, -5],\n [-3, 19, 33, 0, -12, 25, -8, 24, 3, -5, -35, -23],\n [30, 6, 1, 21, -1, 1, -16, 30, -13, 19, 21, 14],\n [2, 11, -6, 32, 7, -9, 28, -30, -5, -7, -33, -16],\n [22, 21, 35, -32, 6, -2, -18, 29, -11, 9, -22, -25],\n [16, -28, 24, 6, -20, 3, 6, -18, -29, -32, -6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "807", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[9, -5, -5, 16, -2, -4, -21, 8, -3, -3, 12, 2],\n [-5, -9, -20, 4, -12, -8, 2, -10, 8, 4, 15, 8],\n [-5, -20, 13, -12, -18, 9, -26, 2, -24, -2, -4, -12],\n [16, 4, -12, -15, 10, 4, -8, -20, -8, 8, 0, -1],\n [-2, -12, -18, 10, 35, 0, -25, 26, -3, -4, -8, 20],\n [-4, -8, 9, 4, 0, -28, 16, -16, 9, 10, -26, -2],\n [-21, 2, -26, -8, -25, 16, -27, 12, 1, 12, -4, 10],\n [8, -10, 2, -20, 26, -16, 12, -17, -4, -6, -2, 2],\n [-3, 8, -24, -8, -3, 9, 1, -4, 26, 12, 12, -18],\n [-3, 4, -2, 8, -4, 10, 12, -6, 12, -14, -10, -17],\n [12, 15, -4, 0, -8, -26, -4, -2, 12, -10, -19, -19],\n [2, 8, -12, -1, 20, -2, 10, 2, -18, -17, -19, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-515", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[13, 6, 13, -23, 32, -22, 0, 20, 33, 10, -21, -28],\n [20, -25, 35, -13, 9, -9, -5, 11, 30, 25, -28, 29],\n [-11, -19, -6, -12, 16, 27, 25, 22, -4, -1, -20, -27],\n [-17, 4, 4, 10, -33, -10, 34, -31, -9, 8, 2, 35],\n [5, 22, -7, 15, 34, 27, -17, -9, 17, 9, -25, -26],\n [-16, -17, -34, 4, -18, -34, 11, 13, -13, 11, 9, -15],\n [11, -4, -17, -18, -12, 11, -6, -15, 12, 30, 9, -35],\n [-14, 20, 4, 2, -17, -17, 30, 11, 22, 21, 12, 9],\n [-8, 24, -31, -18, 1, -11, 2, -35, 4, 19, 3, -11],\n [-13, 7, 12, 2, -12, -31, 24, -19, 1, -21, 30, -16],\n [-6, -20, 8, 23, -32, -5, -10, 5, -34, -28, -12, 4],\n [-11, 26, 22, 35, -4, 10, -10, 6, -29, 20, 11, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[9, 32, 8, -11, 16, -18, -29, -14, -32, -7, 4, 16],\n [0, 5, -21, 21, -1, -17, -15, -23, -15, -10, 20, -5],\n [0, 0, -6, -10, 18, -15, -13, -8, -13, 23, 17, 17],\n [0, 0, 0, -34, -11, 32, 8, -2, -30, 3, 14, -12],\n [0, 0, 0, 0, 33, -30, -20, 24, -22, -3, 33, 4],\n [0, 0, 0, 0, 0, -26, -30, 26, -5, -30, -2, 31],\n [0, 0, 0, 0, 0, 0, -15, 0, -29, -1, 13, -25],\n [0, 0, 0, 0, 0, 0, 0, 8, -4, 22, 20, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 27, -15, -31, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 10, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40615", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[0, -4, 5, -6, 16, -33, 4, 8, 8, -16, -24, 2],\n [-4, -1, -12, -10, 14, 12, -2, 6, 1, -12, -14, 2],\n [5, -12, -27, 27, -3, 1, -14, 20, -6, 6, -4, -14],\n [-6, -10, 27, -33, 0, -26, 0, 2, 3, -12, 2, -6],\n [16, 14, -3, 0, -17, -24, -8, 4, -4, -10, 24, -15],\n [-33, 12, 1, -26, -24, 3, 8, -18, 28, -35, -2, -8],\n [4, -2, -14, 0, -8, 8, 20, 3, -22, -18, -14, 6],\n [8, 6, 20, 2, 4, -18, 3, -34, 4, -28, -16, -2],\n [8, 1, -6, 3, -4, 28, -22, 4, 16, -2, 0, -29],\n [-16, -12, 6, -12, -10, -35, -18, -28, -2, 5, -10, 32],\n [-24, -14, -4, 2, 24, -2, -14, -16, 0, -10, 1, -20],\n [2, 2, -14, -6, -15, -8, 6, -2, -29, 32, -20, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-185", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 17, -19, -24, -35, 20, -13, -29, 5, 17, -29, 30],\n [17, -31, 0, 8, -25, 28, -15, -32, -1, -1, -1, 3],\n [-3, 32, 8, 15, 2, 6, 9, -6, -1, -8, 5, 9],\n [12, 19, -28, -10, -7, 19, 30, 34, 12, -29, -30, 1],\n [-27, -33, 17, -28, 4, -19, 34, 11, -25, -26, 25, -34],\n [-7, 34, 15, 30, 32, 21, 5, 28, -32, -35, -29, -28],\n [22, -26, 30, -14, 16, 13, 31, -32, 21, 33, 17, 19],\n [-12, -24, 19, 11, -9, -18, 15, 24, 21, 31, -34, -25],\n [-23, 4, -30, -24, 7, -32, 1, 0, -4, 21, -24, -18],\n [25, -5, 4, 10, 3, 27, 19, 4, -7, -25, 3, 8],\n [-16, -9, 2, -25, 0, -4, 26, -20, 6, -5, 34, -23],\n [0, -25, 12, -16, -7, -17, -30, 20, -18, 6, 24, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "707", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-33, 3, 7, -8, 6, -27, -18, -15, -10, -13, -26, 8],\n [0, 17, 1, 20, 23, -24, -33, -22, -1, -6, 35, 30],\n [0, 0, 10, -24, 22, 21, -4, 28, 30, 1, -22, -26],\n [0, 0, 0, -15, 33, -27, -27, -18, 33, 26, -20, -32],\n [0, 0, 0, 0, -32, 15, -34, -4, -34, 22, -14, -17],\n [0, 0, 0, 0, 0, 9, 11, 21, -5, 16, 10, -29],\n [0, 0, 0, 0, 0, 0, -18, -29, 2, 9, -8, 23],\n [0, 0, 0, 0, 0, 0, 0, 33, -17, -9, -6, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 3, -13, 29, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 7, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1992", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[11, 18, 11, 16, -18, 10, -10, -18, 13, 29, -29, -6],\n [-11, -11, -9, -1, -6, -22, -1, -2, -21, -29, -23, 4],\n [24, -2, -23, -32, -23, 12, -23, -3, -13, 31, -4, 19],\n [-33, -24, 20, 32, -3, -4, -19, 16, -31, -15, -33, 31],\n [1, -1, -3, 18, -33, 12, -18, -33, -31, -27, -20, 14],\n [21, 21, -19, 29, 21, 27, 31, -31, -14, -35, 11, 13],\n [-32, -14, 19, -4, 30, 33, 35, -28, 0, -24, -8, -34],\n [-17, 13, 1, 16, 24, 6, -29, 6, 21, -20, -11, 2],\n [8, 2, 9, -6, -20, -32, -1, 25, -31, 5, 5, -8],\n [-26, 16, -4, 9, -20, 28, -1, -19, 6, -14, 14, -15],\n [10, 21, -31, 16, -5, -3, 11, -33, 17, 20, -18, -8],\n [-21, 14, -3, -8, 10, -35, 35, 19, 22, -15, 20, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-19, -29, 24, 12, -26, 5, -17, 26, 30, -28, -6, 0],\n [14, -34, -31, 10, 4, 21, -25, 2, -19, -10, 3, 31],\n [-11, -6, 10, 5, 14, 8, -26, -34, -15, -11, 33, -14],\n [33, -25, 8, -31, -30, -20, 10, -12, -22, -12, -13, 3],\n [-30, -15, 10, 5, 23, 33, 6, 23, -1, 5, 31, 29],\n [-17, -17, -11, 3, -3, 4, -24, -6, 34, 6, -22, -31],\n [0, 23, 21, 24, 27, 13, 29, 16, -27, -20, -1, -20],\n [-3, 15, 25, 23, -32, -34, 35, 22, 26, -11, 35, -11],\n [30, -10, 19, -33, 10, -7, 22, -25, -15, 7, -32, 33],\n [34, -14, -30, -14, -20, 0, 14, 22, 35, 15, 11, 17],\n [-30, -11, -33, -23, 17, 31, -5, 31, 19, 30, -31, -27],\n [-7, -1, -1, 14, -6, -21, -7, -11, 21, 15, 32, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-110", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-24, 33, 1, -11, 32, -12, 0, -34, -1, -28, -8, 24],\n [0, 8, -26, -31, 11, -5, -7, -33, -10, -34, 20, -22],\n [0, 0, 11, -16, -18, 25, -31, 22, 24, -23, 4, 31],\n [0, 0, 0, 31, -25, -25, -26, -8, -25, -29, -7, 29],\n [0, 0, 0, 0, 19, -33, -16, -33, -7, -16, -26, 25],\n [0, 0, 0, 0, 0, -12, -5, -13, 17, 6, 0, -2],\n [0, 0, 0, 0, 0, 0, 18, 16, -23, 30, 20, 11],\n [0, 0, 0, 0, 0, 0, 0, 7, -33, 7, 35, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 9, 0, -2, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 11, -4, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3574", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-32, -9, 0, -8, 29, -8, -12, -2, 8, 5, 19, -6],\n [-9, -21, -2, -2, 8, 1, -19, 11, -4, 23, 10, 10],\n [0, -2, -1, 16, -4, -30, -4, -8, -2, 19, -12, -8],\n [-8, -2, 16, 7, 4, 10, 14, -1, 9, 16, -26, 0],\n [29, 8, -4, 4, -29, 1, 4, -4, 7, 18, -1, -10],\n [-8, 1, -30, 10, 1, 13, 17, -32, 8, -2, -7, 17],\n [-12, -19, -4, 14, 4, 17, -14, 16, -8, 0, -30, -14],\n [-2, 11, -8, -1, -4, -32, 16, 18, 12, 7, -2, -16],\n [8, -4, -2, 9, 7, 8, -8, 12, 12, -8, -4, 26],\n [5, 23, 19, 16, 18, -2, 0, 7, -8, -7, 14, 6],\n [19, 10, -12, -26, -1, -7, -30, -2, -4, 14, -2, 2],\n [-6, 10, -8, 0, -10, 17, -14, -16, 26, 6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[8, -16, 12, -3, 0, -29, 26, 7, -8, 20, -10, 8],\n [-16, 9, 13, -30, -7, 6, 20, -12, -3, 12, 16, -3],\n [12, 13, -1, -4, 17, -6, -9, 12, -16, -4, -6, -17],\n [-3, -30, -4, 32, -6, -8, 13, 2, -16, -20, -22, 1],\n [0, -7, 17, -6, -30, -22, -23, 14, 4, -16, -22, 30],\n [-29, 6, -6, -8, -22, 6, 2, 6, 8, -8, -10, 11],\n [26, 20, -9, 13, -23, 2, -18, 2, -18, 18, 6, 12],\n [7, -12, 12, 2, 14, 6, 2, -1, 12, 2, 4, -4],\n [-8, -3, -16, -16, 4, 8, -18, 12, -34, -18, -18, 6],\n [20, 12, -4, -20, -16, -8, 18, 2, -18, -11, -16, 26],\n [-10, 16, -6, -22, -22, -10, 6, 4, -18, -16, 22, -10],\n [8, -3, -17, 1, 30, 11, 12, -4, 6, 26, -10, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1455", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -31, 35, -10, 13, 34, 25, -33, 3, 13, -22, -16],\n [0, 8, -27, 27, 26, -30, 30, 7, 28, 8, -31, -23],\n [0, 0, 20, -6, 20, -11, 32, 11, -8, 1, 0, -35],\n [0, 0, 0, 33, 21, -33, -28, 12, 23, 0, 19, 5],\n [0, 0, 0, 0, 34, 19, -14, -14, -23, -13, -18, 30],\n [0, 0, 0, 0, 0, 12, -31, 3, 7, -17, 3, 23],\n [0, 0, 0, 0, 0, 0, -1, -35, 11, 27, -18, -10],\n [0, 0, 0, 0, 0, 0, 0, 13, 20, 13, 5, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 18, 35, -30, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27, 4, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-157917", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-33, 27, 6, -20, -12, -12, 4, -12, 1, 9, -32, -19],\n [27, 19, 19, 2, 6, -4, 19, 1, -14, -6, -24, -12],\n [6, 19, -15, -10, 8, 2, 28, -1, 6, 18, 0, -8],\n [-20, 2, -10, -12, -14, -7, -6, -20, 1, -13, 2, 5],\n [-12, 6, 8, -14, 15, 3, 2, -24, 4, 0, -22, -6],\n [-12, -4, 2, -7, 3, 31, 8, 3, -33, 14, -4, -16],\n [4, 19, 28, -6, 2, 8, 15, -25, -4, 10, -10, -1],\n [-12, 1, -1, -20, -24, 3, -25, 16, -27, 0, 22, -10],\n [1, -14, 6, 1, 4, -33, -4, -27, -14, 26, 4, -16],\n [9, -6, 18, -13, 0, 14, 10, 0, 26, -16, -12, -24],\n [-32, -24, 0, 2, -22, -4, -10, 22, 4, -12, -3, -2],\n [-19, -12, -8, 5, -6, -16, -1, -10, -16, -24, -2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-27, 23, -3, -29, -3, 30, 23, -1, -4, -35, 16, -1],\n [4, 8, 3, -16, -33, 17, -24, -28, 28, 5, -25, -10],\n [2, -31, -4, 33, -21, 25, 16, -8, -17, 18, -21, -23],\n [-13, 26, -11, -4, -15, -35, -8, -24, -16, 15, -10, 7],\n [14, -8, -10, -11, -5, -18, 4, 31, 27, -25, -9, 1],\n [-24, -8, -30, 34, 8, 11, 0, 8, 33, -13, -13, -1],\n [33, 25, 2, 16, -34, -17, 27, 31, -13, -10, -6, -17],\n [3, -8, 25, 12, -23, -25, 4, 15, 34, -6, -6, 18],\n [-29, 31, -26, 25, 1, -21, 14, -32, 6, 32, -26, -14],\n [-5, -8, 33, -17, 11, -12, 20, -25, 18, 23, 29, -4],\n [-18, -32, 15, 11, 18, -11, -26, -29, 29, -17, -29, 9],\n [2, -29, 10, 31, -28, -33, -24, 7, -29, 12, 9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-124", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-32, -12, 12, 2, 22, 23, -14, 4, -32, 2, 10, -20],\n [-12, -8, -11, -2, 4, 16, 0, -17, 2, -20, -3, 27],\n [12, -11, -17, 12, 20, -12, 4, -5, -24, 21, 10, -18],\n [2, -2, 12, 30, -5, 12, 6, -21, -2, -8, -14, -2],\n [22, 4, 20, -5, 12, 8, -4, 0, 20, 19, -24, -5],\n [23, 16, -12, 12, 8, -10, 5, 18, -24, 8, -23, -14],\n [-14, 0, 4, 6, -4, 5, -27, 13, -8, 10, 19, 22],\n [4, -17, -5, -21, 0, 18, 13, 24, -12, -5, 13, 6],\n [-32, 2, -24, -2, 20, -24, -8, -12, 4, -16, 9, 28],\n [2, -20, 21, -8, 19, 8, 10, -5, -16, 33, 15, -17],\n [10, -3, 10, -14, -24, -23, 19, 13, 9, 15, 2, 19],\n [-20, 27, -18, -2, -5, -14, 22, 6, 28, -17, 19, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2754", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[2, -24, 27, 29, 24, -16, 30, -18, 6, -30, 30, 33],\n [0, -14, 29, 13, -24, 27, -23, 26, 23, -25, -35, 32],\n [0, 0, -27, 33, -14, 33, -13, -31, 3, -33, -10, -28],\n [0, 0, 0, -9, -14, 20, 7, -9, 9, 10, -3, -8],\n [0, 0, 0, 0, -30, 22, -13, -22, 20, -11, -16, 35],\n [0, 0, 0, 0, 0, 23, 35, 21, -24, -33, -4, -21],\n [0, 0, 0, 0, 0, 0, 11, -15, 14, 11, -31, -29],\n [0, 0, 0, 0, 0, 0, 0, 15, 12, 17, 12, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, -4, -16, 10, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -17, -5, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203522", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-23, -5, -13, 1, 23, 22, -20, 3, -27, 28, -14, 18],\n [-14, -22, 30, 14, -31, -19, -35, -22, 19, -19, -27, -24],\n [30, -21, -2, 1, 17, 5, -32, -28, 35, -19, -14, -28],\n [-14, 4, -14, -31, -27, 24, -16, -2, 0, 35, 2, 31],\n [-4, 10, -11, 28, -3, 11, 33, -7, 23, -5, -10, 27],\n [22, 13, 29, 23, 26, 32, 11, -14, 28, 10, 23, -4],\n [1, 31, 16, 7, -2, 25, 35, 31, 9, 5, 16, 30],\n [-24, -21, -20, -33, -9, -13, 28, -3, 12, 19, -9, 11],\n [-5, -1, 0, -12, -19, 9, 26, -35, -16, 34, 33, 28],\n [34, 14, 17, 2, 16, 25, -11, -7, -1, 11, 21, -4],\n [10, 0, 35, -26, 10, -10, 12, 12, -23, -6, 34, 30],\n [-29, 20, -6, 19, -3, 6, -30, -28, 34, 4, 20, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 11) of the inverse of matrix 1/839 * A where A =\n[[-29, 4, 22, 26, 18, -27, 15, -26, 13, -6, -27, 10],\n [0, 28, -2, -9, -9, 5, -18, 14, 7, 5, -18, 25],\n [0, 0, -23, -10, 20, 25, 14, -15, -28, 34, 28, 14],\n [0, 0, 0, -14, 10, 25, -1, 26, 33, 21, -11, -11],\n [0, 0, 0, 0, -28, -9, 18, -33, -3, -8, 16, -7],\n [0, 0, 0, 0, 0, -6, -22, 12, -18, -4, 2, 17],\n [0, 0, 0, 0, 0, 0, 28, -17, 20, 1, 22, -27],\n [0, 0, 0, 0, 0, 0, 0, -28, -9, -10, 9, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, 31, -27, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27, -18, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[35, 8, 35, 21, 12, 26, 25, 31, 9, 25, 35, -34],\n [0, 31, -7, 27, -11, -32, 11, 33, 27, -30, -18, 0],\n [0, 0, -22, 3, -34, -2, 22, -1, -2, -28, 7, 27],\n [0, 0, 0, 10, -32, 26, -26, 4, -31, -18, 25, 21],\n [0, 0, 0, 0, -13, 33, -3, -32, -1, 23, 6, 13],\n [0, 0, 0, 0, 0, 14, 7, -9, -2, 27, 31, -9],\n [0, 0, 0, 0, 0, 0, -25, -29, 30, -5, 10, 34],\n [0, 0, 0, 0, 0, 0, 0, 24, -19, 14, -27, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, -26, 0, 21, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -35, -24, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "397", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-6, -18, -19, 0, -23, -8, -22, 12, 16, -19, 14, 34],\n [-18, -27, -26, -4, -18, -4, 26, 1, 20, -2, -4, 4],\n [-19, -26, 22, 27, -4, 4, -1, 4, 3, 0, -3, -22],\n [0, -4, 27, -32, -2, -24, -2, 10, 13, 17, -20, -6],\n [-23, -18, -4, -2, -8, -2, 16, -4, 9, 5, 10, 15],\n [-8, -4, 4, -24, -2, 20, -8, 11, -24, 14, 4, 0],\n [-22, 26, -1, -2, 16, -8, 28, -6, -8, -22, 13, 23],\n [12, 1, 4, 10, -4, 11, -6, 23, -4, -14, -15, 10],\n [16, 20, 3, 13, 9, -24, -8, -4, -17, 12, 26, 6],\n [-19, -2, 0, 17, 5, 14, -22, -14, 12, -1, -22, 6],\n [14, -4, -3, -20, 10, 4, 13, -15, 26, -22, -2, 14],\n [34, 4, -22, -6, 15, 0, 23, 10, 6, 6, 14, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-335", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-5, 18, 11, -10, -10, 12, 3, -20, -14, 3, 16, -4],\n [18, 2, 0, -6, -8, -12, 16, 1, -29, 11, 21, 18],\n [11, 0, 0, -20, -6, 8, -8, 16, 25, 22, 14, -2],\n [-10, -6, -20, -25, 19, -30, 21, -16, 32, 13, 0, 11],\n [-10, -8, -6, 19, -25, 23, -13, 0, 25, -23, -6, 2],\n [12, -12, 8, -30, 23, -24, 0, 6, -20, 18, -18, -10],\n [3, 16, -8, 21, -13, 0, 18, -26, -24, -13, 22, 3],\n [-20, 1, 16, -16, 0, 6, -26, -15, 4, -10, 2, -34],\n [-14, -29, 25, 32, 25, -20, -24, 4, 8, -26, -4, -4],\n [3, 11, 22, 13, -23, 18, -13, -10, -26, 8, -10, -13],\n [16, 21, 14, 0, -6, -18, 22, 2, -4, -10, 6, -7],\n [-4, 18, -2, 11, 2, -10, 3, -34, -4, -13, -7, -32]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "558", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-32, -33, 19, 33, -4, 22, 31, -2, 27, -26, -4, -31],\n [0, -29, -21, -34, -26, -25, 17, 20, 4, 22, 32, -9],\n [0, 0, -14, 25, 2, -20, 33, -19, 25, 8, 8, 5],\n [0, 0, 0, 15, 18, -18, 4, -26, 5, 8, -28, 0],\n [0, 0, 0, 0, 6, -6, 11, -2, 26, -20, -7, -21],\n [0, 0, 0, 0, 0, 28, -34, -4, 18, 6, -6, -27],\n [0, 0, 0, 0, 0, 0, -7, 30, -5, 5, 3, 21],\n [0, 0, 0, 0, 0, 0, 0, 17, 21, -10, -20, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, -35, 35, 25, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 15, -3, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8666", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-9, 11, 4, 33, -4, 9, 1, -21, -27, 19, -27, 28],\n [0, -21, 0, 0, 29, -8, -3, 29, 18, -30, 12, 33],\n [0, 0, -10, 14, 18, -23, 29, -1, -7, -5, -24, 33],\n [0, 0, 0, -9, 3, -15, -20, -7, 35, -22, 5, 5],\n [0, 0, 0, 0, 23, 3, 35, -29, -8, 15, -1, 22],\n [0, 0, 0, 0, 0, 5, 11, -34, 6, -32, -35, -14],\n [0, 0, 0, 0, 0, 0, -12, -9, -1, 32, -14, -25],\n [0, 0, 0, 0, 0, 0, 0, -13, -32, 17, 4, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, -14, -25, -20, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -14, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1459630", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-34, 21, -2, -25, -1, 6, -12, 30, 0, -2, -5, 12],\n [21, 11, -4, -6, -12, -6, 13, -14, 16, 7, 8, -28],\n [-2, -4, 14, -22, 10, -30, -19, -16, 6, -3, 6, -26],\n [-25, -6, -22, 22, -22, 3, -10, -8, 13, 18, 14, 4],\n [-1, -12, 10, -22, -7, -11, 23, 14, 2, 16, -2, -14],\n [6, -6, -30, 3, -11, 26, -20, -18, 14, -22, 6, -6],\n [-12, 13, -19, -10, 23, -20, -27, 0, -6, 14, 0, -24],\n [30, -14, -16, -8, 14, -18, 0, 33, -4, 8, -5, -22],\n [0, 16, 6, 13, 2, 14, -6, -4, -9, -12, 0, 29],\n [-2, 7, -3, 18, 16, -22, 14, 8, -12, -20, -10, 6],\n [-5, 8, 6, 14, -2, 6, 0, -5, 0, -10, 8, -2],\n [12, -28, -26, 4, -14, -6, -24, -22, 29, 6, -2, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-470", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-25, 32, 31, -16, 29, -3, -26, 31, 19, -4, 9, 23],\n [-5, 16, -26, -30, -35, 10, -6, 27, 27, -35, -16, -7],\n [-2, 30, 30, -34, 18, -18, -6, -28, 6, -7, 15, -12],\n [-26, -20, 14, 5, 18, 8, 24, 33, -13, 35, -16, 3],\n [-33, -33, -5, -29, -35, 20, -9, 29, 34, 3, -33, 23],\n [-34, 11, -16, -9, -17, 19, 27, 7, -31, -16, 25, 26],\n [27, -14, 2, -24, 25, 12, -19, 16, 10, 20, -7, 15],\n [-10, -7, 23, -28, -11, -15, -32, 0, 7, -10, 0, -13],\n [5, 8, 14, -27, 11, 5, -23, 22, 30, 22, 30, -3],\n [33, -9, 14, 23, -9, 23, 20, -2, 13, -19, 34, 2],\n [-35, 2, -10, 33, 32, -11, 22, 9, -14, 12, -23, -11],\n [-26, -18, 19, -9, 20, 20, 13, -10, -34, 24, 2, -33]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[17, 8, -13, -8, -4, -16, -30, -33, -33, -13, -3, 0],\n [28, -24, 26, -10, 1, 12, 8, -25, 33, -12, -17, 34],\n [20, 13, 21, -25, 27, -19, -21, 34, 26, -4, 4, -25],\n [-23, -8, -8, 12, 19, -20, 0, 4, -16, -34, -34, 33],\n [34, 14, 12, -12, -27, 4, 4, -34, -30, -17, -17, -3],\n [25, -6, 26, -23, -18, -34, -33, -30, -8, -4, 24, -5],\n [25, -27, 31, 18, 32, -19, 23, -5, 25, 4, -33, 14],\n [-35, -28, 26, 28, 5, -19, 7, -34, 11, 24, 13, -21],\n [14, 10, -34, -7, -7, 25, 30, 8, -32, 3, 24, 13],\n [-31, 30, 9, 24, -28, 14, 0, 34, 5, -26, 0, 32],\n [-22, -19, -15, 18, -23, 12, 9, -27, 19, 14, -16, 4],\n [-35, 28, -1, 29, 17, 25, -31, 33, 24, -17, 21, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (9, 12) of the inverse. Round your answer to the nearest integer:\n[[-18, -28, 8, 0, -8, -2, -6, 6, 4, -10, 6, 0],\n [-28, -25, 6, 16, -22, -10, 6, 28, 8, -12, 28, -20],\n [8, 6, -23, -5, 32, -14, 29, -8, 6, -11, 1, 22],\n [0, 16, -5, -21, -12, 10, 20, -30, -20, -2, -27, 4],\n [-8, -22, 32, -12, -9, 2, 8, 0, -15, -25, -24, 22],\n [-2, -10, -14, 10, 2, 15, -22, 26, 12, -20, -7, -16],\n [-6, 6, 29, 20, 8, -22, -34, 6, -6, 0, -8, -20],\n [6, 28, -8, -30, 0, 26, 6, -23, -18, 14, 12, -12],\n [4, 8, 6, -20, -15, 12, -6, -18, 25, 8, 14, 18],\n [-10, -12, -11, -2, -25, -20, 0, 14, 8, -21, 14, 19],\n [6, 28, 1, -27, -24, -7, -8, 12, 14, 14, 35, 17],\n [0, -20, 22, 4, 22, -16, -20, -12, 18, 19, 17, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 4) of the inverse of matrix 1/839 * A where A =\n[[5, 21, -4, -18, 10, -15, -8, 4, 5, 10, -19, 2],\n [21, -13, 15, 0, 2, 16, 19, 23, -13, -8, 4, 17],\n [-4, 15, 6, -14, 12, 20, -18, 18, -20, 4, 0, -4],\n [-18, 0, -14, 6, 8, 4, -2, -16, 2, -2, 1, -16],\n [10, 2, 12, 8, -26, -7, 12, 10, 16, 13, 6, -10],\n [-15, 16, 20, 4, -7, 26, 4, -18, -3, 27, -4, -12],\n [-8, 19, -18, -2, 12, 4, 18, -6, -16, 26, -30, 10],\n [4, 23, 18, -16, 10, -18, -6, 4, -11, -12, -16, -20],\n [5, -13, -20, 2, 16, -3, -16, -11, 33, -12, 12, 14],\n [10, -8, 4, -2, 13, 27, 26, -12, -12, 16, 12, -1],\n [-19, 4, 0, 1, 6, -4, -30, -16, 12, 12, -12, 12],\n [2, 17, -4, -16, -10, -12, 10, -20, 14, -1, 12, 25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[23, -4, 5, -12, 29, -26, 14, 27, 29, 22, 10, -8],\n [0, -32, 5, 24, 26, -25, -16, -29, 26, -29, 28, 22],\n [0, 0, -13, 0, -12, -15, 27, 11, 33, -21, -5, -32],\n [0, 0, 0, 27, -10, 14, -3, -32, 21, 26, -2, -2],\n [0, 0, 0, 0, -24, 0, -35, 6, -20, 13, -30, -23],\n [0, 0, 0, 0, 0, -4, 29, 16, 30, -32, -11, 27],\n [0, 0, 0, 0, 0, 0, 15, -11, 5, -31, 28, -30],\n [0, 0, 0, 0, 0, 0, 0, -29, 14, 24, 29, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 14, -5, 33, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27, 33, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10880", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-29, -9, -29, -28, 6, -10, 25, -16, 15, -34, -6, -19],\n [31, 7, 13, -32, -7, -2, -27, 22, -12, 20, 25, 27],\n [6, -19, 35, 30, 12, 34, -3, 2, -35, 19, 19, -26],\n [19, -12, -8, 15, 10, -7, -17, -31, 13, 19, 10, -21],\n [3, -14, 26, 33, -5, 1, -13, -32, 7, 2, -21, -25],\n [-11, -10, 3, 20, 15, -3, -16, 16, -2, 9, -32, -23],\n [23, 31, 17, -19, 35, 9, 11, -10, -5, -5, 24, -35],\n [10, -2, 18, 23, 5, 15, -31, -26, 2, -1, 30, -17],\n [2, 17, 14, -2, -32, 25, 34, -27, 16, -5, 32, -3],\n [23, -1, -23, 25, 12, 2, 29, 18, -5, 13, -14, -7],\n [29, 12, 30, -11, -15, -10, -35, -4, 10, -31, 4, -19],\n [17, -7, -28, 7, -21, -2, -1, -3, -15, -17, -35, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, -10, 12, -4, 14, 6, 18, -1, -14, -12, -3, 0],\n [-10, 24, 16, -28, -22, -2, 6, 16, -26, -10, 16, 20],\n [12, 16, 21, 0, -20, -4, 5, 6, -2, -20, 8, -18],\n [-4, -28, 0, 12, -8, -14, -6, -10, 13, -12, 20, -4],\n [14, -22, -20, -8, 24, -4, -6, -14, 4, 1, -12, -11],\n [6, -2, -4, -14, -4, 17, -2, -2, -16, 23, 0, 3],\n [18, 6, 5, -6, -6, -2, 26, -6, -1, -12, -6, -24],\n [-1, 16, 6, -10, -14, -2, -6, -21, 6, 8, -31, 21],\n [-14, -26, -2, 13, 4, -16, -1, 6, 6, -20, -4, 4],\n [-12, -10, -20, -12, 1, 23, -12, 8, -20, -30, -12, 14],\n [-3, 16, 8, 20, -12, 0, -6, -31, -4, -12, -7, 10],\n [0, 20, -18, -4, -11, 3, -24, 21, 4, 14, 10, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-487", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-9, 32, -15, -16, -19, 10, -2, -26, -16, 28, 26, 3],\n [26, -24, -12, 17, -3, 33, 10, -29, 7, -29, 25, -4],\n [23, -6, -32, -2, -27, 24, -12, 19, -7, 18, 15, -14],\n [-16, 1, 15, 14, 30, 26, 8, -13, -25, 18, 19, 25],\n [16, -14, -33, 29, 22, 7, 25, 17, -3, -11, 14, 11],\n [22, 30, -23, 6, -21, -30, 6, -1, -30, -18, 7, -16],\n [17, 12, -9, -35, -22, -4, 31, -26, -10, 29, 14, 13],\n [-4, 29, -10, 33, -10, 29, -24, 0, -12, 6, 19, 19],\n [-28, 25, -9, 27, -4, 24, -1, -20, 0, 20, -6, -4],\n [-15, 20, 4, 18, -6, -16, -35, -18, 21, 23, -23, -4],\n [34, -3, 29, -33, -31, -24, -3, -9, -23, 0, 22, 28],\n [14, 15, -32, 8, -18, -18, -30, 23, 27, 7, 33, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5138", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (9, 10) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-27, -11, -26, -3, 6, 14, 12, -13, 10, 18, -23, 6],\n [-11, -1, 0, -6, -2, 26, 28, 22, 13, 26, 0, 0],\n [-26, 0, 24, -4, -4, 28, 30, 28, -8, -12, 0, -14],\n [-3, -6, -4, -26, -11, 0, 4, 4, 0, -12, -31, -3],\n [6, -2, -4, -11, -7, 22, -31, -8, -1, -19, -14, 13],\n [14, 26, 28, 0, 22, 31, -13, 0, 24, -12, -16, 8],\n [12, 28, 30, 4, -31, -13, -19, 7, 0, 17, 6, -12],\n [-13, 22, 28, 4, -8, 0, 7, 34, -16, 10, -17, 4],\n [10, 13, -8, 0, -1, 24, 0, -16, -14, 10, -22, 20],\n [18, 26, -12, -12, -19, -12, 17, 10, 10, -15, 20, 3],\n [-23, 0, 0, -31, -14, -16, 6, -17, -22, 20, -15, -14],\n [6, 0, -14, -3, 13, 8, -12, 4, 20, 3, -14, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-28, -5, 2, 26, -3, 12, -3, 0, 7, 20, 1, 0],\n [-5, 7, -28, -32, -11, -12, -12, 16, 7, -2, -24, 8],\n [2, -28, 15, 0, -7, -24, 16, 22, -4, -12, 10, 17],\n [26, -32, 0, -21, -14, 3, 8, -4, -18, 12, -2, -2],\n [-3, -11, -7, -14, -8, -26, -7, 11, 9, 13, -26, -20],\n [12, -12, -24, 3, -26, 32, 4, 17, 8, 10, -20, 3],\n [-3, -12, 16, 8, -7, 4, 24, -24, -13, -12, -12, -14],\n [0, 16, 22, -4, 11, 17, -24, -13, 11, -2, 3, -8],\n [7, 7, -4, -18, 9, 8, -13, 11, 24, -10, 20, -20],\n [20, -2, -12, 12, 13, 10, -12, -2, -10, 9, 4, -5],\n [1, -24, 10, -2, -26, -20, -12, 3, 20, 4, -7, 6],\n [0, 8, 17, -2, -20, 3, -14, -8, -20, -5, 6, 15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-92", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-31, 16, -4, 18, -6, -14, -16, 1, -6, -24, -8, 13],\n [16, -26, 9, 4, 4, -18, -4, 8, -12, -13, -4, -20],\n [-4, 9, 11, 0, -10, 12, -24, 2, 2, 8, 0, -20],\n [18, 4, 0, -29, 20, 11, -3, -19, 10, -21, -14, -14],\n [-6, 4, -10, 20, 22, -26, -2, 8, -18, 7, 4, -6],\n [-14, -18, 12, 11, -26, 2, -26, -4, 12, 12, -22, 8],\n [-16, -4, -24, -3, -2, -26, -30, -17, -2, -14, -10, 16],\n [1, 8, 2, -19, 8, -4, -17, 12, 2, -18, 16, 15],\n [-6, -12, 2, 10, -18, 12, -2, 2, -15, 0, -22, 3],\n [-24, -13, 8, -21, 7, 12, -14, -18, 0, 10, 18, -30],\n [-8, -4, 0, -14, 4, -22, -10, 16, -22, 18, 15, 20],\n [13, -20, -20, -14, -6, 8, 16, 15, 3, -30, 20, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-43", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 11) of the inverse of matrix 1/839 * A where A =\n[[19, -24, 27, -1, -14, -26, 14, -1, -20, 0, 25, -19],\n [0, -24, -33, -17, -14, -35, 17, 8, -26, -28, -19, 34],\n [0, 0, 1, 32, 28, -29, -20, -22, 0, -25, -35, -27],\n [0, 0, 0, -12, 35, 10, -18, 31, 27, -12, -5, 2],\n [0, 0, 0, 0, 27, 29, 27, -31, 31, 16, -32, 15],\n [0, 0, 0, 0, 0, 21, -12, 17, -6, -29, -27, -15],\n [0, 0, 0, 0, 0, 0, -26, -6, -29, -21, -17, 3],\n [0, 0, 0, 0, 0, 0, 0, 13, 35, -17, -2, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, -19, -21, -25, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-299500", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[23, 15, 21, -31, 16, 29, -24, -13, 16, 27, -33, -12],\n [6, -15, -11, -24, 12, 34, 21, -7, -7, 10, -27, -4],\n [-23, 17, 18, -7, 15, 13, 5, -24, -1, -32, 9, 13],\n [-18, 10, 22, -21, 22, -13, -13, -10, -2, 5, 21, -11],\n [18, 8, -23, 18, -9, -28, 7, 34, 19, 28, -31, 23],\n [-9, -17, 29, 32, 30, -10, -3, 2, -29, -31, -27, -23],\n [4, 12, 10, 28, 28, -7, -18, -6, -17, 12, -27, -35],\n [3, 19, 16, 35, 28, -12, -9, 30, 30, 26, -20, -24],\n [4, -26, 28, 19, -32, -13, 13, -32, -35, 29, 3, -33],\n [21, 23, -18, -15, 20, 16, -28, -11, -4, 34, 4, -7],\n [33, -1, -3, 10, -5, 32, 4, 33, 6, 8, -19, -16],\n [17, 8, -19, -9, -13, 22, 33, 20, 9, -7, -22, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-120", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[10, -9, 34, -29, -10, 6, -6, -30, 31, 18, -1, -1],\n [0, -30, -13, 23, 15, 26, -4, -35, 13, -8, 35, 1],\n [0, 0, -17, 15, -21, -12, 25, 17, 23, -29, 32, -2],\n [0, 0, 0, -24, 22, 16, 20, -33, -23, 27, -31, -11],\n [0, 0, 0, 0, -22, 16, -11, 20, 1, 34, -30, -11],\n [0, 0, 0, 0, 0, 25, 19, -16, -33, 29, 1, -1],\n [0, 0, 0, 0, 0, 0, 6, -19, -12, 1, -34, -22],\n [0, 0, 0, 0, 0, 0, 0, -23, -1, 0, -2, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, -6, 21, -13, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 29, -7, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15425", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (3, 6) of the inverse. Round your answer to the nearest integer:\n[[-17, 20, 21, 2, 23, 2, -26, 12, 12, -30, 4, -6],\n [20, -21, -4, -26, -2, -8, 6, -2, 0, 14, 18, -8],\n [21, -4, -25, 10, -20, 17, 4, -16, -28, -27, 4, 1],\n [2, -26, 10, 10, -6, 26, 0, 20, -13, 12, 32, 8],\n [23, -2, -20, -6, -35, -32, -12, 0, 4, -8, 2, 6],\n [2, -8, 17, 26, -32, 12, 6, 2, -25, 12, 8, -6],\n [-26, 6, 4, 0, -12, 6, -31, 20, -18, 4, -22, -12],\n [12, -2, -16, 20, 0, 2, 20, 30, -6, -8, 10, -24],\n [12, 0, -28, -13, 4, -25, -18, -6, 19, 4, 13, 18],\n [-30, 14, -27, 12, -8, 12, 4, -8, 4, 29, 25, 22],\n [4, 18, 4, 32, 2, 8, -22, 10, 13, 25, 14, -2],\n [-6, -8, 1, 8, 6, -6, -12, -24, 18, 22, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[12, -17, -5, 24, 8, -13, -9, -35, -14, -28, 33, -12],\n [0, -24, -32, 28, 24, -27, 6, 17, 24, -22, 15, 29],\n [0, 0, -14, 28, -12, -6, 4, -13, -26, -3, -31, -9],\n [0, 0, 0, -16, 7, 31, 22, 5, 28, 10, 24, -21],\n [0, 0, 0, 0, -13, -28, -20, 34, 25, 22, -7, 27],\n [0, 0, 0, 0, 0, -12, 3, 11, 25, -7, -16, -31],\n [0, 0, 0, 0, 0, 0, -30, 9, -10, -13, -31, -11],\n [0, 0, 0, 0, 0, 0, 0, -27, -2, 23, -19, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, -28, -4, -25, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 15, -21, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15120", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[21, 20, -6, 4, -8, 9, -31, 12, -13, 31, -18, -1],\n [20, -15, 23, -5, 16, 5, 4, 5, -14, 0, 13, -5],\n [-6, 23, 35, -20, 10, -16, 2, 1, 10, -8, -7, 6],\n [4, -5, -20, 12, 2, 25, -4, 28, -23, 0, 20, -14],\n [-8, 16, 10, 2, -10, 1, -3, 9, -3, -4, 12, 0],\n [9, 5, -16, 25, 1, -27, -28, 20, 9, -25, 22, 1],\n [-31, 4, 2, -4, -3, -28, -33, -30, 10, 8, 14, -2],\n [12, 5, 1, 28, 9, 20, -30, -12, 2, -5, 2, 18],\n [-13, -14, 10, -23, -3, 9, 10, 2, 12, 9, 12, 6],\n [31, 0, -8, 0, -4, -25, 8, -5, 9, -8, -2, -14],\n [-18, 13, -7, 20, 12, 22, 14, 2, 12, -2, -21, 8],\n [-1, -5, 6, -14, 0, 1, -2, 18, 6, -14, 8, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-21, 27, 7, -9, 25, 18, 23, 3, -1, -27, 24, 26],\n [0, -20, -20, -4, 2, 3, 26, 27, -20, 18, -21, -18],\n [0, 0, 4, 27, 32, -19, 12, -17, 3, 29, 17, -18],\n [0, 0, 0, -2, -21, -17, 27, -10, 13, -32, 30, -19],\n [0, 0, 0, 0, 12, 12, -21, 9, -34, 22, 2, -33],\n [0, 0, 0, 0, 0, 25, 13, 28, -16, 9, -19, 30],\n [0, 0, 0, 0, 0, 0, -19, -16, 1, 16, -10, -11],\n [0, 0, 0, 0, 0, 0, 0, -7, -19, 34, 28, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, -19, -26, 31, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -31, -31, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-390383", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[4, -7, 9, -2, -21, 34, 35, -34, -35, 18, -34, 0],\n [0, -8, -16, 1, 23, 8, -24, -4, 2, -5, -18, -7],\n [0, 0, 27, -16, -5, -5, 22, -29, -24, 25, 7, 13],\n [0, 0, 0, 27, -21, -24, -10, -6, -6, 26, 7, -14],\n [0, 0, 0, 0, 1, 21, 34, -14, -32, 22, 8, -19],\n [0, 0, 0, 0, 0, 8, -17, -11, 1, -18, 22, -24],\n [0, 0, 0, 0, 0, 0, 5, 29, 25, -1, -14, 33],\n [0, 0, 0, 0, 0, 0, 0, 4, -6, 28, 5, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, -21, -17, -18, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 29, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1401505", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (2, 11) rounded to the nearest integer?\n[[-34, -5, 19, -1, -9, -31, 15, -20, 4, 32, 8, 5],\n [-20, 6, -16, 26, -8, 24, 5, -35, -20, -32, 18, -7],\n [30, -12, 5, 27, 20, -22, 17, 8, 7, -35, -25, -16],\n [-15, -16, -19, 27, -31, 10, 16, 0, 13, 2, -9, 33],\n [14, 7, 34, -27, 29, -6, -21, -4, -32, 24, 19, -2],\n [25, 2, 15, 22, -11, -25, -28, -2, -9, -14, 26, 3],\n [-14, -5, -2, 32, 23, -28, 17, 18, 34, -18, -28, -29],\n [-29, -26, 0, 26, 15, -5, -26, -1, -7, 13, -5, 32],\n [-19, 1, -8, 2, -26, -8, 33, -29, -34, 21, -26, -22],\n [-4, 17, -33, 12, -28, -27, -20, -5, -31, 3, -20, 28],\n [11, 23, -16, -15, 17, 18, 13, -20, -20, -13, 32, 1],\n [-12, 25, -28, 33, -7, -26, 20, -14, -26, -16, 15, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, 4, -31, 7, 31, -12, -5, 23, 31, 27, -35, 33],\n [0, -3, 27, 6, -5, 16, 14, -23, 29, 2, 3, 6],\n [0, 0, 34, 6, -7, 32, -11, -20, 21, -2, -27, -1],\n [0, 0, 0, 24, 7, 25, 33, -20, -34, -17, 28, -16],\n [0, 0, 0, 0, -1, -26, 0, 17, 18, -20, 14, -10],\n [0, 0, 0, 0, 0, 13, -17, 21, -28, 26, -27, -29],\n [0, 0, 0, 0, 0, 0, -35, 13, 8, 33, -22, -29],\n [0, 0, 0, 0, 0, 0, 0, 29, 31, -16, 22, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 25, 6, -10, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -18, -5, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, -16, 24, -8, 5, -10, 14, -12, -6, -18, 10, 0],\n [-16, -8, -18, -12, 18, 10, 2, 14, 5, 10, -3, -16],\n [24, -18, -14, 2, 6, 29, 3, -8, 10, -18, -10, 8],\n [-8, -12, 2, -16, -3, -4, 4, 4, 14, 10, -11, 24],\n [5, 18, 6, -3, 13, 30, 6, 32, -6, -4, 23, -4],\n [-10, 10, 29, -4, 30, -23, 5, -8, -16, -15, 12, 4],\n [14, 2, 3, 4, 6, 5, 21, -14, 14, -28, 16, -13],\n [-12, 14, -8, 4, 32, -8, -14, 35, -1, -19, 10, -4],\n [-6, 5, 10, 14, -6, -16, 14, -1, -21, 10, -34, 26],\n [-18, 10, -18, 10, -4, -15, -28, -19, 10, -31, 4, 13],\n [10, -3, -10, -11, 23, 12, 16, 10, -34, 4, -34, -1],\n [0, -16, 8, 24, -4, 4, -13, -4, 26, 13, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-261", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[1, 11, 35, 35, -1, -10, 20, 7, -17, -14, 21, 29],\n [-2, 14, -4, 17, 15, -16, 22, 9, 14, -28, -15, -18],\n [-21, -26, 27, -16, 26, 16, -6, -33, -35, -26, 13, 29],\n [-3, -1, 1, 15, 18, 27, 10, 10, 14, -29, 25, -24],\n [2, 3, -15, -13, 8, 8, -15, 25, -12, -5, -31, 29],\n [1, -4, 30, -2, -7, -31, -6, 9, -18, 1, -25, -32],\n [10, -33, 17, -12, -28, -30, -18, -30, 3, -35, -21, -22],\n [10, 5, -30, -16, 32, 4, -17, 33, -34, 8, 17, -30],\n [7, -17, -18, -6, 35, -19, 17, 32, 28, -33, -11, -6],\n [0, 5, -13, 14, -20, -6, 24, 25, -30, 3, -31, -33],\n [-6, -25, -33, -21, 8, 18, -35, -23, 27, 20, 3, 3],\n [31, -6, 5, -25, 34, -14, 2, -24, 0, 14, -19, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 1, 31, -11, 13, 7, -17, -10, -21, 17, -16, -31],\n [28, 12, 4, -12, 34, -24, -32, 7, 16, -15, 33, -23],\n [-34, -30, -13, 0, -26, -9, -29, 14, -15, 10, -35, 19],\n [17, -15, -4, -22, 3, 6, -11, -7, -4, -25, -8, 33],\n [-11, 16, 5, 15, -29, -3, 6, 21, -25, 34, 31, -6],\n [-13, 15, -31, 14, 8, -21, -34, -12, 18, -26, -1, 5],\n [11, -6, 2, -10, -16, 0, 28, 7, 4, -18, -14, -20],\n [-33, 33, -9, 4, -32, 7, 16, 16, 30, 26, 27, 15],\n [28, 20, -25, -1, -25, -3, 30, -35, -3, -9, 29, 9],\n [8, 4, 9, -34, 5, 16, -19, 14, 5, -31, 16, 12],\n [-23, 19, -2, 19, 8, 5, -34, 20, -23, 12, 4, 24],\n [1, -15, -18, 19, 27, 24, 10, -20, 8, -24, 28, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4054", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[19, -8, 2, 19, -22, -5, 27, 10, -32, -16, -12, 2],\n [-12, 33, 12, 9, -15, 30, 17, 29, -28, -2, -26, -35],\n [-1, 19, -10, 32, -31, 31, -17, 7, 3, -9, -14, 13],\n [22, 23, 4, -21, -4, 22, 20, 16, -8, -12, 1, 26],\n [-31, 8, 14, -35, 28, -35, -21, -35, 16, 5, 27, 10],\n [-15, 29, 16, -5, 35, 0, -12, 2, 32, -34, 30, 21],\n [27, 35, 5, -29, 21, 9, -28, -33, -4, 32, -26, -18],\n [17, -25, -4, -30, 2, 19, -8, -10, -14, -30, 0, -25],\n [-2, -33, 14, 0, 19, -6, 26, 17, 14, -4, -27, -20],\n [2, -17, 0, -25, 27, 7, -3, 13, 15, 14, -12, -15],\n [-10, -17, 31, 30, 5, 28, -3, -4, -11, 24, -33, 15],\n [-29, 25, -11, -28, -11, 27, -4, -4, 17, -11, -10, -28]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-309", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (9, 12) of the inverse. Round your answer to the nearest integer:\n[[33, -34, -17, 31, 34, -28, 23, -31, -5, -23, -35, 10],\n [-32, -16, -4, -33, 16, -25, -27, 21, 26, 20, 15, -34],\n [-21, 33, 3, -2, 7, 30, 9, -9, 31, 26, 28, -34],\n [-8, 5, 16, -22, 25, 14, -23, 32, -17, 0, 34, -24],\n [-23, -12, 10, -21, 10, -1, -18, -14, -11, -12, -30, 0],\n [-26, -24, 33, -16, 1, -18, 5, -24, 33, 28, -6, -19],\n [-1, 4, -17, 24, 11, -34, 34, 6, 24, -25, -9, -22],\n [23, -28, 30, -31, -6, -11, -11, 26, 29, -35, 11, -9],\n [2, -17, 4, -24, 30, -3, -23, 7, -15, -2, -6, -16],\n [0, -29, 33, -27, 9, -18, 11, -35, 17, 1, -16, 35],\n [22, 5, 2, 8, -21, -1, -9, -15, 4, 8, 8, -31],\n [13, 33, -15, -28, 30, 1, -22, -2, 24, 25, 10, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, 25, 33, -2, 18, -7, 5, 34, 22, -6, -3, 27],\n [0, 13, -24, -14, -12, 20, -11, 30, -35, -2, -31, -19],\n [0, 0, -30, 3, 23, -16, 28, -12, 5, 31, 2, 2],\n [0, 0, 0, 26, 16, 35, -12, 14, 2, 33, -18, 13],\n [0, 0, 0, 0, -31, -34, 26, -31, -5, 27, -18, 21],\n [0, 0, 0, 0, 0, -15, 24, 9, -14, 29, -30, 29],\n [0, 0, 0, 0, 0, 0, 31, 15, 3, -31, 22, -19],\n [0, 0, 0, 0, 0, 0, 0, -16, 31, 18, 14, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 24, 31, 12, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -26, -31, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-170", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -31, -14, -22, 34, -19, -35, -18, -25, -24, -2, -28],\n [0, -22, 15, -27, 2, -7, -7, -8, -30, -34, 17, -5],\n [0, 0, 4, -24, 19, 21, 9, -11, 6, -18, -6, -18],\n [0, 0, 0, 33, -3, -30, 12, -32, -23, -10, 13, -16],\n [0, 0, 0, 0, -33, -15, 7, -11, 31, -1, -13, -23],\n [0, 0, 0, 0, 0, 25, -8, -2, -20, 7, -25, -12],\n [0, 0, 0, 0, 0, 0, 18, -12, 15, -12, 14, 18],\n [0, 0, 0, 0, 0, 0, 0, 15, 1, -23, -5, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, -9, -13, -1, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -7, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17245", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[19, -12, -10, 18, -3, 21, -27, 28, 23, -20, -31, 8],\n [10, -26, 22, 34, 28, 34, 24, -11, -25, 27, -10, 5],\n [17, -12, -29, 28, 10, 15, 35, -30, -6, -20, 21, 29],\n [25, -19, 27, -29, -1, 33, -6, 8, -30, 20, -28, -16],\n [-6, 26, -10, 30, 25, 25, 9, 10, -12, -20, -20, 30],\n [-35, -11, -22, -29, -15, 13, -32, -24, -14, -2, -10, -8],\n [-17, -5, -22, -13, -28, 2, -26, -6, -29, -34, -14, -31],\n [31, 33, 20, -16, 34, 32, 21, -15, -19, -9, 3, 31],\n [34, 33, -23, 14, -26, 20, 8, -8, 1, 0, 20, 21],\n [0, -35, 7, -27, 31, -4, 34, 22, 16, 34, -8, 29],\n [4, -16, -26, 26, 1, 24, 31, 16, -1, 26, -24, -7],\n [-6, -14, 17, -14, 24, 13, 13, -29, 10, -25, -20, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7157", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[21, 0, 15, -14, 1, -33, -1, 2, 19, 5, 2, -2],\n [0, -22, -15, -8, 24, -2, 29, -32, 20, 34, -26, -1],\n [0, 0, -11, -4, 20, -10, 32, -9, -25, 17, -4, 23],\n [0, 0, 0, -19, -25, 21, 14, 17, 30, 7, 3, 6],\n [0, 0, 0, 0, -26, -2, -10, -1, 20, 20, 12, -13],\n [0, 0, 0, 0, 0, -33, -8, -9, -25, -24, -29, 6],\n [0, 0, 0, 0, 0, 0, -32, -14, -26, -32, -29, 27],\n [0, 0, 0, 0, 0, 0, 0, 4, 23, 33, 5, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 21, 27, 2, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1217", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -4, -1, -12, -1, -6, -26, -4, 28, -8, 20, 18],\n [-4, 32, 28, -4, -6, -8, -16, -2, 0, -2, -24, -22],\n [-1, 28, -7, 16, -1, 5, -18, 4, -30, 3, -12, -19],\n [-12, -4, 16, -35, 15, 17, 2, -16, 20, -13, -12, 12],\n [-1, -6, -1, 15, 11, 9, 5, -8, 10, -14, 12, 6],\n [-6, -8, 5, 17, 9, -7, -12, -22, -26, -13, -16, -12],\n [-26, -16, -18, 2, 5, -12, 0, 22, 10, 24, -6, 18],\n [-4, -2, 4, -16, -8, -22, 22, -30, 13, -30, 14, 10],\n [28, 0, -30, 20, 10, -26, 10, 13, 9, 1, 14, 12],\n [-8, -2, 3, -13, -14, -13, 24, -30, 1, 14, 28, 32],\n [20, -24, -12, -12, 12, -16, -6, 14, 14, 28, 26, 8],\n [18, -22, -19, 12, 6, -12, 18, 10, 12, 32, 8, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (5, 12) rounded to the nearest integer?\n[[-32, -6, 4, 6, -3, 23, 2, -4, -30, 8, 4, 12],\n [-6, 13, -12, -32, -14, 4, -10, 0, -22, -6, -2, -2],\n [4, -12, 20, -16, -22, 11, -10, -6, 4, 10, -8, -10],\n [6, -32, -16, -17, -7, 4, -22, -10, -8, 12, -2, -2],\n [-3, -14, -22, -7, 2, 3, 6, 4, -4, 6, 18, 8],\n [23, 4, 11, 4, 3, -22, 10, -18, -24, 4, 12, 10],\n [2, -10, -10, -22, 6, 10, -21, 21, -30, -2, -18, 6],\n [-4, 0, -6, -10, 4, -18, 21, -31, -18, -26, -18, -20],\n [-30, -22, 4, -8, -4, -24, -30, -18, -11, 30, -17, 20],\n [8, -6, 10, 12, 6, 4, -2, -26, 30, 15, -1, -5],\n [4, -2, -8, -2, 18, 12, -18, -18, -17, -1, 6, -1],\n [12, -2, -10, -2, 8, 10, 6, -20, 20, -5, -1, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (4, 5) rounded to the nearest integer?\n[[17, 13, -10, 31, 0, -13, 3, 23, -13, -13, 7, -11],\n [24, -3, -3, 29, 11, -3, 2, -12, 13, -6, 22, 23],\n [-20, -20, -3, 3, 10, 2, -13, -10, 13, -12, 6, -9],\n [-34, -28, 5, -23, -14, 11, 11, 29, 33, -7, -6, 10],\n [-30, -30, 16, -31, 5, -16, -16, 3, -6, 12, 24, -13],\n [24, 14, -23, 2, 3, 32, -17, 16, 5, -9, -13, -17],\n [-1, -31, -31, -30, 5, 5, 18, 8, 12, 1, 20, -3],\n [-1, -30, 10, 0, 8, -29, -29, -7, 29, 24, -1, 21],\n [-7, 2, -24, 22, -30, 0, 16, -9, -11, 4, 0, 24],\n [-7, -33, -23, 32, -25, 12, 24, -34, 34, -23, -1, 15],\n [20, 4, 23, -24, -20, 17, 5, -16, 4, 25, -2, -17],\n [9, -7, -17, 20, -9, -34, 4, 29, -28, -9, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-98", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[13, 20, 29, -5, 24, -2, -19, -7, -30, -30, -33, -5],\n [16, -28, -10, -21, 20, 26, -23, 10, 18, -27, -33, -13],\n [-24, 5, 8, 22, -25, -17, 23, 1, -26, -3, -16, 8],\n [-23, 27, -22, 18, 6, 2, 0, -27, -31, -21, -12, 28],\n [12, 7, 3, -11, -31, 24, -29, -18, -30, -24, -3, -15],\n [22, 6, 10, -33, 21, 17, 26, -23, 15, -17, 23, 26],\n [1, -21, 34, -24, 14, 11, -20, -20, 31, -2, 10, 28],\n [13, -15, 17, 26, 18, -33, 17, -24, 2, -18, -1, 34],\n [35, -19, -15, 34, 11, 1, 18, -21, -25, -27, 32, -33],\n [-23, -30, -35, -31, 30, 5, 14, -29, -15, 17, -16, 29],\n [-4, -30, 5, -3, -11, -12, -24, 1, 14, -27, 31, -32],\n [18, -30, 30, 1, 9, -22, 7, 30, -29, 19, 1, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-19, 2, -32, -18, 13, 2, 20, -8, -16, 0, -2, 18],\n [2, 11, -2, 4, -10, 20, 17, 14, -3, -15, -8, -10],\n [-32, -2, 16, 20, 2, 7, 20, -18, -20, 6, -28, -26],\n [-18, 4, 20, 20, 18, 4, -2, 26, 18, 10, 6, -7],\n [13, -10, 2, 18, 23, -25, -8, 2, 4, -14, 0, 12],\n [2, 20, 7, 4, -25, -3, -6, -4, 6, -5, -4, 5],\n [20, 17, 20, -2, -8, -6, -4, 2, 2, 24, 5, 10],\n [-8, 14, -18, 26, 2, -4, 2, -29, 2, -17, -2, 20],\n [-16, -3, -20, 18, 4, 6, 2, 2, 10, 13, -4, 6],\n [0, -15, 6, 10, -14, -5, 24, -17, 13, -12, 23, 8],\n [-2, -8, -28, 6, 0, -4, 5, -2, -4, 23, 21, -7],\n [18, -10, -26, -7, 12, 5, 10, 20, 6, 8, -7, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-72", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (7, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-26, -16, -20, 21, 10, -35, -11, 20, 10, 23, 26, 25],\n [0, 5, -21, 8, -35, 29, -2, -32, -34, 3, 18, -26],\n [0, 0, -10, -9, 3, -11, -7, -14, 24, 16, -15, -28],\n [0, 0, 0, -33, 23, 19, -4, -25, 17, -7, 31, -32],\n [0, 0, 0, 0, 29, -1, 11, -2, 27, -27, -17, -10],\n [0, 0, 0, 0, 0, 4, 19, 22, -5, 11, 1, 21],\n [0, 0, 0, 0, 0, 0, -18, -7, 4, -33, 22, 35],\n [0, 0, 0, 0, 0, 0, 0, 33, -33, -7, -23, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 34, 15, 31, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -22, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[27, -14, 17, -24, -14, 3, 11, 28, 8, -20, 23, -2],\n [0, 34, 19, -12, -9, -20, -34, -5, 27, 11, -17, 20],\n [0, 0, -30, -5, 14, -7, -15, 5, 33, 33, 20, -8],\n [0, 0, 0, 8, -4, -7, -33, 33, -25, 12, 17, 20],\n [0, 0, 0, 0, 20, -8, -13, -5, 30, 25, -20, 23],\n [0, 0, 0, 0, 0, 1, -6, -20, 11, -8, -15, 5],\n [0, 0, 0, 0, 0, 0, 27, -35, -13, -3, 21, 18],\n [0, 0, 0, 0, 0, 0, 0, -18, 6, 3, -10, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 19, 18, -21, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 24, -13, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23618", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[23, -17, 26, 17, 30, -28, 10, -24, 29, -13, 3, 24],\n [-9, 21, 8, 34, -8, -13, -2, -11, -25, 12, 29, -26],\n [-10, -26, -18, 24, 9, -10, -27, 0, -21, -12, 4, -34],\n [-32, -16, 3, 9, -10, 24, 33, 32, 34, -5, 33, -29],\n [33, -32, 1, -34, 13, -19, -19, 4, 15, -8, 10, 13],\n [-19, -9, 26, -25, 8, 0, -20, 24, 16, -14, 35, 2],\n [29, 15, -13, -21, -5, -8, 31, 6, -11, -3, -13, 17],\n [-20, 1, -31, -25, -24, -15, -18, -22, -3, -15, -10, -11],\n [-1, 27, -16, 27, 30, -24, -4, 12, 23, -16, 1, 4],\n [25, 20, -22, 0, -2, -30, 10, -14, -13, 28, 8, -25],\n [32, 25, 20, 15, 27, -6, -26, -13, -35, 12, -32, -8],\n [8, 31, -34, 22, -30, 6, -19, 1, 8, -13, 4, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-558", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, 1, 34, -20, -16, 10, -11, 23, -4, -19, -26, -19],\n [0, 30, -7, -32, -6, 25, 22, -2, -12, -11, -11, -6],\n [0, 0, 3, -34, -2, -20, 12, -12, 14, -34, 3, 23],\n [0, 0, 0, -21, 24, 28, -34, 34, 28, 0, -23, -34],\n [0, 0, 0, 0, -1, 21, 5, 9, -2, -17, 6, -19],\n [0, 0, 0, 0, 0, -13, 7, 17, 31, 30, -2, -1],\n [0, 0, 0, 0, 0, 0, -25, -32, 15, 2, 15, 12],\n [0, 0, 0, 0, 0, 0, 0, 12, 21, -3, 2, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 26, 10, 12, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -5, -15, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1281701", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, 12, 20, 0, 2, 3, 14, -2, 20, 20, -10, 6],\n [12, -12, -16, -7, -5, 2, -21, 1, 24, -10, -4, -2],\n [20, -16, -27, 15, 18, -6, 8, -22, -16, -7, -12, 5],\n [0, -7, 15, -1, 17, -4, 24, -5, 10, -18, 12, 5],\n [2, -5, 18, 17, 16, 10, -7, 32, -4, 1, -4, 23],\n [3, 2, -6, -4, 10, 17, 3, -14, -6, -12, 17, 8],\n [14, -21, 8, 24, -7, 3, 34, 9, -10, -24, -10, -20],\n [-2, 1, -22, -5, 32, -14, 9, -7, -7, -10, -22, -2],\n [20, 24, -16, 10, -4, -6, -10, -7, 19, -8, -6, 20],\n [20, -10, -7, -18, 1, -12, -24, -10, -8, 22, -4, 18],\n [-10, -4, -12, 12, -4, 17, -10, -22, -6, -4, 19, -14],\n [6, -2, 5, 5, 23, 8, -20, -2, 20, 18, -14, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2586", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, 12, 21, -1, 7, -10, -1, 10, -10, 10, 22, 26],\n [12, -34, 10, -15, -5, -13, 8, -29, -8, -15, 5, -14],\n [21, 10, -20, 28, 20, 16, -22, 16, -28, -9, 2, 12],\n [-1, -15, 28, -13, -23, 18, -23, 6, -6, -25, 16, -13],\n [7, -5, 20, -23, -18, -8, 5, 0, -10, 26, -24, 8],\n [-10, -13, 16, 18, -8, 19, -8, 8, -16, 9, 8, 24],\n [-1, 8, -22, -23, 5, -8, -33, -12, -4, 10, 6, -6],\n [10, -29, 16, 6, 0, 8, -12, 9, -18, 16, -10, -6],\n [-10, -8, -28, -6, -10, -16, -4, -18, -9, 30, 6, 14],\n [10, -15, -9, -25, 26, 9, 10, 16, 30, 17, 8, -24],\n [22, 5, 2, 16, -24, 8, 6, -10, 6, 8, 4, 13],\n [26, -14, 12, -13, 8, 24, -6, -6, 14, -24, 13, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5711", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[14, -14, -14, 4, -4, -30, 26, -32, -6, -14, 11, -4],\n [-14, -7, 24, 3, -27, 8, 7, 16, -10, 6, -11, 6],\n [-14, 24, 10, 2, 20, -14, 27, -25, -6, 2, -2, 14],\n [4, 3, 2, -13, 4, -2, -7, -4, -9, 26, 32, -7],\n [-4, -27, 20, 4, -9, -13, 14, -7, 0, -3, 17, -6],\n [-30, 8, -14, -2, -13, -3, -1, 4, 24, 8, -5, 16],\n [26, 7, 27, -7, 14, -1, -33, -1, -18, -21, -16, -5],\n [-32, 16, -25, -4, -7, 4, -1, -19, -12, 14, 8, 30],\n [-6, -10, -6, -9, 0, 24, -18, -12, -9, -23, 21, 4],\n [-14, 6, 2, 26, -3, 8, -21, 14, -23, -28, 0, 4],\n [11, -11, -2, 32, 17, -5, -16, 8, 21, 0, 15, -18],\n [-4, 6, 14, -7, -6, 16, -5, 30, 4, 4, -18, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "319", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-32, -24, -24, -19, 0, -2, -14, 24, 12, 1, -4, -10],\n [-24, -24, -8, 10, -25, 2, -3, 0, -2, 20, 13, 4],\n [-24, -8, 18, -5, -14, 6, 12, 10, 14, -10, -28, -6],\n [-19, 10, -5, -14, 18, 32, -8, 2, -2, 29, -17, 0],\n [0, -25, -14, 18, 25, -14, -3, 0, 6, 2, -27, 2],\n [-2, 2, 6, 32, -14, 20, -14, -7, -3, -2, 14, 2],\n [-14, -3, 12, -8, -3, -14, -15, -13, -28, 9, -3, 10],\n [24, 0, 10, 2, 0, -7, -13, -32, 8, 16, 14, -8],\n [12, -2, 14, -2, 6, -3, -28, 8, 29, -23, 10, -25],\n [1, 20, -10, 29, 2, -2, 9, 16, -23, 30, -2, 12],\n [-4, 13, -28, -17, -27, 14, -3, 14, 10, -2, 24, 6],\n [-10, 4, -6, 0, 2, 2, 10, -8, -25, 12, 6, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-274", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-4, 18, -22, 6, 2, -18, -8, -14, -2, -4, -2, -24],\n [18, 20, 6, -23, -5, -21, -24, 0, -29, -24, 15, -4],\n [-22, 6, 24, -3, -9, 8, 16, 22, 24, 4, -2, 4],\n [6, -23, -3, -22, 8, 14, -6, 11, -26, 0, 4, 8],\n [2, -5, -9, 8, -32, 0, 4, -2, -5, 4, 2, 11],\n [-18, -21, 8, 14, 0, 10, 18, 2, -10, 26, 19, 22],\n [-8, -24, 16, -6, 4, 18, -18, 22, -12, -23, -30, 17],\n [-14, 0, 22, 11, -2, 2, 22, 11, 2, 1, 16, 14],\n [-2, -29, 24, -26, -5, -10, -12, 2, -13, -8, 4, -8],\n [-4, -24, 4, 0, 4, 26, -23, 1, -8, 26, -8, -6],\n [-2, 15, -2, 4, 2, 19, -30, 16, 4, -8, 14, -25],\n [-24, -4, 4, 8, 11, 22, 17, 14, -8, -6, -25, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "476", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[15, 23, -34, -34, -31, -14, -3, 33, -8, 22, -22, 14],\n [0, -21, 32, 7, 19, 13, -18, -11, -24, 19, 11, 31],\n [0, 0, 24, 7, 1, -4, 16, 17, 20, -34, 12, -20],\n [0, 0, 0, -34, 4, 6, -11, -35, -20, 6, 1, 1],\n [0, 0, 0, 0, 4, 18, 10, 0, 5, 31, -13, 7],\n [0, 0, 0, 0, 0, -15, -20, 26, 24, -27, 30, -10],\n [0, 0, 0, 0, 0, 0, -25, 27, 7, 31, 7, -35],\n [0, 0, 0, 0, 0, 0, 0, 14, -23, -1, 19, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, -18, 29, -26, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 21, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-537", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-3, 22, -14, 14, -2, 2, -16, 19, -12, 22, -2, -20],\n [22, 19, 19, -18, -1, 7, 20, -12, -9, 10, -8, -8],\n [-14, 19, 20, -10, 10, 24, 28, -9, -9, -6, 9, -13],\n [14, -18, -10, -13, -12, -8, -10, -8, -4, 2, 10, -14],\n [-2, -1, 10, -12, 9, -24, -18, 10, -2, 25, -4, 24],\n [2, 7, 24, -8, -24, 4, 0, -7, 8, 12, 12, 5],\n [-16, 20, 28, -10, -18, 0, 25, 19, 14, 26, 18, 0],\n [19, -12, -9, -8, 10, -7, 19, -10, -12, -16, 0, -19],\n [-12, -9, -9, -4, -2, 8, 14, -12, 30, 24, 27, -10],\n [22, 10, -6, 2, 25, 12, 26, -16, 24, 27, 18, -28],\n [-2, -8, 9, 10, -4, 12, 18, 0, 27, 18, -22, -22],\n [-20, -8, -13, -14, 24, 5, 0, -19, -10, -28, -22, -26]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-149", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[17, -2, -6, -4, -25, -6, -35, -30, 20, 31, 22, -17],\n [25, 26, 35, -1, 7, -31, 10, -1, 0, -32, 25, -34],\n [-1, 10, -32, 24, 12, -32, 34, 15, -19, -32, 21, -29],\n [12, -3, 32, 20, -11, -1, 3, -13, -25, -14, 11, -24],\n [-1, -2, -35, -4, -32, -12, 35, -14, -1, -7, -19, -8],\n [11, 5, -19, -32, 5, -30, 8, -12, 18, -5, -27, 17],\n [-34, -16, -32, 8, 26, -23, -16, 16, -30, -21, 28, 0],\n [0, -33, 4, 2, 9, 26, 30, -12, -30, -34, -10, 8],\n [-35, -34, -25, -6, -2, 25, -2, 35, -34, 28, -33, 30],\n [-6, -1, -14, 26, 18, 24, 2, -6, -34, -16, 8, 32],\n [-27, -22, -25, -26, 35, 21, -30, -19, -23, 23, 11, -32],\n [-10, -4, 20, 31, -25, 22, 16, -7, -34, 32, 13, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-47", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-19, -33, 6, 12, -5, -35, 33, -35, 0, 23, 25, -32],\n [13, 5, 24, -15, 4, 4, -9, 6, 0, -25, -1, 1],\n [-24, 14, -11, 27, -26, 22, -33, 33, 19, -24, 9, 5],\n [6, -3, 34, -30, -34, -10, 12, 21, 33, 10, 12, 5],\n [-20, 16, -24, -21, -15, -11, -6, -3, 30, -3, -8, 5],\n [-35, 27, -1, 12, 3, -16, 2, -13, -24, -30, -29, 15],\n [-22, -20, -13, -18, -29, 32, -11, -3, 15, -13, 14, -15],\n [27, -15, -9, -10, -17, 22, -29, -21, 30, 30, 11, 10],\n [8, -27, 35, -25, 20, -32, 1, -2, 11, -6, 10, 34],\n [-3, 14, -21, -16, 4, -4, -24, -21, 23, 24, -32, -9],\n [22, 17, 3, -21, -17, -22, 35, -30, -2, -11, 5, 14],\n [6, 31, 30, -14, -8, -35, 8, -13, -31, -21, 33, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[8, -3, 24, 34, 10, -9, -8, 10, -2, -7, 19, 21],\n [-14, -21, -9, 24, -15, 1, -12, 12, -13, -23, 23, -31],\n [-21, -12, 20, -28, 6, -29, -12, -9, -33, 12, -14, 4],\n [12, 13, -7, -19, -29, 7, -1, 4, 31, -30, -34, 3],\n [-3, -13, -3, -6, -27, 35, 26, 35, -11, 11, 15, -8],\n [0, 25, 31, -3, 26, -10, 28, 19, -30, 31, -22, 13],\n [14, -19, 19, 24, 10, 27, 12, 26, -20, 29, 12, 18],\n [26, -30, -3, 35, 6, -6, -29, 4, 25, -22, 25, 28],\n [19, 31, 8, 22, -2, 21, -7, 1, 32, 26, -35, 16],\n [21, 21, 30, 25, 16, 13, -13, 33, -15, 22, -27, 35],\n [22, 12, 25, 1, -31, -3, 29, -29, 6, 24, -32, -32],\n [-18, 14, -23, -5, 6, 34, -25, -15, -10, -21, -12, 24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-193", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-1, -8, 9, -5, 4, 18, -12, 16, 24, 12, 9, -5],\n [-8, 8, 24, 7, -16, 11, 14, -29, -4, 0, 16, -10],\n [9, 24, -20, -9, 4, 15, -6, 7, -26, 4, 16, 21],\n [-5, 7, -9, 7, 14, -10, 0, 2, -23, 12, 4, -14],\n [4, -16, 4, 14, 16, 16, -4, -22, 0, -15, 0, 29],\n [18, 11, 15, -10, 16, 25, -18, 16, 10, 21, 6, -7],\n [-12, 14, -6, 0, -4, -18, 34, 4, 10, 29, 4, 13],\n [16, -29, 7, 2, -22, 16, 4, -10, 18, -4, -24, 3],\n [24, -4, -26, -23, 0, 10, 10, 18, 29, 4, -24, -2],\n [12, 0, 4, 12, -15, 21, 29, -4, 4, -2, -30, -12],\n [9, 16, 16, 4, 0, 6, 4, -24, -24, -30, -15, 15],\n [-5, -10, 21, -14, 29, -7, 13, 3, -2, -12, 15, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2426", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[-12, -12, -1, 11, 9, 8, 0, -10, -6, 12, -16, -12],\n [-12, 11, -4, 12, -24, -8, -16, 19, -1, 17, 20, -19],\n [-1, -4, -24, 10, 9, -8, -4, -22, -6, -8, -19, -22],\n [11, 12, 10, 4, -18, 16, -15, 16, -12, 2, -22, 16],\n [9, -24, 9, -18, -11, -6, 0, -20, 30, -10, -4, -2],\n [8, -8, -8, 16, -6, -14, 22, -14, -11, 2, 28, -4],\n [0, -16, -4, -15, 0, 22, 8, 22, 5, 1, 12, 10],\n [-10, 19, -22, 16, -20, -14, 22, 26, 29, -12, 0, 18],\n [-6, -1, -6, -12, 30, -11, 5, 29, -35, -25, 0, -8],\n [12, 17, -8, 2, -10, 2, 1, -12, -25, -1, -8, -2],\n [-16, 20, -19, -22, -4, 28, 12, 0, 0, -8, -1, -23],\n [-12, -19, -22, 16, -2, -4, 10, 18, -8, -2, -23, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-33, -18, -12, 5, -21, 0, -4, -10, 0, 2, -10, 9],\n [-18, 7, -8, 4, 2, -24, -22, 20, -4, 12, 1, -4],\n [-12, -8, -6, -10, 5, -10, 9, 22, 7, -7, 4, 4],\n [5, 4, -10, 6, 11, 0, -17, -32, 15, -16, 6, 2],\n [-21, 2, 5, 11, 28, -2, 12, -15, -17, 8, -31, -10],\n [0, -24, -10, 0, -2, -5, 26, 24, -21, 10, 6, -10],\n [-4, -22, 9, -17, 12, 26, -8, 12, 18, -26, 7, 14],\n [-10, 20, 22, -32, -15, 24, 12, -4, 10, 12, -14, -12],\n [0, -4, 7, 15, -17, -21, 18, 10, -15, -4, 8, 20],\n [2, 12, -7, -16, 8, 10, -26, 12, -4, -12, -24, -5],\n [-10, 1, 4, 6, -31, 6, 7, -14, 8, -24, -11, -22],\n [9, -4, 4, 2, -10, -10, 14, -12, 20, -5, -22, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2143", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (9, 7) of the inverse. Round your answer to the nearest integer:\n[[-28, -29, -11, 12, -1, -18, -25, -7, -20, -30, -21, -7],\n [0, 30, -23, 35, 21, 15, -8, -13, -35, 35, -1, 0],\n [0, 0, 26, -24, -22, 26, -14, -7, 23, -21, -15, 35],\n [0, 0, 0, -10, 33, 0, 19, 33, -17, -2, 34, 27],\n [0, 0, 0, 0, -14, 22, -11, -17, 18, 35, -34, -14],\n [0, 0, 0, 0, 0, 23, -25, -24, -18, -35, 25, -35],\n [0, 0, 0, 0, 0, 0, 21, 5, -13, -1, 12, 6],\n [0, 0, 0, 0, 0, 0, 0, 9, 29, -24, 10, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, -25, -14, -11, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 10, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-35, 6, 21, 21, -1, -4, -20, -25, -7, 8, -10, -17],\n [6, 8, 10, 24, -24, 28, -14, -4, -2, -3, 22, -28],\n [21, 10, -14, 8, -8, -12, -20, -24, 0, 9, 8, 0],\n [21, 24, 8, -23, -8, -12, 14, 10, 20, -8, 0, -10],\n [-1, -24, -8, -8, 2, 8, 8, -12, -2, 0, 4, 8],\n [-4, 28, -12, -12, 8, -5, -2, -24, 30, 31, -14, 18],\n [-20, -14, -20, 14, 8, -2, -34, 6, 10, 6, -10, -13],\n [-25, -4, -24, 10, -12, -24, 6, -19, -22, 22, -12, 4],\n [-7, -2, 0, 20, -2, 30, 10, -22, -23, 22, -2, 24],\n [8, -3, 9, -8, 0, 31, 6, 22, 22, 30, -7, 16],\n [-10, 22, 8, 0, 4, -14, -10, -12, -2, -7, -21, -24],\n [-17, -28, 0, -10, 8, 18, -13, 4, 24, 16, -24, 21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6601", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[19, -22, -35, 21, -22, 15, 22, -27, 12, -9, -8, 20],\n [-2, -34, -12, 13, 4, -28, 33, 31, -6, 16, 3, 35],\n [-23, -34, 30, 30, -21, 23, -18, 33, -6, -31, 4, -15],\n [28, -28, -30, 32, 22, 16, -6, 21, -9, 8, 33, -25],\n [7, -1, -25, 18, 14, 25, -31, -10, -3, -13, 22, 35],\n [-27, -20, 8, -8, -13, -24, 6, -27, 22, -17, 0, 30],\n [21, 21, -11, -23, 23, -23, -9, 4, 16, -19, 15, -34],\n [-24, -8, -11, -5, -9, 23, -35, -1, -35, -27, -3, 8],\n [17, 11, 10, -18, -20, 23, 16, 17, 24, -27, -8, 30],\n [-14, -1, 5, -5, 27, 23, -26, 0, 11, 22, 11, -14],\n [-6, -13, 11, 18, -20, -26, 0, -8, 6, -19, 12, 16],\n [24, 3, 15, 15, -31, 28, 0, 3, -25, 18, -32, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-198", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (8, 2) of the inverse. Round your answer to the nearest integer:\n[[19, -2, -23, 15, 4, 14, -8, 29, 32, 12, 1, 10],\n [-2, -3, 10, 0, -2, 24, 0, -22, 23, 2, 6, -17],\n [-23, 10, 8, -2, 14, -8, -9, 8, -24, -18, -2, -7],\n [15, 0, -2, -11, 5, -2, -12, -8, -5, 0, -6, -16],\n [4, -2, 14, 5, 24, -6, 16, 11, 3, -31, 23, -2],\n [14, 24, -8, -2, -6, 4, -27, -4, -16, -29, 14, -2],\n [-8, 0, -9, -12, 16, -27, 8, -5, -1, -14, 12, -27],\n [29, -22, 8, -8, 11, -4, -5, -29, 2, -6, 2, -10],\n [32, 23, -24, -5, 3, -16, -1, 2, 0, -16, -10, -12],\n [12, 2, -18, 0, -31, -29, -14, -6, -16, -5, -28, -3],\n [1, 6, -2, -6, 23, 14, 12, 2, -10, -28, 25, -12],\n [10, -17, -7, -16, -2, -2, -27, -10, -12, -3, -12, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (9, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-22, -24, -20, 4, -16, 7, 15, -12, 24, -12, 34, 10],\n [-24, -25, -20, -20, 14, 23, -32, -29, 25, -2, 0, 0],\n [-20, -20, 16, 7, 16, 4, 0, 14, 0, -1, -26, 16],\n [4, -20, 7, -34, 8, -2, 10, 9, 13, -17, 24, -14],\n [-16, 14, 16, 8, -16, -8, -17, 25, 10, 12, 4, -9],\n [7, 23, 4, -2, -8, -5, -10, -20, -8, 12, -15, -26],\n [15, -32, 0, 10, -17, -10, -20, -26, 8, -9, 4, 10],\n [-12, -29, 14, 9, 25, -20, -26, 1, 2, 8, 25, -2],\n [24, 25, 0, 13, 10, -8, 8, 2, 29, 3, 15, -4],\n [-12, -2, -1, -17, 12, 12, -9, 8, 3, 25, 0, 2],\n [34, 0, -26, 24, 4, -15, 4, 25, 15, 0, 26, 18],\n [10, 0, 16, -14, -9, -26, 10, -2, -4, 2, 18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[32, -29, -12, -27, -2, 19, -24, 22, 23, 32, -19, -6],\n [0, 26, 26, -18, -15, -1, -19, 18, -12, -21, -22, 11],\n [0, 0, 4, 26, 18, 24, -25, -10, -9, -6, 17, 1],\n [0, 0, 0, -10, -1, 33, -25, -6, -15, -32, -19, 24],\n [0, 0, 0, 0, 14, -9, -34, 29, -22, -21, 15, -14],\n [0, 0, 0, 0, 0, -3, 29, 5, 23, 22, -32, -33],\n [0, 0, 0, 0, 0, 0, 25, 26, -29, -17, 34, 26],\n [0, 0, 0, 0, 0, 0, 0, 3, 32, 7, 6, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 20, 10, -30, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -29, -29, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5133671", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[20, -9, 16, -16, -10, -15, -9, -2, -4, 11, -11, 12],\n [-9, 7, 0, -6, -2, -4, -18, 19, -12, 26, 17, -26],\n [16, 0, 18, 6, -18, -10, -22, 4, -22, 0, -14, 2],\n [-16, -6, 6, -13, -19, 0, 13, -22, 27, -2, 10, 3],\n [-10, -2, -18, -19, -32, -6, -2, 19, 13, 12, 13, -8],\n [-15, -4, -10, 0, -6, -20, -29, 4, -28, 11, -17, 7],\n [-9, -18, -22, 13, -2, -29, -34, 5, -20, -6, -12, 6],\n [-2, 19, 4, -22, 19, 4, 5, -22, 1, -6, -2, 25],\n [-4, -12, -22, 27, 13, -28, -20, 1, -23, 18, 0, 5],\n [11, 26, 0, -2, 12, 11, -6, -6, 18, 19, -9, 0],\n [-11, 17, -14, 10, 13, -17, -12, -2, 0, -9, 4, -15],\n [12, -26, 2, 3, -8, 7, 6, 25, 5, 0, -15, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6196", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (7, 3) of the inverse. Round your answer to the nearest integer:\n[[-13, -29, 20, -14, -16, -30, -5, 26, 6, -23, -9, 11],\n [21, -32, -14, 18, -35, 15, 27, -6, -2, -7, 32, 35],\n [21, -3, 29, -2, 14, 21, 13, 12, 20, -24, 20, -27],\n [-7, 1, -15, -35, 29, -9, -12, 13, -2, 21, 14, 10],\n [-26, -29, -22, -21, 15, 19, -4, 23, 3, 11, -3, -3],\n [2, -15, 33, 7, -25, 24, 10, 20, 5, 7, 16, 12],\n [-24, -29, 8, -30, -17, -20, -25, 23, -1, 24, -1, -19],\n [3, -32, 12, 35, 12, 26, -13, 24, -8, 6, 2, 22],\n [27, 23, -15, 14, -34, -23, 20, -19, 9, 17, 1, -22],\n [34, 5, 20, 8, -14, -13, 8, -4, 1, 10, 3, -2],\n [-35, 2, -7, 30, -16, 6, 21, -28, 23, -25, 0, -8],\n [-35, 16, -33, -23, -13, -2, -10, -31, -28, -11, 19, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-28, -17, -23, -10, 3, 15, -30, -23, 16, 0, -19, 29],\n [0, -23, 27, 19, -22, 35, 5, 7, 27, 5, -27, -16],\n [0, 0, 30, -6, -11, -6, -5, 0, 5, 25, -7, -2],\n [0, 0, 0, -7, -33, -11, 33, 19, 20, -7, 5, -34],\n [0, 0, 0, 0, 10, 24, 10, -17, -35, -18, -29, -4],\n [0, 0, 0, 0, 0, 18, -32, -12, -13, 13, -15, 34],\n [0, 0, 0, 0, 0, 0, 22, -35, 28, -10, 13, 8],\n [0, 0, 0, 0, 0, 0, 0, 23, -7, -4, 18, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, -3, 22, -5, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 1, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-271", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (9, 9) of the inverse. Round your answer to the nearest integer:\n[[15, 10, 23, 3, 2, 19, -31, -31, 14, 6, -17, -2],\n [0, -15, 9, 24, 17, -17, -1, -22, -24, 13, -33, -9],\n [0, 0, -9, -21, -6, 23, 9, 17, 9, 25, -25, 15],\n [0, 0, 0, -3, -14, 24, -16, -25, -1, -1, 29, 13],\n [0, 0, 0, 0, 15, -15, 2, 0, -22, -3, -13, 2],\n [0, 0, 0, 0, 0, 32, -11, 21, 16, -29, -29, 20],\n [0, 0, 0, 0, 0, 0, 35, -33, -23, 12, 30, -33],\n [0, 0, 0, 0, 0, 0, 0, -31, 34, 31, -13, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, -35, -29, 34, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -35, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-31, -10, -10, -34, -14, -14, -10, 20, 10, -2, 14, 10],\n [-10, 32, -8, -11, 16, 4, -16, 24, 25, -5, 13, 14],\n [-10, -8, 1, 24, 6, -12, 13, 14, 27, 20, -14, -20],\n [-34, -11, 24, -5, 11, -11, -12, 5, 2, -32, 1, -32],\n [-14, 16, 6, 11, -23, -16, 6, -1, -24, 24, 12, -1],\n [-14, 4, -12, -11, -16, -28, 6, -6, -15, -16, 6, 10],\n [-10, -16, 13, -12, 6, 6, 21, 4, 24, 8, -4, -10],\n [20, 24, 14, 5, -1, -6, 4, 16, 10, 16, 17, -24],\n [10, 25, 27, 2, -24, -15, 24, 10, 11, -4, 12, -16],\n [-2, -5, 20, -32, 24, -16, 8, 16, -4, -28, 18, -18],\n [14, 13, -14, 1, 12, 6, -4, 17, 12, 18, -26, 10],\n [10, 14, -20, -32, -1, 10, -10, -24, -16, -18, 10, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-81", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-27, 30, 23, -23, -30, -11, 27, 23, 10, -21, 30, 6],\n [0, -13, -21, 2, 20, -2, 29, -2, -20, 14, 33, 6],\n [0, 0, 33, -8, -6, 14, -19, -26, -25, 11, -28, -5],\n [0, 0, 0, 10, -33, -23, -8, 16, 25, -12, -26, 6],\n [0, 0, 0, 0, 29, -23, 23, 32, 20, -6, 28, 31],\n [0, 0, 0, 0, 0, -7, 15, 23, -5, -27, 34, -6],\n [0, 0, 0, 0, 0, 0, -16, -31, -2, -22, -23, 25],\n [0, 0, 0, 0, 0, 0, 0, 20, 35, 6, -35, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 27, -24, 16, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -23, 14, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13632", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[7, -6, -12, 24, -26, -9, -18, -7, 8, 2, -20, 23],\n [-6, -14, 28, -2, 16, 26, 8, 6, 20, -9, 0, 6],\n [-12, 28, 30, -13, -24, 24, 8, 3, 18, 11, 8, 12],\n [24, -2, -13, 12, -10, 10, 12, 16, 18, 14, -12, -16],\n [-26, 16, -24, -10, 18, -16, -5, 20, 3, 30, 8, 5],\n [-9, 26, 24, 10, -16, 34, 3, -30, -16, 14, -14, 15],\n [-18, 8, 8, 12, -5, 3, 6, 0, -16, -6, -2, -4],\n [-7, 6, 3, 16, 20, -30, 0, 26, 16, 16, 16, -18],\n [8, 20, 18, 18, 3, -16, -16, 16, -26, 30, -12, 2],\n [2, -9, 11, 14, 30, 14, -6, 16, 30, 16, -9, 11],\n [-20, 0, 8, -12, 8, -14, -2, 16, -12, -9, 3, 20],\n [23, 6, 12, -16, 5, 15, -4, -18, 2, 11, 20, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "293", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[14, -16, 27, 19, -2, -4, 7, -23, -34, 25, -22, 6],\n [-21, -26, 20, 17, 22, 26, 21, 27, -32, -2, -4, -2],\n [34, 4, -1, -21, 15, -16, 1, 2, -15, -26, 18, -27],\n [6, -20, -12, -32, 8, -13, 6, 30, -17, -16, -8, -12],\n [-34, -29, -35, -25, 15, 24, -5, -6, -12, -18, 22, -19],\n [10, -17, -24, -24, 14, 30, -16, -30, -35, -29, 19, -21],\n [-12, -7, 35, -2, 1, 6, 28, -17, -13, 35, -30, 19],\n [3, -11, -32, -3, 30, -34, -22, 14, -25, -2, 2, 3],\n [-14, 6, 21, 2, -27, -7, 33, 6, 24, 3, 24, 17],\n [-28, -15, 20, 12, 11, -27, -35, 19, -5, -25, 30, 24],\n [-5, 14, 24, 26, 3, -33, 22, 32, -6, 31, 32, 22],\n [17, -22, -26, -14, 27, 25, 10, 1, -15, -33, -17, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-12, 12, 22, 4, -29, 10, -21, -31, 23, 34, -14, -8],\n [0, -17, -22, 12, -29, -4, -14, 10, -23, -14, -26, 8],\n [0, 0, 26, 19, 13, 14, -17, 22, 12, -24, -16, 9],\n [0, 0, 0, -33, -18, -15, 21, 6, 26, -6, 25, 0],\n [0, 0, 0, 0, 21, 27, 28, -19, 17, 4, 34, 14],\n [0, 0, 0, 0, 0, -28, 21, 34, -11, -2, -11, -18],\n [0, 0, 0, 0, 0, 0, -21, -20, -22, 11, 18, 22],\n [0, 0, 0, 0, 0, 0, 0, -8, -16, 19, 15, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, -11, -10, 15, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 15, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10518", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[27, -30, -8, 15, 17, 8, 29, -24, -8, 32, -6, -1],\n [-30, -6, 27, -28, -3, 7, 7, 9, 18, 29, -29, 0],\n [-11, 1, -24, -4, 13, 2, 20, 29, -10, 21, -22, 20],\n [34, 5, 15, 31, -24, 13, -35, -17, 30, 22, -32, -28],\n [-9, -10, 7, 4, 14, 31, -7, 6, -18, -15, 31, 26],\n [-9, 11, -10, -27, -24, -20, 11, 20, 30, 15, -9, 30],\n [26, 35, -28, 2, -30, 23, -17, 20, -8, -26, 9, 29],\n [14, -4, 25, -20, -30, 30, 26, 30, 31, -17, -32, 7],\n [-18, 10, 10, -15, -6, 28, 5, -19, -31, -31, 12, 2],\n [-30, 22, -22, 23, 29, -23, -9, -11, 20, 32, 23, 13],\n [-18, -33, 21, -30, 33, -5, -28, -26, -33, -24, -17, -15],\n [-22, -7, -29, 13, 29, -29, -22, -20, -20, -23, -7, 25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-682", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -19, -5, 23, 11, -30, -4, -5, -18, -27, -33, 35],\n [0, -23, -2, 7, -3, 33, 0, 32, 11, 25, 9, 12],\n [0, 0, 32, -25, -20, 29, 35, 31, 35, -35, 35, -32],\n [0, 0, 0, -32, 30, 7, -10, -21, -30, 1, 7, 6],\n [0, 0, 0, 0, 30, 29, -31, -6, 7, -4, 31, 31],\n [0, 0, 0, 0, 0, 32, 34, -17, 8, 2, 8, -30],\n [0, 0, 0, 0, 0, 0, 7, -20, -13, 23, -1, 5],\n [0, 0, 0, 0, 0, 0, 0, -24, 35, -9, -10, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, -9, 5, 11, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 14, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "691", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-35, -17, 20, 28, -2, 28, -26, 24, 3, 30, -4, 15],\n [0, 21, 24, 19, -30, -29, 30, -10, -31, -35, -34, 29],\n [0, 0, 15, 33, 5, 22, 32, -12, 20, 0, -34, 20],\n [0, 0, 0, 26, 28, -8, -8, -32, 9, -23, -32, 25],\n [0, 0, 0, 0, -1, 22, 27, -3, -3, 33, 4, 11],\n [0, 0, 0, 0, 0, -32, -2, 2, -16, 10, -17, -35],\n [0, 0, 0, 0, 0, 0, -6, -11, -35, -3, 1, -7],\n [0, 0, 0, 0, 0, 0, 0, 7, -26, -26, 26, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, -15, 11, -14, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -16, -16, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "296200", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -23, -11, 31, 32, 11, 19, 7, -34, 9, 12, 26],\n [0, 11, -32, 24, 13, -2, 8, 20, 6, 14, 33, -3],\n [0, 0, 8, 32, 21, 0, 5, 20, -33, 20, 20, 29],\n [0, 0, 0, -9, 31, 29, -33, -33, 1, -16, -25, -12],\n [0, 0, 0, 0, 19, 0, 30, 1, -22, 10, 20, 14],\n [0, 0, 0, 0, 0, -23, 13, -11, -13, -10, 12, 0],\n [0, 0, 0, 0, 0, 0, -9, 10, 27, 6, 5, -2],\n [0, 0, 0, 0, 0, 0, 0, -21, 2, -13, -5, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 20, 26, 8, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 4, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2423306", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-19, 33, -6, 3, 25, -12, -1, 25, -21, 0, 19, 1],\n [26, 28, 3, -24, -28, 5, 33, -33, 7, 1, 21, -11],\n [-32, 22, 1, -28, -27, -35, -23, 32, -20, 8, 29, -22],\n [-10, -4, -34, -20, 13, -13, 24, 30, -16, -18, 23, -5],\n [-32, -9, -18, 27, 35, -17, 3, 30, 10, 2, 31, -7],\n [21, 12, 16, 12, 25, 31, 12, -28, 31, -22, 11, -12],\n [26, 22, -2, -5, 12, 9, -7, -7, 27, 12, -24, -9],\n [11, 30, 1, 9, 21, -18, -23, -7, 20, -16, -7, -30],\n [-10, 25, 7, 11, -10, -35, -10, 28, 26, -30, 26, 30],\n [6, -9, 29, -6, 29, 11, -4, -2, 11, -22, -31, 0],\n [-27, -1, -11, 10, -23, 25, -6, -4, -6, 20, 31, 35],\n [19, -28, 7, 12, 22, -4, 33, -29, -16, 26, -15, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[34, 12, -2, -9, -1, -3, -16, 1, 4, 8, 2, 16],\n [12, 12, 10, -7, -6, -2, 22, 18, -2, -2, -10, 3],\n [-2, 10, -25, 2, -4, -16, 0, -8, 4, 7, -14, 10],\n [-9, -7, 2, -26, -8, 14, -2, -4, -2, -4, -3, -2],\n [-1, -6, -4, -8, 2, 16, -3, 12, 16, 2, 6, -1],\n [-3, -2, -16, 14, 16, 18, -16, -8, -20, -11, 26, 7],\n [-16, 22, 0, -2, -3, -16, 33, -18, -13, 4, 7, 4],\n [1, 18, -8, -4, 12, -8, -18, 0, -4, 1, 2, 5],\n [4, -2, 4, -2, 16, -20, -13, -4, -30, 7, 4, -13],\n [8, -2, 7, -4, 2, -11, 4, 1, 7, 13, 12, -14],\n [2, -10, -14, -3, 6, 26, 7, 2, 4, 12, -2, 30],\n [16, 3, 10, -2, -1, 7, 4, 5, -13, -14, 30, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38287", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-12, -12, -8, -33, -33, -7, -4, 18, 2, 20, 29, -15],\n [5, -16, 24, 23, 19, -33, -22, 9, 24, 13, -27, 18],\n [34, 16, 27, 16, -14, 19, -33, -34, 23, -8, 1, 33],\n [-27, 26, -4, -1, 11, -18, 0, -17, -11, 10, 24, -13],\n [-9, -1, 19, 0, 35, -27, -15, -4, 30, 8, 29, -21],\n [-9, -20, 10, 12, 29, -17, 1, 22, 19, 17, 11, -33],\n [26, -35, 3, -3, -13, -2, 13, 13, 13, -26, 30, 35],\n [31, 3, 6, -35, 10, 0, 8, -5, 22, -32, 17, 21],\n [14, -31, 16, -19, -4, -30, 33, 25, -26, -13, 17, 25],\n [-17, -32, 10, -4, 10, 26, 18, 31, -12, 30, -18, 12],\n [10, 12, 26, -9, 26, 29, 16, -35, 14, 4, -19, -35],\n [-6, 31, -14, -1, 20, -22, 9, -3, -24, -12, 33, 21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "424", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (7, 9) rounded to the nearest integer?\n[[-27, -12, 20, -5, 1, -14, -8, -8, 0, 4, -16, 18],\n [-12, 28, 24, 2, -16, 29, -11, 14, 0, 24, 14, 26],\n [20, 24, -18, 11, 24, -6, -14, -1, -14, 0, 4, -8],\n [-5, 2, 11, -7, 4, 14, 5, 5, -16, -5, 2, 9],\n [1, -16, 24, 4, 21, -16, -4, -2, 11, -22, 4, 0],\n [-14, 29, -6, 14, -16, 9, -6, -9, 5, -10, 24, -18],\n [-8, -11, -14, 5, -4, -6, 30, 8, 2, 28, 0, 2],\n [-8, 14, -1, 5, -2, -9, 8, 2, 1, 4, -18, -12],\n [0, 0, -14, -16, 11, 5, 2, 1, -32, 10, 6, 3],\n [4, 24, 0, -5, -22, -10, 28, 4, 10, 12, 6, -2],\n [-16, 14, 4, 2, 4, 24, 0, -18, 6, 6, 9, 14],\n [18, 26, -8, 9, 0, -18, 2, -12, 3, -2, 14, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[20, 2, -4, -7, -14, 14, 17, 30, -10, 9, -23, -6],\n [2, -5, -4, 18, -12, 4, -14, 11, -6, -5, -20, 10],\n [-4, -4, 8, -12, 3, 12, -10, 16, -6, 8, -26, 21],\n [-7, 18, -12, 7, -33, -18, -13, 10, 18, -23, -8, 12],\n [-14, -12, 3, -33, 28, -17, 2, -18, -6, -10, -4, 0],\n [14, 4, 12, -18, -17, -5, 6, 14, -1, 16, -2, -24],\n [17, -14, -10, -13, 2, 6, 26, -13, -12, -12, 24, 5],\n [30, 11, 16, 10, -18, 14, -13, 12, 8, 0, -3, 10],\n [-10, -6, -6, 18, -6, -1, -12, 8, -24, -20, -14, 5],\n [9, -5, 8, -23, -10, 16, -12, 0, -20, 27, 10, 17],\n [-23, -20, -26, -8, -4, -2, 24, -3, -14, 10, 21, -1],\n [-6, 10, 21, 12, 0, -24, 5, 10, 5, 17, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-10, 16, 7, 14, -15, 2, 2, -3, -22, -10, -9, -16],\n [16, -34, 4, -15, 12, -15, 4, 2, -24, -14, -6, -1],\n [7, 4, 30, 12, 4, 26, -14, -10, 20, 22, 8, 12],\n [14, -15, 12, -18, -17, -21, 8, -8, 1, 0, -2, -24],\n [-15, 12, 4, -17, -14, -14, -6, -4, 6, -15, -4, -14],\n [2, -15, 26, -21, -14, -27, 15, 10, -23, 3, 23, -16],\n [2, 4, -14, 8, -6, 15, -21, -1, -12, -16, -17, -19],\n [-3, 2, -10, -8, -4, 10, -1, -13, 16, -11, -22, 12],\n [-22, -24, 20, 1, 6, -23, -12, 16, -4, 28, 4, -2],\n [-10, -14, 22, 0, -15, 3, -16, -11, 28, 20, 26, -2],\n [-9, -6, 8, -2, -4, 23, -17, -22, 4, 26, -31, 0],\n [-16, -1, 12, -24, -14, -16, -19, 12, -2, -2, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "245", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[13, -28, -33, 29, -34, 5, 17, -20, -27, 3, 28, 0],\n [0, 11, 13, 19, -26, 27, -10, 12, -6, -34, -7, 18],\n [0, 0, -15, -9, -2, -13, 3, 33, 9, 27, -28, -29],\n [0, 0, 0, 28, -7, 19, -24, -14, -13, 12, 9, -10],\n [0, 0, 0, 0, -8, 17, -22, 10, 31, 34, -16, -1],\n [0, 0, 0, 0, 0, 32, -25, 26, 25, 22, -7, 2],\n [0, 0, 0, 0, 0, 0, -12, 10, -11, -7, 31, -14],\n [0, 0, 0, 0, 0, 0, 0, -22, -24, 8, -27, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 28, -9, 17, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -35, -9, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-169", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[26, -26, -32, 3, -2, -11, 16, -21, -24, -35, -27, 23],\n [-22, -5, 17, 27, -26, 7, -18, 31, 23, -13, 10, 13],\n [-13, -24, -7, 23, 17, 32, 27, -7, -33, 1, 27, -13],\n [13, -33, -14, 0, -26, -27, 20, 19, -17, -3, -16, -1],\n [-5, 14, 10, -26, 31, -2, 15, 3, 32, -24, -10, 35],\n [31, -34, -24, 23, -4, 15, -25, -4, 28, 9, 18, -30],\n [-10, -28, -28, 2, -28, -19, -33, 5, 17, 34, 26, 17],\n [23, -13, 11, -1, -22, 29, 13, 0, -35, -14, -1, -33],\n [-24, 1, 22, -24, -34, 29, 22, 24, 5, -1, -25, 16],\n [16, 26, 27, -21, 34, 4, -27, 34, -19, -13, 22, 15],\n [21, -20, 9, 25, -24, -30, -32, -1, 11, -17, -9, -25],\n [34, 23, 5, 7, -8, 27, 31, 9, -12, 28, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[25, 0, 18, 1, 7, 10, -14, -23, -3, 5, -6, 1],\n [0, -23, 12, -24, 8, 7, 3, -22, -6, -22, -14, -26],\n [18, 12, 16, 6, -2, -10, 19, 11, 0, -2, -31, -3],\n [1, -24, 6, -31, 1, 17, 0, 22, -11, 0, -31, 14],\n [7, 8, -2, 1, -11, 12, 7, 2, 12, 9, -24, -6],\n [10, 7, -10, 17, 12, 17, -10, -21, -18, 6, 3, -20],\n [-14, 3, 19, 0, 7, -10, 20, 0, 26, 12, -5, 24],\n [-23, -22, 11, 22, 2, -21, 0, -4, -26, -2, 4, 21],\n [-3, -6, 0, -11, 12, -18, 26, -26, 20, -9, -12, -8],\n [5, -22, -2, 0, 9, 6, 12, -2, -9, 13, -14, -4],\n [-6, -14, -31, -31, -24, 3, -5, 4, -12, -14, -28, -1],\n [1, -26, -3, 14, -6, -20, 24, 21, -8, -4, -1, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "113", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[20, -8, -18, -2, 0, 8, 28, -10, 10, 2, 9, -2],\n [-8, 14, -2, 6, 24, 14, -16, 12, -19, 26, -8, 28],\n [-18, -2, -21, 12, -10, 4, -6, 6, -26, -16, 2, -15],\n [-2, 6, 12, 8, 0, 24, -12, -16, 2, 10, -15, -2],\n [0, 24, -10, 0, -34, -16, 6, 21, 6, 6, 28, 18],\n [8, 14, 4, 24, -16, -8, -11, -20, 14, -5, -11, -4],\n [28, -16, -6, -12, 6, -11, -2, -20, -14, 20, -20, 8],\n [-10, 12, 6, -16, 21, -20, -20, -19, 11, 4, -6, 2],\n [10, -19, -26, 2, 6, 14, -14, 11, 22, 16, -7, -6],\n [2, 26, -16, 10, 6, -5, 20, 4, 16, -35, 18, -20],\n [9, -8, 2, -15, 28, -11, -20, -6, -7, 18, -25, -16],\n [-2, 28, -15, -2, 18, -4, 8, 2, -6, -20, -16, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1620", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-29, -17, 4, -15, 22, -10, 0, 8, 28, -9, -28, -35],\n [0, -5, -29, -27, 35, 17, -20, -12, 10, -7, -6, 15],\n [0, 0, -2, -17, -8, -30, -19, 0, -35, -20, 32, 11],\n [0, 0, 0, -21, 31, 7, -28, 8, -10, 31, -4, 28],\n [0, 0, 0, 0, 12, -30, 18, 26, 18, 20, -6, -33],\n [0, 0, 0, 0, 0, -7, -5, 35, 35, 19, 7, -11],\n [0, 0, 0, 0, 0, 0, 9, -17, -31, 6, -6, 29],\n [0, 0, 0, 0, 0, 0, 0, 24, -13, -14, -13, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 9, -24, 1, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 26, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-485329", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-24, 32, 27, -10, 24, 25, -21, -31, -4, -14, -14, -24],\n [0, -20, 29, 15, -4, 17, -33, -23, 22, 9, -12, 15],\n [0, 0, -31, 14, 13, -18, -3, 22, -5, -2, -5, -9],\n [0, 0, 0, 32, -13, 16, 21, 15, 27, -8, -12, -14],\n [0, 0, 0, 0, -15, 31, 3, 26, 22, 26, 34, 0],\n [0, 0, 0, 0, 0, 35, -27, 35, -11, 29, -16, -8],\n [0, 0, 0, 0, 0, 0, -11, -14, 25, 16, -16, -16],\n [0, 0, 0, 0, 0, 0, 0, -24, -9, -17, -11, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 25, 11, 13, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -4, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-183", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-25, 17, -18, -29, -1, 8, 35, 3, -25, -26, -27, -28],\n [0, -15, -30, 23, 32, -13, -1, -24, 35, 21, -7, 31],\n [0, 0, -6, -9, -6, 19, -13, 1, -10, 0, 27, 1],\n [0, 0, 0, 1, -5, -11, -11, 10, -6, -16, -13, -35],\n [0, 0, 0, 0, 16, -6, -27, 33, 11, -2, -3, 29],\n [0, 0, 0, 0, 0, -3, 15, -31, 2, -31, 20, 35],\n [0, 0, 0, 0, 0, 0, -5, 27, -15, 14, -7, 24],\n [0, 0, 0, 0, 0, 0, 0, 16, -30, 34, 12, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, -10, 3, 27, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -12, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-393499", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 9) of the inverse of matrix 1/839 * A where A =\n[[23, 14, -10, 2, -12, 0, -8, 2, -5, 3, 2, 14],\n [14, -2, -23, 12, 4, 4, -6, 4, -2, 4, 2, -18],\n [-10, -23, -11, 22, -6, 24, -25, 0, -8, -4, 12, -18],\n [2, 12, 22, 13, -14, 23, 28, -6, -13, 10, -5, 0],\n [-12, 4, -6, -14, 1, 2, -21, 22, -12, 16, -22, 2],\n [0, 4, 24, 23, 2, -13, 11, -12, -4, -3, -10, -12],\n [-8, -6, -25, 28, -21, 11, 16, 2, -32, 15, 0, -18],\n [2, 4, 0, -6, 22, -12, 2, 25, 6, -5, 11, 28],\n [-5, -2, -8, -13, -12, -4, -32, 6, -27, -7, 12, -16],\n [3, 4, -4, 10, 16, -3, 15, -5, -7, 4, 24, -15],\n [2, 2, 12, -5, -22, -10, 0, 11, 12, 24, 30, 15],\n [14, -18, -18, 0, 2, -12, -18, 28, -16, -15, 15, -20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-29, 6, -5, 0, 25, 4, -12, -9, -6, 4, 14, -18],\n [6, -3, 7, 2, -2, 14, 8, 31, -6, 35, -23, 10],\n [-5, 7, -32, 4, 14, -8, -5, -26, 8, -26, -20, 16],\n [0, 2, 4, 10, 24, -18, -6, -34, 4, 22, -4, 16],\n [25, -2, 14, 24, 10, 0, 20, -22, 8, -2, -8, -7],\n [4, 14, -8, -18, 0, -21, 4, 0, -12, -8, 12, -18],\n [-12, 8, -5, -6, 20, 4, 22, 16, 26, -2, 10, -20],\n [-9, 31, -26, -34, -22, 0, 16, 19, 11, 0, -8, 34],\n [-6, -6, 8, 4, 8, -12, 26, 11, -13, 18, 18, -20],\n [4, 35, -26, 22, -2, -8, -2, 0, 18, 24, 2, 4],\n [14, -23, -20, -4, -8, 12, 10, -8, 18, 2, 32, 4],\n [-18, 10, 16, 16, -7, -18, -20, 34, -20, 4, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "916", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[33, 8, -34, 9, -6, -12, -28, -2, 7, -32, 13, 0],\n [8, 13, -12, -28, 26, -25, -12, 7, -18, 8, 34, -30],\n [-34, -12, 11, 14, -13, 0, -12, 8, 6, -12, -12, 8],\n [9, -28, 14, 25, -12, 6, -4, 19, 2, 4, 21, 18],\n [-6, 26, -13, -12, 4, 3, -22, 2, -14, -10, 16, -13],\n [-12, -25, 0, 6, 3, -32, -22, 6, 22, 17, 8, -20],\n [-28, -12, -12, -4, -22, -22, 3, -23, 10, 4, -8, 20],\n [-2, 7, 8, 19, 2, 6, -23, -31, 12, -28, -4, -4],\n [7, -18, 6, 2, -14, 22, 10, 12, 10, -22, -26, 15],\n [-32, 8, -12, 4, -10, 17, 4, -28, -22, -8, 0, -15],\n [13, 34, -12, 21, 16, 8, -8, -4, -26, 0, 1, 6],\n [0, -30, 8, 18, -13, -20, 20, -4, 15, -15, 6, 21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "870", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (12, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-22, -14, 16, -17, -3, 28, -12, -6, -5, 25, 24, 9],\n [-14, -23, -7, -14, -10, -16, -16, 0, -18, -14, -2, 0],\n [16, -7, -31, -9, 2, -20, -4, -2, 12, 27, -24, 12],\n [-17, -14, -9, -35, 0, -18, -2, -10, -27, 10, -23, 18],\n [-3, -10, 2, 0, 35, 8, -2, -27, -12, 10, -18, -4],\n [28, -16, -20, -18, 8, 28, -14, -26, 26, 14, 0, -28],\n [-12, -16, -4, -2, -2, -14, 9, -5, -8, 6, -18, -8],\n [-6, 0, -2, -10, -27, -26, -5, 17, 14, -14, -10, -18],\n [-5, -18, 12, -27, -12, 26, -8, 14, -20, -28, -10, -8],\n [25, -14, 27, 10, 10, 14, 6, -14, -28, -15, -10, 4],\n [24, -2, -24, -23, -18, 0, -18, -10, -10, -10, -26, -6],\n [9, 0, 12, 18, -4, -28, -8, -18, -8, 4, -6, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-17, -19, 8, 25, -35, 22, 5, -12, 7, -27, 30, -4],\n [0, -25, 29, -18, -28, -9, -27, -34, 10, 34, -31, -24],\n [0, 0, -6, 16, 11, 0, 34, -4, 8, -20, 35, -19],\n [0, 0, 0, -23, -24, 9, -20, 16, -15, -12, 7, -31],\n [0, 0, 0, 0, -28, -19, -16, -14, 18, 35, 32, -5],\n [0, 0, 0, 0, 0, -1, 18, -15, -6, 10, 6, 35],\n [0, 0, 0, 0, 0, 0, 17, -26, -12, -3, -14, 25],\n [0, 0, 0, 0, 0, 0, 0, -6, 3, -11, 22, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 31, 33, -23, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 20, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5844", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[32, -4, -2, -4, 15, -3, 20, 4, 0, 1, 0, 14],\n [-4, 7, -4, 15, 22, 29, 4, -6, 21, 11, -14, 12],\n [-2, -4, -13, 30, 23, 2, 24, 3, -6, -26, 4, 6],\n [-4, 15, 30, 22, -14, 14, 20, 13, 4, 10, 10, 26],\n [15, 22, 23, -14, -31, -7, -21, 8, -1, 22, 12, 15],\n [-3, 29, 2, 14, -7, -12, 6, 7, -18, -19, 24, 20],\n [20, 4, 24, 20, -21, 6, -17, 23, -16, -7, 6, 4],\n [4, -6, 3, 13, 8, 7, 23, 14, -10, -4, 22, 8],\n [0, 21, -6, 4, -1, -18, -16, -10, 19, 3, -10, 8],\n [1, 11, -26, 10, 22, -19, -7, -4, 3, -18, 2, -11],\n [0, -14, 4, 10, 12, 24, 6, 22, -10, 2, 3, 0],\n [14, 12, 6, 26, 15, 20, 4, 8, 8, -11, 0, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-49", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[3, 23, 29, -35, 9, -17, 12, 13, -22, 31, -6, 29],\n [0, -30, 10, 6, 25, -5, -10, 22, -3, 16, -4, 18],\n [0, 0, -14, -31, -28, 34, 27, -26, 26, 4, 11, 20],\n [0, 0, 0, 16, 26, 6, 11, 1, -25, 31, -7, -32],\n [0, 0, 0, 0, -7, 7, 3, -25, -9, -12, 1, 29],\n [0, 0, 0, 0, 0, -7, -30, 21, -22, 33, 26, 15],\n [0, 0, 0, 0, 0, 0, 29, 25, 13, -5, 6, 14],\n [0, 0, 0, 0, 0, 0, 0, 3, 6, 30, -16, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 12, -18, 27, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -1, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-380132", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-26, 25, 3, -22, 11, -26, 19, -12, 4, 27, -2, 13],\n [0, -27, 11, 9, 0, -27, -25, -12, -35, 25, 33, -15],\n [0, 0, -29, -35, 33, 28, -28, 24, -2, -27, 9, -19],\n [0, 0, 0, 21, -11, -14, 19, -2, -21, -20, -20, 2],\n [0, 0, 0, 0, 2, -13, 0, 14, -23, -32, 0, 27],\n [0, 0, 0, 0, 0, -14, 29, 29, -5, 29, -14, 30],\n [0, 0, 0, 0, 0, 0, -31, 19, -34, -11, -4, 22],\n [0, 0, 0, 0, 0, 0, 0, 10, 35, -6, -22, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, -14, -24, -4, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -29, 28, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18731", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[2, 31, 33, 23, -5, -33, 33, 31, -21, -9, -18, -26],\n [0, 32, 30, -6, 16, 21, 10, -33, 27, 8, 33, 19],\n [0, 0, -29, -17, -17, 12, 21, -15, -35, -12, -6, 26],\n [0, 0, 0, -9, 31, -32, 9, 21, -35, 8, 31, -32],\n [0, 0, 0, 0, -25, -33, -18, -6, 10, -19, 3, -3],\n [0, 0, 0, 0, 0, -4, -22, 2, -31, 10, 20, 24],\n [0, 0, 0, 0, 0, 0, -25, -4, -27, 16, 5, -24],\n [0, 0, 0, 0, 0, 0, 0, -16, 34, -23, -31, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 28, -5, -35, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 11, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89086", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-17, -2, -13, 31, -32, 17, -21, -19, -14, -2, -3, -11],\n [0, 14, -6, -14, -32, 9, -8, 18, 22, 29, 1, 18],\n [0, 0, 29, 8, 7, -9, -35, -6, 28, 1, -13, -9],\n [0, 0, 0, -34, 35, -1, -7, -5, 6, 30, 15, -20],\n [0, 0, 0, 0, 14, -9, -4, -8, -7, 13, 0, -12],\n [0, 0, 0, 0, 0, 8, -10, 34, 13, -10, -4, -2],\n [0, 0, 0, 0, 0, 0, -15, 31, 6, 10, -31, 1],\n [0, 0, 0, 0, 0, 0, 0, 19, 19, 33, -22, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, -13, -15, -2, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 7, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7184", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (11, 8) of the inverse. Round your answer to the nearest integer:\n[[-25, 15, -9, 13, -20, 14, -21, 18, -22, -10, 4, -18],\n [-10, -18, -35, -20, -15, 30, -33, -28, -18, -11, -18, -12],\n [33, -10, -25, -32, -26, -24, -24, -31, -31, -13, 20, 10],\n [-34, -35, -23, 24, 0, 26, 27, 31, -20, 4, 12, 10],\n [-31, -11, 2, 18, 9, 3, -8, 17, 18, -16, 19, 29],\n [-14, 15, -24, 23, 18, 17, 2, -24, -29, 32, -7, 9],\n [-26, -32, -12, -10, 20, -13, -27, -11, -4, -29, 23, 23],\n [26, -19, -1, 22, -7, 27, 20, 27, 11, -21, 21, -29],\n [-18, -30, 7, 21, 5, 15, 25, -17, -15, -1, 35, 18],\n [-10, 5, -24, -31, -10, -31, 2, -30, -35, 3, 13, 1],\n [-35, 1, -17, 1, 20, 31, -1, -10, 10, -1, -14, -22],\n [-7, 22, -5, -19, -13, 23, 0, 23, -34, -24, -26, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, 0, 13, 0, -30, -34, -8, -29, -15, 26, 5, 7],\n [-28, -22, -25, -26, -7, 19, -34, -35, 11, -18, -1, 26],\n [-11, -7, -17, 30, 33, -26, -11, -9, 25, -26, 0, 3],\n [-29, -21, -23, -3, 30, -25, -15, -13, 8, 29, 34, 0],\n [26, 6, 33, 16, -35, -6, -35, 12, -22, -5, 26, -5],\n [-29, -16, -5, -27, -25, -30, 7, 23, -18, -7, -35, 8],\n [-3, 31, 2, 5, -20, 2, 27, -27, -9, -5, -21, -7],\n [-27, 8, 24, 3, 15, 4, 27, -30, 2, -4, -30, 18],\n [15, -2, -27, -31, 25, -30, 14, -4, -17, 22, 12, -19],\n [24, -26, 14, 2, 4, -33, -5, -20, -8, 9, 1, 7],\n [-8, 35, 24, 28, 24, 0, 11, 2, 29, -2, -14, 15],\n [9, 35, -34, 22, -24, -9, 2, -16, 7, -4, -13, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1148", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-14, 26, -10, -22, -27, -29, 11, 22, -16, 20, 7, 24],\n [0, 30, -16, -23, -11, 0, -33, 11, -24, 24, -8, -22],\n [0, 0, 30, 24, -16, -25, -32, 16, 11, 31, -25, 14],\n [0, 0, 0, -22, 11, -18, 31, -13, 24, 23, 14, 25],\n [0, 0, 0, 0, -14, 4, 16, -8, 8, 18, 12, -14],\n [0, 0, 0, 0, 0, 17, -30, -22, 0, 15, 8, 9],\n [0, 0, 0, 0, 0, 0, 31, -23, 20, -24, -31, 19],\n [0, 0, 0, 0, 0, 0, 0, -21, -1, -5, -2, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, -30, 3, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 2, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-99", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (1, 10) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 4, 18, 2, 30, 30, -28, -12, -11, -12, 18, -20],\n [4, 9, 16, 7, 8, -20, -18, -15, -10, 16, 32, -12],\n [18, 16, 16, -11, -6, -28, -12, 3, 14, 27, 4, -9],\n [2, 7, -11, 7, 16, -17, -8, -8, 10, -6, -16, -17],\n [30, 8, -6, 16, -15, 32, -6, -4, -4, 0, 2, -18],\n [30, -20, -28, -17, 32, -9, -4, -10, -3, 18, -18, -6],\n [-28, -18, -12, -8, -6, -4, 30, -12, 1, 18, 14, 8],\n [-12, -15, 3, -8, -4, -10, -12, -7, 0, 7, -16, 15],\n [-11, -10, 14, 10, -4, -3, 1, 0, 3, -34, 24, -8],\n [-12, 16, 27, -6, 0, 18, 18, 7, -34, 3, 2, -18],\n [18, 32, 4, -16, 2, -18, 14, -16, 24, 2, -25, -14],\n [-20, -12, -9, -17, -18, -6, 8, 15, -8, -18, -14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[1, -11, 8, 24, -22, 31, 32, 0, -11, -28, -11, 0],\n [0, 24, 9, 11, 14, 33, 6, 14, -29, -32, 18, 9],\n [0, 0, 9, -33, 11, 13, -33, -33, -32, 23, -1, 17],\n [0, 0, 0, 2, 32, -2, -15, 5, 23, -33, 20, 26],\n [0, 0, 0, 0, 3, 28, 21, 27, -29, -13, -30, 22],\n [0, 0, 0, 0, 0, -11, -9, 24, -32, -7, -29, -4],\n [0, 0, 0, 0, 0, 0, 4, 31, 1, 23, -16, 27],\n [0, 0, 0, 0, 0, 0, 0, -35, 10, -5, 27, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, -20, -15, 28, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 15, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8336218", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-21, 12, -12, 14, 13, -2, -22, 9, -8, 2, 22, -22],\n [12, -1, 14, -4, 20, 2, -22, 0, -2, -12, 18, -22],\n [-12, 14, 31, 10, -2, 0, 22, 8, 13, 2, 13, 12],\n [14, -4, 10, -16, 10, -4, 18, -1, -8, -4, -28, -12],\n [13, 20, -2, 10, -34, 30, -26, -2, -26, -17, 15, 0],\n [-2, 2, 0, -4, 30, -15, -19, -10, -16, -6, 12, 10],\n [-22, -22, 22, 18, -26, -19, -31, -4, 0, -18, -2, 12],\n [9, 0, 8, -1, -2, -10, -4, -22, -10, 2, 14, 2],\n [-8, -2, 13, -8, -26, -16, 0, -10, -26, -29, 22, 2],\n [2, -12, 2, -4, -17, -6, -18, 2, -29, 23, 0, 5],\n [22, 18, 13, -28, 15, 12, -2, 14, 22, 0, 15, -1],\n [-22, -22, 12, -12, 0, 10, 12, 2, 2, 5, -1, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-50", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[5, 27, 26, -34, -29, -28, -33, -22, -3, -9, -25, -25],\n [0, 6, -33, -4, 0, -26, 19, 35, -11, 26, -2, -11],\n [0, 0, -26, -35, 22, -17, -16, 12, 22, 2, 6, -29],\n [0, 0, 0, -10, 20, 34, 35, 26, 26, 0, -16, -18],\n [0, 0, 0, 0, 16, -33, 22, -11, 32, 5, 26, 5],\n [0, 0, 0, 0, 0, 25, -20, 8, -5, -9, 5, -33],\n [0, 0, 0, 0, 0, 0, -22, -32, 9, 3, 18, -10],\n [0, 0, 0, 0, 0, 0, 0, 1, -3, 12, 12, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 4, 13, -17, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 31, 9, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6877103", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[12, -22, -9, -29, 8, 20, 23, -12, 4, -10, 2, 16],\n [-22, -3, 20, -9, -9, 18, 12, -20, -2, 26, 0, 28],\n [-9, 20, 23, -12, 3, -13, -10, 2, 10, 16, -2, 16],\n [-29, -9, -12, -34, 6, -6, 24, -6, 29, 19, -12, -20],\n [8, -9, 3, 6, 30, -28, 0, 7, 10, 6, -26, -3],\n [20, 18, -13, -6, -28, -11, 3, 24, 10, -4, -4, 10],\n [23, 12, -10, 24, 0, 3, 31, 8, 24, -14, 10, -4],\n [-12, -20, 2, -6, 7, 24, 8, -15, -6, 19, 0, 12],\n [4, -2, 10, 29, 10, 10, 24, -6, 13, -6, 5, -15],\n [-10, 26, 16, 19, 6, -4, -14, 19, -6, 13, 26, 12],\n [2, 0, -2, -12, -26, -4, 10, 0, 5, 26, -11, 23],\n [16, 28, 16, -20, -3, 10, -4, 12, -15, 12, 23, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "214", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-21, -31, 28, -19, -28, 21, 21, 12, -18, 6, 33, 18],\n [-20, -19, 8, -3, -25, 4, 1, -8, -6, 10, 7, -28],\n [7, -3, 19, 22, -15, 11, 15, -7, -20, 32, 33, -17],\n [3, 34, -6, -8, 27, -23, 31, 28, 22, 32, -26, 15],\n [34, -35, -35, -29, -32, -20, 35, -11, -21, -27, -25, 35],\n [17, 3, -33, 35, -33, -24, -33, 35, -13, 2, 6, -31],\n [5, 17, 26, -12, -8, -27, 25, 17, -19, 29, -27, 34],\n [-21, -30, -18, 22, -13, -9, -21, -6, -30, -11, -5, -25],\n [32, -12, -22, -12, 33, -10, 6, 12, 15, 31, -18, -8],\n [-6, -34, 29, 0, -15, 26, 18, -8, -4, 22, 34, -13],\n [34, 28, -5, -17, -28, 28, 5, 15, -29, 16, -33, -19],\n [-31, 24, 34, -28, 8, -10, 12, -10, 22, 31, 22, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-21, -25, -30, -34, -13, -29, 26, -6, -35, 0, -35, -14],\n [0, 8, -27, 2, -14, 5, -34, -35, -26, 14, -12, 11],\n [0, 0, 24, -13, -13, 26, -32, -9, 21, 32, 30, 35],\n [0, 0, 0, 6, -24, 18, -1, 4, 17, -4, -31, -7],\n [0, 0, 0, 0, 34, -28, 9, 30, 26, 19, 2, 30],\n [0, 0, 0, 0, 0, -31, -32, 32, 1, -23, -15, -25],\n [0, 0, 0, 0, 0, 0, 28, 19, 29, 15, 33, -11],\n [0, 0, 0, 0, 0, 0, 0, 11, -18, -35, 34, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 4, -11, -26, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "922196", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[2, 5, -5, -20, -33, -20, 32, 33, 18, 6, 28, -17],\n [0, -33, -28, -5, -17, 29, 17, -23, 23, 21, 7, -24],\n [0, 0, -27, 12, 32, 12, -11, -12, -13, 26, 25, -26],\n [0, 0, 0, 24, 29, 21, -22, 0, 26, -21, 13, -21],\n [0, 0, 0, 0, -34, -32, 4, -29, 25, 8, 32, -34],\n [0, 0, 0, 0, 0, 28, -12, 31, -35, 10, 7, -26],\n [0, 0, 0, 0, 0, 0, -19, 10, -34, -25, -26, -13],\n [0, 0, 0, 0, 0, 0, 0, 11, 13, 30, 9, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 22, 1, -2, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -14, -26, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9487", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[31, 5, -8, 1, 1, 30, 19, -8, 29, 17, 13, -10],\n [5, -20, -2, 27, 4, 27, -6, 0, -8, -9, 9, 10],\n [-8, -2, 24, -14, 28, -15, 22, -16, 2, -16, -16, 34],\n [1, 27, -14, 10, -16, -18, -9, 2, -22, -2, -9, 0],\n [1, 4, 28, -16, 10, -11, -7, -20, -10, 16, 27, 2],\n [30, 27, -15, -18, -11, -5, 22, -10, 0, -28, -16, -6],\n [19, -6, 22, -9, -7, 22, -10, -2, 4, 20, -27, -2],\n [-8, 0, -16, 2, -20, -10, -2, 16, -20, -20, 8, 7],\n [29, -8, 2, -22, -10, 0, 4, -20, 26, 8, 0, -17],\n [17, -9, -16, -2, 16, -28, 20, -20, 8, -3, -8, 9],\n [13, 9, -16, -9, 27, -16, -27, 8, 0, -8, -4, 2],\n [-10, 10, 34, 0, 2, -6, -2, 7, -17, 9, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (5, 12) rounded to the nearest integer?\n[[2, -8, 33, 9, 26, -19, 4, -1, 21, -11, -21, -17],\n [15, -23, -11, -13, 23, -20, 15, -26, 19, 26, 9, 30],\n [-11, 22, 28, 8, -12, 15, 27, -12, 12, -16, -4, -2],\n [16, 2, -22, -12, -28, -30, 7, 19, -9, -12, 31, -30],\n [30, -20, 21, 26, 29, -18, 2, -18, -22, -10, 34, -25],\n [-34, -11, 31, 25, 4, -6, -27, -6, -15, 9, -24, 6],\n [17, -6, 10, 34, 24, 19, 18, -6, 23, 0, 22, 21],\n [-29, 16, 15, -22, -12, 2, -34, 35, -1, 4, 14, -10],\n [-21, -26, -9, -10, -18, 29, 30, -4, 23, 27, 23, -33],\n [32, -20, 27, -26, -22, 15, 7, 32, 26, 26, -4, -13],\n [-2, -17, -13, 8, 15, 4, 20, -27, -22, 22, 27, -2],\n [29, -4, -28, -13, -4, 2, -14, -9, 25, 16, -7, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 6, 9, 6, -2, -2, -9, 6, -10, 16, -9, 15],\n [32, 25, -2, -33, -11, -11, 29, 1, -23, -21, -30, 3],\n [-23, -10, -9, -14, 29, 7, 7, 29, -25, -2, 31, 22],\n [-25, 14, -26, -28, 28, -6, 0, -6, 20, 33, -17, 13],\n [26, 25, -11, -25, -6, 35, 30, -1, 7, 31, 15, 10],\n [26, 26, -4, -19, 15, -8, 15, -17, 21, -29, -28, -6],\n [-29, 22, -9, 4, 0, -17, 20, 34, -12, -12, -6, 3],\n [9, 13, -1, -16, 0, -17, 4, -14, 29, -13, -12, 3],\n [2, 11, -29, 8, 5, 6, 12, -14, 27, 21, 20, -2],\n [-13, -8, 5, -26, 16, 20, -13, -26, 29, -7, 10, 5],\n [33, 8, -7, 14, -16, 27, -28, 29, 8, -20, 33, 14],\n [-23, 29, -35, -16, -11, -7, 31, -18, 21, 17, 34, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "691", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, -10, 35, -25, -15, 33, -5, 9, 28, -9, -2, 14],\n [33, -10, 12, 16, -31, -24, -23, -20, 15, 18, 32, -23],\n [-18, -17, 6, 35, -15, 17, -35, -22, -33, -27, -25, -13],\n [-6, 11, -31, -6, 32, -7, 9, -29, -20, 5, 25, 15],\n [19, 28, 15, -15, 22, 11, -25, 25, -30, -8, 6, 16],\n [-25, 34, 4, -6, 20, -30, 13, -3, -25, 29, -9, -6],\n [10, -10, -8, -4, -24, -20, 35, 16, -34, -8, 26, -7],\n [20, -11, 5, -31, 26, 26, -31, 32, 1, 32, -4, -22],\n [27, -6, 7, 17, 17, -7, -8, 35, 13, 0, -9, 21],\n [-8, -6, 8, 7, 19, 29, -9, -35, -26, 7, 33, -27],\n [31, -7, -34, -22, 26, 19, -7, -31, 33, 30, 3, -13],\n [-20, -14, -7, 33, -24, -23, -28, -12, 1, 0, -21, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-34, 22, 35, -26, 19, 6, 34, 32, -23, 1, -28, 4],\n [0, 24, -26, 35, -14, 20, 10, -18, 23, 25, 16, -27],\n [0, 0, -22, -19, -19, 15, 20, -12, 0, 26, -18, 19],\n [0, 0, 0, -26, -31, -14, 1, -3, -26, 28, 22, 27],\n [0, 0, 0, 0, -27, 9, -9, -4, 5, -15, -29, -14],\n [0, 0, 0, 0, 0, 17, -8, 22, -31, 19, 24, 9],\n [0, 0, 0, 0, 0, 0, -1, 27, -17, 23, 28, 29],\n [0, 0, 0, 0, 0, 0, 0, -32, -15, -9, -25, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 9, -12, -17, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 10, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-112179", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[20, -2, 31, -15, 3, 1, 6, 0, 30, -19, 18, -7],\n [0, -15, -17, -7, -33, 19, 15, 3, -5, -1, 33, -9],\n [0, 0, -23, -13, 29, 33, 35, -14, -35, -21, 17, 31],\n [0, 0, 0, 20, -11, 26, 7, -22, 16, -9, 16, -35],\n [0, 0, 0, 0, 28, -15, 30, 9, 24, -18, -21, 10],\n [0, 0, 0, 0, 0, 29, -6, 17, -30, 9, 27, -35],\n [0, 0, 0, 0, 0, 0, 6, -34, 24, -18, 25, 23],\n [0, 0, 0, 0, 0, 0, 0, -3, 29, 29, -19, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, -25, -7, -25, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -20, -13, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[18, 18, 29, 26, 34, 16, -17, 7, -30, 32, -26, 7],\n [0, -27, 29, 15, 27, 20, -24, 10, -20, 34, 11, 24],\n [0, 0, -6, -31, -21, -5, -18, 7, -25, 15, -24, 20],\n [0, 0, 0, 30, 2, -16, 16, -13, 29, -30, -19, 0],\n [0, 0, 0, 0, -25, -26, -32, -17, 18, 3, 26, 6],\n [0, 0, 0, 0, 0, 23, -21, -33, -8, 17, 6, -21],\n [0, 0, 0, 0, 0, 0, -33, 33, 30, 24, 2, -34],\n [0, 0, 0, 0, 0, 0, 0, -11, 21, 24, -16, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 32, 19, 30, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 34, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1042", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-25, 0, -20, -14, 2, -20, 4, 8, -24, 30, 22, -16],\n [0, -23, -4, -15, 24, 11, 12, -12, 23, 24, 0, 8],\n [-20, -4, -21, -8, -9, 0, -2, 2, -4, -16, 19, -2],\n [-14, -15, -8, -30, 16, 2, 23, -8, -6, -22, -5, 28],\n [2, 24, -9, 16, 3, -15, 1, 12, -20, -28, -6, -20],\n [-20, 11, 0, 2, -15, -20, 2, 0, 20, -3, -12, -8],\n [4, 12, -2, 23, 1, 2, -5, -8, 24, -9, -30, -6],\n [8, -12, 2, -8, 12, 0, -8, 5, -16, -27, -12, -4],\n [-24, 23, -4, -6, -20, 20, 24, -16, 34, 15, 28, -20],\n [30, 24, -16, -22, -28, -3, -9, -27, 15, -24, -8, -17],\n [22, 0, 19, -5, -6, -12, -30, -12, 28, -8, -1, -4],\n [-16, 8, -2, 28, -20, -8, -6, -4, -20, -17, -4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1885", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, 0, -16, 20, 12, 4, -4, -16, 8, -8, 10, 10],\n [0, -20, -9, 1, 29, -14, -12, 0, 15, -4, -5, -1],\n [-16, -9, 30, -14, -14, 6, 16, -20, 4, 10, 7, -16],\n [20, 1, -14, 31, 22, 20, 8, -10, 0, 26, 34, 9],\n [12, 29, -14, 22, 31, 2, 2, -15, -10, 3, -14, 28],\n [4, -14, 6, 20, 2, 29, -10, 18, -6, 14, -6, 2],\n [-4, -12, 16, 8, 2, -10, -20, -9, -10, -12, 10, 21],\n [-16, 0, -20, -10, -15, 18, -9, 34, -8, 12, -10, 3],\n [8, 15, 4, 0, -10, -6, -10, -8, 22, 3, -5, -14],\n [-8, -4, 10, 26, 3, 14, -12, 12, 3, 10, -2, 22],\n [10, -5, 7, 34, -14, -6, 10, -10, -5, -2, -20, 10],\n [10, -1, -16, 9, 28, 2, 21, 3, -14, 22, 10, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-18, 25, -20, 29, 25, 28, -6, -26, 34, -7, -14, -22],\n [-30, 8, 27, 14, 25, -16, 30, -21, 2, -31, -21, -25],\n [15, -3, 0, 5, -1, 21, 28, -3, -3, -18, -25, 26],\n [11, 25, 20, -12, 29, -30, -10, 29, 18, 26, -24, -12],\n [3, -14, 12, -32, -7, -30, 11, 19, 19, 13, -11, 9],\n [-28, -25, -35, 34, -8, -27, 13, 30, -14, 3, -13, 25],\n [31, 7, 9, 5, -17, 8, -10, -20, -14, -30, 1, 33],\n [-12, 4, -26, -5, 15, 18, 17, -16, -5, -20, 34, 7],\n [-25, 12, 4, -17, 29, 22, -9, 5, -22, -1, -34, -23],\n [0, 6, -12, -21, -29, -33, -16, 7, -10, 9, -8, 9],\n [24, 4, -27, 35, 4, -22, -26, 12, -21, 9, 32, 22],\n [-17, 12, -8, 8, -14, 4, 8, -5, -31, -7, 33, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1829", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-22, 23, 17, -7, -32, -4, 13, 2, -7, -35, -33, 6],\n [-4, -13, -10, 2, -14, -24, 27, -20, 22, -21, -31, 15],\n [5, -32, 11, -14, -5, -7, 5, 25, 17, -20, 19, -19],\n [-18, 1, 24, -7, -14, 18, 9, 16, 22, -33, -35, 19],\n [9, 21, -19, -7, -18, -27, -21, -27, -5, -34, 18, 12],\n [-35, 27, -2, 29, -25, -27, -29, 10, 1, 13, -28, 25],\n [0, -34, 9, -30, 1, 21, -17, 16, -5, 11, 3, 15],\n [19, -15, -3, -15, -26, -32, 12, 21, -24, -26, 31, -28],\n [33, -14, -1, -32, -20, 1, -14, 26, 14, 24, -9, 16],\n [4, 35, -6, 16, 2, -21, -8, 23, 4, -31, 3, 20],\n [-1, -19, -17, -18, -34, 30, 13, -4, 2, -10, 17, 14],\n [33, -4, -14, 11, -35, 2, 19, -30, -16, 26, -18, 35]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "202", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (3, 10) of the inverse. Round your answer to the nearest integer:\n[[-4, -16, 8, 20, -3, 2, -1, 20, 12, 2, 6, -10],\n [-16, -17, -27, 29, -8, 10, -9, -14, -23, 0, -23, -4],\n [8, -27, 21, -12, -3, -14, 13, -8, -19, 12, 0, -19],\n [20, 29, -12, -18, -23, -17, 30, 5, 24, -19, 18, -6],\n [-3, -8, -3, -23, 6, -28, 5, 9, -2, -17, 18, 4],\n [2, 10, -14, -17, -28, 33, -4, -8, 21, 8, 1, 6],\n [-1, -9, 13, 30, 5, -4, -2, -15, 1, 9, 10, 0],\n [20, -14, -8, 5, 9, -8, -15, 32, 21, 28, 6, -6],\n [12, -23, -19, 24, -2, 21, 1, 21, -9, -6, -12, -6],\n [2, 0, 12, -19, -17, 8, 9, 28, -6, 15, 11, -30],\n [6, -23, 0, 18, 18, 1, 10, 6, -12, 11, 1, -28],\n [-10, -4, -19, -6, 4, 6, 0, -6, -6, -30, -28, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[2, 8, -27, 32, -6, 26, -3, -24, 28, -1, 26, -19],\n [-2, 25, 26, -26, 14, 16, -29, 6, 21, -3, 18, 19],\n [-27, 9, 2, -17, 8, 26, -23, -1, 13, 5, 19, -21],\n [-22, 23, 10, -8, 23, 2, 4, 15, 33, -27, -25, -16],\n [-2, 33, -3, -8, 17, 0, 5, -6, -9, 14, -25, -19],\n [14, -4, -13, 9, -18, -14, -8, 13, 6, -21, -16, -4],\n [20, 17, 7, -14, -16, -35, 15, 21, 6, 16, -10, 27],\n [25, 26, 31, 25, 10, 13, -12, 10, 21, -22, -34, -30],\n [25, 0, 32, -6, 12, -20, 28, -28, -1, -12, -5, -2],\n [-31, -22, 1, -16, 29, -20, -25, 32, 8, 25, -5, 33],\n [25, -27, 14, -18, -21, -12, 11, 35, -2, -13, -16, 9],\n [0, 10, -27, -22, 7, 25, -14, -31, 23, -4, -1, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[11, 18, 24, 15, -23, -1, -20, 32, -33, 26, -5, -35],\n [0, -35, -3, 6, 29, -20, 1, 16, -1, 11, -34, 8],\n [0, 0, 9, 22, -12, -14, 5, -31, -32, 23, -14, 24],\n [0, 0, 0, 5, -29, -12, -28, -24, -26, -25, -16, 8],\n [0, 0, 0, 0, 3, 5, 20, 31, -1, -20, -18, -23],\n [0, 0, 0, 0, 0, 28, 2, 15, 22, -14, 20, -7],\n [0, 0, 0, 0, 0, 0, 31, 34, -27, -10, 12, -17],\n [0, 0, 0, 0, 0, 0, 0, -18, -27, -29, 17, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, -14, -16, 24, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -18, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115391", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 3) of the inverse of matrix 1/839 * A where A =\n[[7, -12, 10, 16, 22, 20, -4, -3, 7, -20, 30, -10],\n [-12, 25, 6, -9, 8, -4, 6, -20, -4, -2, 20, 10],\n [10, 6, -16, -6, 8, -15, -29, -12, 20, -24, -17, 30],\n [16, -9, -6, 16, 1, 6, -25, 15, -26, 16, 14, -10],\n [22, 8, 8, 1, 28, 7, -14, -10, -2, 22, 3, -1],\n [20, -4, -15, 6, 7, -34, -24, -15, -4, 9, 19, -8],\n [-4, 6, -29, -25, -14, -24, 12, -6, -5, -24, -8, -28],\n [-3, -20, -12, 15, -10, -15, -6, -29, -16, 11, 12, -24],\n [7, -4, 20, -26, -2, -4, -5, -16, -18, -12, 6, -4],\n [-20, -2, -24, 16, 22, 9, -24, 11, -12, -26, -4, 10],\n [30, 20, -17, 14, 3, 19, -8, 12, 6, -4, -7, -2],\n [-10, 10, 30, -10, -1, -8, -28, -24, -4, 10, -2, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[35, 12, -33, -33, 11, 2, -7, 9, -15, 13, 13, -10],\n [0, -8, -14, -8, 28, -17, 11, 11, 12, -34, -13, -31],\n [0, 0, -8, -30, -16, 32, 31, -5, 14, 7, -24, 12],\n [0, 0, 0, -3, 7, -35, -26, -18, -27, -23, 7, -32],\n [0, 0, 0, 0, 30, -8, -22, 32, 33, -23, -22, -18],\n [0, 0, 0, 0, 0, 8, -26, -4, 34, -10, 5, 10],\n [0, 0, 0, 0, 0, 0, 30, -7, 19, -27, -5, -18],\n [0, 0, 0, 0, 0, 0, 0, 18, -11, -7, -1, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 21, -18, -20, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 28, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4777", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (6, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -26, -12, 19, 2, -26, 10, -14, -28, -6, -18, -4],\n [-26, -20, -4, -2, 12, 2, 22, 24, 8, -26, 10, -32],\n [-12, -4, -8, -20, -2, 9, -12, 4, -6, 3, -16, 0],\n [19, -2, -20, -15, 6, -4, 12, -12, -6, -18, -27, 1],\n [2, 12, -2, 6, 28, -26, -4, 1, 16, -9, 13, -8],\n [-26, 2, 9, -4, -26, -2, -32, 0, 3, 10, 22, -33],\n [10, 22, -12, 12, -4, -32, 5, -25, 13, 2, 12, -4],\n [-14, 24, 4, -12, 1, 0, -25, 29, 6, -13, 16, 16],\n [-28, 8, -6, -6, 16, 3, 13, 6, -34, 2, -23, 5],\n [-6, -26, 3, -18, -9, 10, 2, -13, 2, -1, -18, -11],\n [-18, 10, -16, -27, 13, 22, 12, 16, -23, -18, 22, -12],\n [-4, -32, 0, 1, -8, -33, -4, 16, 5, -11, -12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-35, 30, -2, 23, 29, -14, 17, -5, 30, -33, 10, 8],\n [5, -23, -26, 26, -30, 33, 14, 3, 7, 6, 4, -31],\n [31, 25, -21, -26, -35, 27, -20, -8, 1, 18, -25, 1],\n [2, -2, -14, 19, -32, 8, -31, 20, -17, -21, 15, -11],\n [17, 31, 8, 2, 25, 33, 10, 24, -4, -13, -17, -9],\n [-2, 30, 17, -27, -5, 20, 0, -11, -35, -31, 15, -3],\n [17, 25, -1, -1, -9, -25, -8, -26, -1, -18, -31, -30],\n [-6, 29, 32, 26, 12, -12, 7, -18, -3, -27, 16, -25],\n [32, -34, -9, -18, -2, 18, -25, 30, -5, 8, 20, -17],\n [-4, 0, 35, -22, 9, -35, 16, -3, -2, -20, -34, 26],\n [-17, -21, -20, -8, -30, -9, 3, -25, -23, -11, 5, 1],\n [-22, -15, 7, 8, 6, -9, -3, -5, -20, -29, -20, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (3, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-32, -33, -17, -7, 29, -15, 19, -25, 0, 3, 14, -8],\n [-16, 3, -11, 10, -4, 27, 8, 5, -27, 2, 1, 6],\n [-13, -20, 3, 18, -9, 10, 10, -16, 9, -4, -4, 13],\n [11, 4, -31, 26, -27, 35, -18, 10, -35, -30, -15, -1],\n [22, 13, -22, 32, -30, -16, -13, -22, 15, -34, 13, -29],\n [14, -22, -16, -23, 21, 13, 35, 31, -31, 17, 16, 10],\n [23, -27, 17, -21, -32, -2, 26, 16, 0, 22, 35, 10],\n [1, 30, 5, -8, 18, -6, -5, -28, 35, 12, 22, -32],\n [-18, -14, -9, -4, 35, 4, 25, 0, -26, 35, -33, 27],\n [-26, -15, 2, -16, -21, -15, -17, -28, 6, -14, -19, -24],\n [27, 23, 12, -9, 28, 27, 7, 34, -8, -7, -18, 10],\n [21, -26, 16, -9, -18, 5, 17, -23, -13, 15, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-60", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[14, -7, -14, 22, 6, -13, 32, -34, 4, -10, -14, 10],\n [24, -21, 11, 24, -19, -18, 30, 1, -12, -21, 15, -12],\n [-13, 11, 26, 27, -24, -26, 19, 9, 1, -27, 20, 13],\n [30, 22, 17, -13, -24, -7, -9, 34, -16, 18, 12, 20],\n [-14, -13, -2, -32, -20, 32, -8, -14, -28, 17, -27, 6],\n [18, -11, -26, 33, -24, -28, 34, -35, -11, 9, 11, -25],\n [26, 0, 4, 35, -31, 21, -20, -25, 18, -4, 14, 26],\n [-29, 24, 3, 15, -29, 3, 0, -24, 17, 25, -13, -13],\n [-7, 14, -12, -14, -24, 29, -6, 0, 6, -12, 3, 2],\n [-4, 22, 18, -4, -26, 21, -6, 17, 12, 7, -35, 3],\n [-24, 14, -27, 13, -32, -12, 32, 24, -8, 16, -16, 27],\n [-6, 31, -17, -15, 4, -15, 19, -3, 2, -27, 14, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "570", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the inverse of matrix 1/839 * A where A =\n[[5, -12, 18, -3, -6, 24, 24, -8, 23, 16, -15, 33],\n [-12, 16, 12, 4, 1, 24, -30, -16, 6, 12, -2, 8],\n [18, 12, 34, -4, 4, 17, 12, 2, 10, -3, 16, -12],\n [-3, 4, -4, -14, -2, -26, 1, -2, 10, 0, -1, -14],\n [-6, 1, 4, -2, -7, -11, 18, 4, 10, -18, -2, 20],\n [24, 24, 17, -26, -11, -8, -4, 0, 14, 2, 3, -8],\n [24, -30, 12, 1, 18, -4, 30, -2, -8, 4, 0, -6],\n [-8, -16, 2, -2, 4, 0, -2, 20, -12, 6, -6, 12],\n [23, 6, 10, 10, 10, 14, -8, -12, 6, 23, -6, 14],\n [16, 12, -3, 0, -18, 2, 4, 6, 23, -25, 10, -15],\n [-15, -2, 16, -1, -2, 3, 0, -6, -6, 10, 6, -12],\n [33, 8, -12, -14, 20, -8, -6, 12, 14, -15, -12, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 3) of the inverse of matrix 1/839 * A where A =\n[[-22, 21, 34, 11, -17, 26, -26, 20, -25, -29, 17, 32],\n [-20, 24, 15, -27, 13, 0, -27, -4, 21, 21, 8, -17],\n [7, 32, 28, -23, -26, 12, -16, -30, 8, 12, 28, -7],\n [-27, -13, 19, -8, 11, -21, 22, -18, 4, -18, -29, -34],\n [15, -1, -26, -16, 21, -23, -12, 6, 27, 10, 25, 27],\n [-16, -20, -1, -27, 0, -22, 7, -13, 13, -35, 14, 22],\n [-7, -34, -20, -9, 0, -10, -29, 2, 2, -11, 16, 20],\n [14, 22, -30, -7, 31, 0, -30, -35, -7, -24, 20, -30],\n [23, 16, 1, 35, 6, 3, 3, 19, 10, 32, 17, 25],\n [-26, -29, -1, 33, -29, 2, -28, 7, 6, -10, -30, 22],\n [-26, -24, -7, -15, -15, 6, -7, -22, -11, 3, 23, 26],\n [-9, -31, -32, 16, -30, -7, 19, 31, 0, -19, 1, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (2, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[28, 21, -15, 30, -25, -19, 25, -7, -15, 33, 15, -8],\n [0, -32, 2, 31, -7, -25, 15, 0, 21, -31, -20, -11],\n [0, 0, -33, 1, 35, -33, 22, -15, -18, 22, -26, -16],\n [0, 0, 0, -4, 34, -17, 32, 34, -24, 1, 10, -5],\n [0, 0, 0, 0, -24, -30, -14, 26, 5, -20, 10, 26],\n [0, 0, 0, 0, 0, 15, -26, 10, -30, -4, 32, 25],\n [0, 0, 0, 0, 0, 0, -16, 1, 22, -35, 18, -23],\n [0, 0, 0, 0, 0, 0, 0, -21, -6, -11, 3, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 26, 16, 26, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -22, -7, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2330", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 3) of the inverse of matrix 1/839 * A where A =\n[[-6, 11, 25, -29, 18, -16, -20, -34, -26, 7, -8, -26],\n [0, -2, -20, 19, 28, 17, 6, -6, 24, -34, -2, 6],\n [0, 0, -4, -6, 28, -17, -6, 22, 5, -9, -20, -11],\n [0, 0, 0, -4, 1, 16, -2, 14, -2, -27, 6, 3],\n [0, 0, 0, 0, 31, -19, 27, -33, 35, -26, 19, -16],\n [0, 0, 0, 0, 0, -14, 11, -3, 24, -10, 8, -33],\n [0, 0, 0, 0, 0, 0, -22, 34, -3, 34, -18, 32],\n [0, 0, 0, 0, 0, 0, 0, 9, 18, 28, 16, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, -19, -13, 1, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 23, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-210", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[4, -27, 28, 13, 32, -3, -30, -7, -17, -9, -27, -18],\n [0, 35, -4, -10, 16, -14, -8, 19, -8, -7, 29, -5],\n [0, 0, 17, -18, 1, 25, 15, -31, 19, 8, -26, -11],\n [0, 0, 0, -16, 6, 27, -33, 7, -32, -8, 5, 2],\n [0, 0, 0, 0, -33, -23, 20, 15, 1, -22, 0, 34],\n [0, 0, 0, 0, 0, 18, 21, -28, 6, 34, 32, 8],\n [0, 0, 0, 0, 0, 0, 35, -19, -21, -4, -13, -10],\n [0, 0, 0, 0, 0, 0, 0, 30, 35, -9, -28, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 29, 27, 22, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -29, -30, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6306", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[0, 16, -27, 28, -24, -20, 34, -27, -2, -29, -4, 13],\n [18, 6, -35, -16, 2, -24, 23, 14, -29, -9, -23, -16],\n [-18, 22, 32, -13, 32, -34, 8, 14, 23, 8, 29, -2],\n [-5, -22, 16, -17, -7, 19, -6, 23, 17, 30, 3, -11],\n [9, -28, 35, 23, -34, -21, -16, -25, 5, 32, -32, 12],\n [-35, 25, -9, 35, -2, 32, -34, -13, 0, -26, 27, 35],\n [15, -15, 33, -18, -13, 20, 8, 16, -15, -14, -23, 26],\n [34, 26, -16, 25, -12, 6, -1, 3, 6, 29, -24, -35],\n [3, 4, -30, -7, 11, 14, 32, -13, -28, -34, -32, 15],\n [-15, 17, -10, -6, -3, -14, -30, 35, -6, 21, -28, -19],\n [-4, 12, -27, 8, 32, -33, 8, 14, 12, -29, -26, -18],\n [-3, 28, 3, 20, 14, -8, 30, -5, 32, -25, -13, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "388", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[28, 24, -13, -1, 16, 13, -4, 2, 10, 33, 26, -4],\n [0, -21, 33, -15, 31, -6, -31, 16, -20, -30, 4, -10],\n [0, 0, 22, 18, -16, 3, -32, 2, 10, 6, -6, 0],\n [0, 0, 0, -31, 8, -31, 3, -15, 24, -4, 31, -23],\n [0, 0, 0, 0, -14, 9, 22, 4, 13, -2, 35, -35],\n [0, 0, 0, 0, 0, 34, 14, -12, 30, -24, -31, -26],\n [0, 0, 0, 0, 0, 0, -14, 33, 26, -17, 5, -14],\n [0, 0, 0, 0, 0, 0, 0, -35, -21, -6, -23, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, -17, -14, 21, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -7, -31, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13620", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, -1, 1, -26, 33, -32, 35, 25, -29, 13, 25, -22],\n [0, 15, -5, -34, 7, 15, 34, -25, 13, -20, 5, -6],\n [0, 0, -20, -5, -25, -28, -24, 25, 2, 19, -23, -1],\n [0, 0, 0, 31, 27, 35, -27, 25, 14, 23, 12, -19],\n [0, 0, 0, 0, 30, 21, -21, -34, -9, 16, 15, 2],\n [0, 0, 0, 0, 0, -17, -17, 5, -21, -8, -8, 14],\n [0, 0, 0, 0, 0, 0, -34, 7, -10, 33, -13, 24],\n [0, 0, 0, 0, 0, 0, 0, 8, -6, -34, 32, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 25, 3, -29, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -30, -26, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18102", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 11) of the inverse of matrix 1/839 * A where A =\n[[-18, 0, -12, -35, 10, -12, -15, -7, 28, -26, -23, -25],\n [0, -30, 15, -26, 28, -1, -19, -33, -6, -9, 9, -32],\n [0, 0, -5, -17, -25, 1, 25, -34, 14, -9, 14, -12],\n [0, 0, 0, -3, -13, -28, -3, 28, -17, -24, -32, 27],\n [0, 0, 0, 0, -18, 3, -3, 3, -5, -9, 5, -9],\n [0, 0, 0, 0, 0, -9, -23, 12, 19, 22, 11, 11],\n [0, 0, 0, 0, 0, 0, -1, -2, 27, -9, 10, 9],\n [0, 0, 0, 0, 0, 0, 0, -14, -25, 4, 6, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, -5, 28, -6, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -8, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29636", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-16, -2, 18, -4, 4, 2, 2, -9, -13, -13, 30, -21],\n [-2, 18, 5, 8, -10, 24, -4, -20, 11, 22, 2, 2],\n [18, 5, 28, 6, -2, -13, 10, -2, 18, -8, -10, -28],\n [-4, 8, 6, -19, 8, 12, 8, 0, 4, 4, -10, 23],\n [4, -10, -2, 8, 10, 0, 1, 0, 11, 2, 10, 18],\n [2, 24, -13, 12, 0, 19, -4, -7, -22, 18, 3, 18],\n [2, -4, 10, 8, 1, -4, -31, 8, 26, -8, -8, -8],\n [-9, -20, -2, 0, 0, -7, 8, 21, -6, -10, -16, -10],\n [-13, 11, 18, 4, 11, -22, 26, -6, -19, -28, 17, -4],\n [-13, 22, -8, 4, 2, 18, -8, -10, -28, -3, -8, -15],\n [30, 2, -10, -10, 10, 3, -8, -16, 17, -8, 18, 0],\n [-21, 2, -28, 23, 18, 18, -8, -10, -4, -15, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28243", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[20, -11, -20, -14, 0, 6, -7, 18, -7, 20, 16, 4],\n [-11, 1, 22, 14, 5, -4, 18, -20, -22, -10, 10, 1],\n [-20, 22, -2, 6, -5, -19, 0, 0, 2, -12, 18, 14],\n [-14, 14, 6, -20, -18, 18, 23, 13, 15, -16, -8, -20],\n [0, 5, -5, -18, 35, 24, 8, 2, -8, 17, -6, -27],\n [6, -4, -19, 18, 24, 7, -34, 16, 6, 4, 8, 6],\n [-7, 18, 0, 23, 8, -34, -13, -26, 26, -2, -10, -15],\n [18, -20, 0, 13, 2, 16, -26, 4, -8, -17, 13, -10],\n [-7, -22, 2, 15, -8, 6, 26, -8, -33, 2, -23, 0],\n [20, -10, -12, -16, 17, 4, -2, -17, 2, 3, 24, -5],\n [16, 10, 18, -8, -6, 8, -10, 13, -23, 24, -8, -28],\n [4, 1, 14, -20, -27, 6, -15, -10, 0, -5, -28, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-30, -3, 34, 12, 1, -14, 14, -17, -8, 28, 22, -11],\n [0, -4, 11, 2, -18, -9, 1, 6, 0, -2, -21, 25],\n [0, 0, -29, 25, -35, -15, -20, 13, -7, 11, -35, -22],\n [0, 0, 0, -18, 0, 17, 32, 26, 33, 30, -26, 22],\n [0, 0, 0, 0, -14, 7, -28, -33, 5, 17, 4, 22],\n [0, 0, 0, 0, 0, 27, -28, 33, -21, -21, -29, -10],\n [0, 0, 0, 0, 0, 0, -18, 17, -13, 33, 25, -2],\n [0, 0, 0, 0, 0, 0, 0, -33, -22, -27, 13, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, -28, 33, -13, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 17, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38605", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-7, -24, -8, 0, 0, -29, -3, 2, 20, 30, -6, -25],\n [-24, -16, 9, 6, 0, 27, 8, -9, 7, 19, 6, -18],\n [-8, 9, 25, -1, 1, -4, 22, 17, 3, 19, 10, 12],\n [0, 6, -1, -15, -28, -3, 22, 18, -28, 24, -1, 11],\n [0, 0, 1, -28, 6, 22, 2, -2, -2, -18, -7, 4],\n [-29, 27, -4, -3, 22, 10, 0, 32, 2, 0, -2, 12],\n [-3, 8, 22, 22, 2, 0, -34, 6, 10, -24, 16, -10],\n [2, -9, 17, 18, -2, 32, 6, -22, -18, -6, 2, -14],\n [20, 7, 3, -28, -2, 2, 10, -18, -7, -4, 20, 26],\n [30, 19, 19, 24, -18, 0, -24, -6, -4, -8, -14, -2],\n [-6, 6, 10, -1, -7, -2, 16, 2, 20, -14, 13, 5],\n [-25, -18, 12, 11, 4, 12, -10, -14, 26, -2, 5, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-72", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-22, 4, -6, -32, 1, 23, -20, 6, -3, -8, 11, -9],\n [4, -25, -2, -26, -20, -6, 17, -8, 7, 0, 4, -5],\n [-6, -2, 8, -6, 12, -6, 6, -30, 10, -20, -24, 16],\n [-32, -26, -6, 25, -26, -8, -6, -4, -16, -6, -16, 12],\n [1, -20, 12, -26, 33, 6, 0, -11, -32, -20, -1, -14],\n [23, -6, -6, -8, 6, -11, 10, 10, -22, 4, 16, -26],\n [-20, 17, 6, -6, 0, 10, 4, 17, -14, -20, -1, 15],\n [6, -8, -30, -4, -11, 10, 17, 8, -20, 2, -6, 19],\n [-3, 7, 10, -16, -32, -22, -14, -20, 13, -5, -6, 6],\n [-8, 0, -20, -6, -20, 4, -20, 2, -5, -31, 6, -6],\n [11, 4, -24, -16, -1, 16, -1, -6, -6, 6, -28, -2],\n [-9, -5, 16, 12, -14, -26, 15, 19, 6, -6, -2, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1668", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-33, 4, 28, 14, -16, 3, -14, 10, -4, -10, 8, 35],\n [0, 25, -25, 23, -20, 32, -26, 23, 17, 5, -31, -33],\n [0, 0, 2, 30, 26, -30, -17, -18, 26, 2, 3, -16],\n [0, 0, 0, -20, -29, 24, -6, -1, 3, 7, -20, -20],\n [0, 0, 0, 0, 16, 35, -34, -4, 7, -18, 6, 27],\n [0, 0, 0, 0, 0, -12, -5, 27, -10, -19, -32, -29],\n [0, 0, 0, 0, 0, 0, -13, 25, -15, -33, 12, -25],\n [0, 0, 0, 0, 0, 0, 0, -10, 25, 29, -24, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 7, 21, -1, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 6, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "341860", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-23, 28, 13, 35, -12, -9, 7, -26, -23, 25, -14, 18],\n [0, 14, -15, 8, 34, -29, -1, 28, -6, 22, 22, -15],\n [0, 0, 34, 11, -11, -4, -9, 10, -24, -23, 33, -24],\n [0, 0, 0, 31, 7, 12, -10, 29, 15, -27, -4, 33],\n [0, 0, 0, 0, 17, 20, 8, 26, 24, 3, -29, 16],\n [0, 0, 0, 0, 0, -28, 5, -26, -28, 16, 16, 1],\n [0, 0, 0, 0, 0, 0, -12, 15, -35, -18, 15, 3],\n [0, 0, 0, 0, 0, 0, 0, -35, -21, -12, 4, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 8, 25, -10, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 29, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "182", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[2, -6, 26, -12, -10, 18, 17, -10, -2, 11, 3, 6],\n [-6, -11, 30, 28, -15, 4, 32, -20, 29, 21, -1, -14],\n [26, 30, 15, -3, -17, -34, 6, 16, -22, 27, 28, -8],\n [-12, 28, -3, -34, -4, 17, 7, -34, 4, -22, -20, 3],\n [-10, -15, -17, -4, 10, -12, 14, 8, 10, 9, 6, -6],\n [18, 4, -34, 17, -12, -6, 10, -1, 6, -27, 6, 26],\n [17, 32, 6, 7, 14, 10, -35, 8, 0, -30, 13, 3],\n [-10, -20, 16, -34, 8, -1, 8, -31, -13, 10, 3, -4],\n [-2, 29, -22, 4, 10, 6, 0, -13, -2, 8, 3, -11],\n [11, 21, 27, -22, 9, -27, -30, 10, 8, 15, 2, -4],\n [3, -1, 28, -20, 6, 6, 13, 3, 3, 2, 20, 14],\n [6, -14, -8, 3, -6, 26, 3, -4, -11, -4, 14, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2225", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (2, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-23, -18, 21, -28, 6, -28, 24, 22, -12, 8, 27, 15],\n [0, 4, -3, -15, -3, 19, 29, 21, 34, -22, -11, 3],\n [0, 0, 20, -19, -5, 16, -8, -29, -18, -30, 30, -16],\n [0, 0, 0, 7, -7, -27, -22, 9, -21, 10, 9, 28],\n [0, 0, 0, 0, -35, 8, 4, -32, 6, -3, -34, -26],\n [0, 0, 0, 0, 0, -28, 33, 30, 14, 35, 5, -26],\n [0, 0, 0, 0, 0, 0, 35, -10, -23, 33, -5, -19],\n [0, 0, 0, 0, 0, 0, 0, 27, 33, 6, 5, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, -27, 10, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 33, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-393", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-6, 4, -10, 10, -24, -10, -12, -4, -28, 21, 6, 13],\n [4, -30, -8, -6, 12, 21, -6, 0, 5, 13, 12, -9],\n [-10, -8, 19, 7, 16, -6, -12, 10, 7, 20, 14, 0],\n [10, -6, 7, 18, 25, -8, 8, 20, -4, -22, -8, 12],\n [-24, 12, 16, 25, -28, 0, 17, -18, 8, -1, -10, 10],\n [-10, 21, -6, -8, 0, -6, -10, 0, -4, -3, -7, -29],\n [-12, -6, -12, 8, 17, -10, -22, 14, 18, 2, -8, 8],\n [-4, 0, 10, 20, -18, 0, 14, 24, -15, -6, -16, 15],\n [-28, 5, 7, -4, 8, -4, 18, -15, 26, 18, -10, -2],\n [21, 13, 20, -22, -1, -3, 2, -6, 18, 33, 2, -1],\n [6, 12, 14, -8, -10, -7, -8, -16, -10, 2, -5, -16],\n [13, -9, 0, 12, 10, -29, 8, 15, -2, -1, -16, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[21, 8, 17, -18, 22, 8, -14, 15, 8, 12, 3, -16],\n [8, -14, 3, -2, -11, 20, 6, 10, 18, -26, -19, 10],\n [17, 3, -28, 7, 19, -26, 6, -23, 30, 3, -18, 3],\n [-18, -2, 7, -23, 21, 5, 3, -16, 6, 12, -12, -6],\n [22, -11, 19, 21, 2, -17, 22, 15, 3, -28, -2, 0],\n [8, 20, -26, 5, -17, 13, 9, 26, -12, -16, 32, 22],\n [-14, 6, 6, 3, 22, 9, -21, -1, -2, -22, 8, -6],\n [15, 10, -23, -16, 15, 26, -1, 15, 2, 1, -6, 24],\n [8, 18, 30, 6, 3, -12, -2, 2, -35, -1, 16, 2],\n [12, -26, 3, 12, -28, -16, -22, 1, -1, -28, -10, -22],\n [3, -19, -18, -12, -2, 32, 8, -6, 16, -10, -18, 0],\n [-16, 10, 3, -6, 0, 22, -6, 24, 2, -22, 0, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5233", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[8, -7, -29, -11, -28, -33, -5, 32, -4, -29, -22, -2],\n [33, -24, 1, -9, -2, 6, 28, 12, -19, -15, -21, -10],\n [-3, -24, -14, 9, -29, 27, -8, 4, 25, 14, -26, -11],\n [-24, -35, 2, 1, 23, -24, 1, -24, 20, 3, 20, 20],\n [-4, -3, -12, -5, 26, -34, 16, -35, 16, -32, -28, 11],\n [-15, -24, -2, 32, 28, -8, 5, 35, 11, -21, -15, 12],\n [3, -4, -30, -18, 20, -27, -23, -9, -28, 17, 30, -32],\n [-22, -11, 5, -30, -31, -15, 13, -13, 1, 17, 13, -26],\n [-16, 12, -25, -25, 3, -35, 28, 11, -28, 12, -17, 30],\n [28, 26, 17, -13, -7, 35, -31, 4, -4, -33, -26, 26],\n [4, 9, 10, 15, -25, 15, -31, -8, -3, -34, -26, 20],\n [-21, -9, -9, -15, -5, 25, 34, -23, 4, -21, 23, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-184", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (7, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, 32, -8, -11, 14, 29, -14, 11, 2, -2, -18, -8],\n [32, -14, 0, -9, 0, -14, -30, 22, 6, -8, -14, -24],\n [-8, 0, -10, 13, 22, -12, -6, 14, -5, -3, 26, -2],\n [-11, -9, 13, -24, -26, 8, 8, 6, 6, -17, -19, 16],\n [14, 0, 22, -26, 26, -3, -2, -12, 18, 3, 10, -7],\n [29, -14, -12, 8, -3, 29, -6, -2, -1, 24, 6, 18],\n [-14, -30, -6, 8, -2, -6, -7, 12, 2, 4, -12, -24],\n [11, 22, 14, 6, -12, -2, 12, 34, 8, -3, 8, 2],\n [2, 6, -5, 6, 18, -1, 2, 8, 1, -1, 18, 26],\n [-2, -8, -3, -17, 3, 24, 4, -3, -1, -10, -8, -12],\n [-18, -14, 26, -19, 10, 6, -12, 8, 18, -8, -24, -21],\n [-8, -24, -2, 16, -7, 18, -24, 2, 26, -12, -21, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (12, 6) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 4, 8, -20, 2, 3, 12, -12, 4, 14, -16, 16],\n [4, 26, 9, -11, -13, -2, -15, -7, -4, 14, 23, 0],\n [8, 9, -4, -12, -22, 18, -2, -15, -9, 1, 2, -9],\n [-20, -11, -12, 7, -15, -20, -6, -3, -10, 7, -28, 12],\n [2, -13, -22, -15, 5, 6, -1, 12, -9, -16, -1, -20],\n [3, -2, 18, -20, 6, -19, 18, 8, -16, -2, -12, 10],\n [12, -15, -2, -6, -1, 18, -17, -2, 0, 7, -2, -3],\n [-12, -7, -15, -3, 12, 8, -2, -6, -13, -32, 4, -20],\n [4, -4, -9, -10, -9, -16, 0, -13, 4, -17, 28, -1],\n [14, 14, 1, 7, -16, -2, 7, -32, -17, -21, 27, 1],\n [-16, 23, 2, -28, -1, -12, -2, 4, 28, 27, -10, 21],\n [16, 0, -9, 12, -20, 10, -3, -20, -1, 1, 21, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-40", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[1, -15, 33, 6, 27, -34, 15, -18, -1, -26, 3, -4],\n [1, 29, -19, 0, -9, 12, 3, 29, 2, 26, -22, 32],\n [11, 7, -34, 2, 23, 12, -23, 8, -17, -24, 24, -5],\n [-2, 5, -13, -20, -5, 19, 6, -13, 2, -13, -10, 4],\n [-33, -35, 14, -9, 8, 19, -21, 8, 33, 33, -14, 26],\n [15, 3, -14, -29, 14, 18, -24, 26, 2, 31, 34, 5],\n [31, -34, 21, 23, -6, 25, 13, 13, 7, -19, 22, -16],\n [18, 22, -32, 28, -27, -1, -8, -9, 35, 14, 9, -22],\n [-7, 24, -7, 21, 25, 24, 30, 15, -26, 15, 12, 21],\n [16, 21, -24, -2, 30, 5, 18, -15, -18, 10, -29, 2],\n [-16, -32, -25, -30, -29, 9, -6, -8, 20, -35, 24, 12],\n [-8, 19, -5, -16, 23, -7, -8, 6, 28, -10, -25, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[0, -6, -3, -2, -22, 4, 18, 27, 20, -3, 32, -2],\n [-6, 23, 1, 22, 6, -12, 17, -22, -19, 12, 0, -4],\n [-3, 1, -15, 4, -6, 14, 4, 2, -13, -4, 0, -10],\n [-2, 22, 4, 6, 15, 5, 27, -8, -12, -24, -8, -6],\n [-22, 6, -6, 15, -18, -3, -7, -6, -18, -6, 0, -7],\n [4, -12, 14, 5, -3, 22, -10, -26, -14, -9, -23, -6],\n [18, 17, 4, 27, -7, -10, -12, -6, -6, -28, -22, -22],\n [27, -22, 2, -8, -6, -26, -6, -10, 12, 6, 8, 32],\n [20, -19, -13, -12, -18, -14, -6, 12, 20, 10, -4, 0],\n [-3, 12, -4, -24, -6, -9, -28, 6, 10, 14, -4, -12],\n [32, 0, 0, -8, 0, -23, -22, 8, -4, -4, -30, -10],\n [-2, -4, -10, -6, -7, -6, -22, 32, 0, -12, -10, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[20, -3, -16, -30, -35, -27, 19, -4, -18, 1, 27, -17],\n [-31, 20, -24, 29, 34, -28, -31, -8, 24, 35, -19, 15],\n [19, 28, -5, 23, 35, 15, 31, -18, -9, -4, 10, 0],\n [-24, 23, 6, 31, -5, -31, 11, 6, -35, 20, -25, 5],\n [0, -5, 27, 27, -21, 21, -34, -7, 23, 5, 5, -25],\n [3, -32, -5, -6, 25, 33, -16, -22, 8, -18, 13, 22],\n [34, -15, 18, 6, -26, 9, 19, -15, 29, 5, 32, 16],\n [-30, -11, 29, -1, -33, 4, 28, 33, -2, 16, -12, 2],\n [17, 20, -19, -21, -22, 25, 29, 10, -22, 1, -4, -34],\n [-18, -20, -31, -20, -25, -28, 31, 17, 24, -29, -34, -5],\n [-25, 29, 25, 21, -3, -24, 19, 7, 32, -31, 27, -18],\n [-32, 14, -16, 17, -16, 18, -8, -1, -18, -3, 1, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-383", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -35, -11, -6, 6, -21, 30, -21, -26, 21, -10, -2],\n [0, 22, 29, -21, 32, 31, 6, -34, -17, -17, 10, 13],\n [0, 0, 30, -11, -2, 3, -24, 12, 24, -22, -10, -35],\n [0, 0, 0, 9, -28, -34, -16, 5, -7, 27, -34, 4],\n [0, 0, 0, 0, 32, -23, -8, 4, -15, 26, -3, 17],\n [0, 0, 0, 0, 0, 13, -2, 33, 29, -26, 6, 0],\n [0, 0, 0, 0, 0, 0, -28, 24, -23, -25, -33, -20],\n [0, 0, 0, 0, 0, 0, 0, 27, 35, -35, 23, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 7, -11, -10, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 27, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2616", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (6, 1) of the inverse. Round your answer to the nearest integer:\n[[29, -31, -31, -2, -35, 26, -26, 2, -28, -11, 14, 25],\n [1, -5, 6, -12, 31, 26, -30, 35, 15, -21, -2, 28],\n [10, -11, 2, 26, 30, -13, -3, 26, -9, 25, -7, 11],\n [2, 25, -15, -13, 22, 16, -18, 8, 16, 26, -27, 9],\n [0, 32, 10, 13, -34, -10, 27, 6, 24, 23, -11, -20],\n [29, -4, 12, 21, -12, -2, 14, 16, 26, 20, 10, 3],\n [3, 21, -8, 1, 27, -9, 9, -21, -23, 7, 18, -13],\n [29, 27, 33, 3, 26, 18, -34, -33, -17, 30, 9, -22],\n [-29, -33, -35, 16, 25, -13, -23, 25, 2, 8, -26, -5],\n [-3, -12, -23, -17, 26, 31, 11, -5, -17, 6, -25, 4],\n [3, -28, -2, 6, 12, -21, -5, 11, 12, -33, 9, 14],\n [-1, 0, 33, -10, 16, -12, -30, 35, 16, -8, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-25, 0, -6, 10, 16, -13, -30, -6, 2, 14, -26, 12],\n [0, 30, -10, -11, 11, 5, -18, -12, -26, -26, 23, 10],\n [-6, -10, 18, 9, -12, -10, 18, 2, -4, 8, -18, -18],\n [10, -11, 9, 17, 0, -5, 22, -4, -2, 32, 30, 4],\n [16, 11, -12, 0, 22, 8, 2, -32, 20, -8, -12, -4],\n [-13, 5, -10, -5, 8, 30, 0, -10, -26, -28, -1, -2],\n [-30, -18, 18, 22, 2, 0, 4, 6, -3, 20, -2, 8],\n [-6, -12, 2, -4, -32, -10, 6, 12, 18, -26, -2, -4],\n [2, -26, -4, -2, 20, -26, -3, 18, 5, 0, -6, 2],\n [14, -26, 8, 32, -8, -28, 20, -26, 0, -9, -12, -18],\n [-26, 23, -18, 30, -12, -1, -2, -2, -6, -12, 14, 2],\n [12, 10, -18, 4, -4, -2, 8, -4, 2, -18, 2, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-74", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (1, 2) rounded to the nearest integer?\n[[-12, -10, 10, 23, 12, -2, -8, 10, 4, 1, 4, 24],\n [-10, 0, -5, 15, 1, -19, -24, 0, -4, -21, -23, -8],\n [10, -5, -33, 10, 8, -11, -8, 6, 9, 18, 24, 20],\n [23, 15, 10, 29, 2, -10, -8, 17, -8, -29, 0, 19],\n [12, 1, 8, 2, -13, -7, 14, -2, 7, 0, 0, -12],\n [-2, -19, -11, -10, -7, 27, 14, -26, 11, -10, 14, -8],\n [-8, -24, -8, -8, 14, 14, -32, 9, 28, -6, -9, -14],\n [10, 0, 6, 17, -2, -26, 9, 31, -30, 18, -2, 20],\n [4, -4, 9, -8, 7, 11, 28, -30, -24, -1, -3, -6],\n [1, -21, 18, -29, 0, -10, -6, 18, -1, -17, -2, -2],\n [4, -23, 24, 0, 0, 14, -9, -2, -3, -2, 14, -11],\n [24, -8, 20, 19, -12, -8, -14, 20, -6, -2, -11, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[12, 25, 27, 21, 1, -32, 32, 21, 26, -20, 3, 27],\n [-20, 11, -13, 16, 22, 30, 21, 2, -31, 11, -22, 12],\n [5, 15, 1, -15, -28, -27, -24, -11, -15, 10, -10, 32],\n [-11, 4, -4, 26, -7, -17, 14, 34, -16, -27, -2, 5],\n [1, 32, 33, 28, 15, 23, 27, 8, 9, 16, -19, -1],\n [-23, 10, 0, -32, 25, 29, 7, -9, 30, -13, 15, 20],\n [16, 18, -20, 31, -35, -10, 24, 34, 8, 0, -27, -29],\n [-5, -3, 18, 32, 34, 15, -18, -10, 15, 26, -31, -26],\n [11, 4, -21, -17, 32, 1, -5, 28, 19, 24, 14, -14],\n [8, 33, -28, -28, -3, -6, -26, 4, -23, 25, 7, 19],\n [15, -17, 18, -13, 26, 5, -24, -32, -24, -9, -22, -20],\n [-24, 17, -21, -35, -8, -28, 24, -30, 27, -27, 16, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[18, -2, -21, 2, -26, 4, -20, -10, -23, -20, -6, 8],\n [-2, 20, -1, -4, -2, -18, 12, 1, 12, -28, 10, -9],\n [-21, -1, 24, -2, -24, 0, -4, 12, 11, 15, 2, -6],\n [2, -4, -2, -33, 0, 9, 16, 4, 3, -11, -16, -7],\n [-26, -2, -24, 0, -8, 2, 12, -19, -19, 10, 22, 18],\n [4, -18, 0, 9, 2, -33, 16, -10, 25, 3, 16, 13],\n [-20, 12, -4, 16, 12, 16, -4, -14, -6, 12, -8, 10],\n [-10, 1, 12, 4, -19, -10, -14, -17, 4, 4, -9, 14],\n [-23, 12, 11, 3, -19, 25, -6, 4, -14, -1, -18, 5],\n [-20, -28, 15, -11, 10, 3, 12, 4, -1, 31, 0, 4],\n [-6, 10, 2, -16, 22, 16, -8, -9, -18, 0, -35, -9],\n [8, -9, -6, -7, 18, 13, 10, 14, 5, 4, -9, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-856", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, 30, -34, -14, 7, -4, 14, -16, -8, 10, -12, 30],\n [30, -16, 6, -10, 1, 22, 9, 12, 2, -24, -6, 24],\n [-34, 6, -30, -20, 26, -16, 9, 26, 2, 15, 17, -6],\n [-14, -10, -20, 35, 2, 0, 20, -19, -4, 0, -7, -24],\n [7, 1, 26, 2, 1, -27, -23, 16, -4, -5, -16, 1],\n [-4, 22, -16, 0, -27, -7, -9, 2, 12, -27, -2, -7],\n [14, 9, 9, 20, -23, -9, 7, 8, 4, -14, 24, 25],\n [-16, 12, 26, -19, 16, 2, 8, -33, -4, 24, 10, 2],\n [-8, 2, 2, -4, -4, 12, 4, -4, -21, 18, 6, 1],\n [10, -24, 15, 0, -5, -27, -14, 24, 18, 24, 18, -2],\n [-12, -6, 17, -7, -16, -2, 24, 10, 6, 18, 18, 2],\n [30, 24, -6, -24, 1, -7, 25, 2, 1, -2, 2, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1164", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (5, 2) rounded to the nearest integer?\n[[-11, 14, -28, -2, 20, 16, -13, 16, -20, -2, 20, -8],\n [14, 4, -23, 5, -8, 12, -22, 32, 28, 4, 2, 16],\n [-28, -23, 2, -2, -4, 22, -10, 14, -10, 24, 14, 26],\n [-2, 5, -2, -20, 10, 20, -2, 14, 6, -8, -14, -16],\n [20, -8, -4, 10, 2, 31, -16, -18, 32, -23, 16, -6],\n [16, 12, 22, 20, 31, -35, -22, 0, -30, 21, -2, -25],\n [-13, -22, -10, -2, -16, -22, -23, -20, -16, -10, -20, -22],\n [16, 32, 14, 14, -18, 0, -20, 4, -9, -18, -13, -2],\n [-20, 28, -10, 6, 32, -30, -16, -9, -9, 18, 14, 16],\n [-2, 4, 24, -8, -23, 21, -10, -18, 18, -6, 8, -28],\n [20, 2, 14, -14, 16, -2, -20, -13, 14, 8, -32, -2],\n [-8, 16, 26, -16, -6, -25, -22, -2, 16, -28, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[8, 0, 23, -6, -20, -27, 10, -31, -18, 8, 3, 30],\n [0, 31, 11, 17, 15, 9, 12, -14, -24, 19, 9, 27],\n [0, 0, -21, -19, 25, -10, -7, -32, -9, 6, -12, -17],\n [0, 0, 0, 28, -24, -7, -7, -6, 33, -23, -34, -3],\n [0, 0, 0, 0, 27, -24, -20, 24, 20, -33, 16, -20],\n [0, 0, 0, 0, 0, -20, 32, 4, -19, -10, -1, -21],\n [0, 0, 0, 0, 0, 0, 13, -19, -8, 34, -30, 19],\n [0, 0, 0, 0, 0, 0, 0, 5, -26, 24, -24, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 31, -31, -20, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 14, -2, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336020", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[27, 12, 9, 13, -5, -7, -11, -30, 1, -19, -5, 22],\n [0, -34, -29, -14, -32, 9, -26, -12, 21, -32, 12, 22],\n [0, 0, 4, 12, 17, -30, -22, 26, 0, -15, -11, 18],\n [0, 0, 0, 25, 1, 8, -33, 13, -8, 21, -23, 5],\n [0, 0, 0, 0, 11, 34, 20, -19, -7, 20, 16, 12],\n [0, 0, 0, 0, 0, -1, -5, -5, -10, 13, 24, 14],\n [0, 0, 0, 0, 0, 0, 27, 27, 15, 34, 6, -28],\n [0, 0, 0, 0, 0, 0, 0, 28, -1, 29, 32, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 34, 35, -9, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 33, -26, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-179", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[8, -26, 11, 24, 13, 21, 26, -20, 3, 14, -4, 12],\n [-26, 11, -12, 29, -20, -4, 14, 10, 8, 16, 15, 22],\n [11, -12, 6, -8, -3, -18, -3, 20, 9, -15, 20, 15],\n [24, 29, -8, 13, -8, -11, -22, 28, 21, -2, -10, -4],\n [13, -20, -3, -8, 12, -6, 0, 2, 12, 7, -6, -28],\n [21, -4, -18, -11, -6, 30, -6, -2, -6, -3, 2, 1],\n [26, 14, -3, -22, 0, -6, 28, 26, -8, 0, -5, 17],\n [-20, 10, 20, 28, 2, -2, 26, 11, -4, 6, -23, -12],\n [3, 8, 9, 21, 12, -6, -8, -4, 24, 15, 15, 6],\n [14, 16, -15, -2, 7, -3, 0, 6, 15, 11, 31, 8],\n [-4, 15, 20, -10, -6, 2, -5, -23, 15, 31, 13, -20],\n [12, 22, 15, -4, -28, 1, 17, -12, 6, 8, -20, 28]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "242", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-16, 0, 26, -12, -27, 22, 13, 17, -25, -30, 23, 15],\n [0, 11, 9, 13, 4, -27, -28, 13, 16, -10, -24, 28],\n [0, 0, -1, 14, -20, 4, -30, 31, -19, -4, -12, -1],\n [0, 0, 0, -11, -13, 19, -29, -31, 35, 32, -30, -26],\n [0, 0, 0, 0, -15, -25, -30, 0, 19, -2, 35, 10],\n [0, 0, 0, 0, 0, -20, -10, 15, 27, -3, 24, 1],\n [0, 0, 0, 0, 0, 0, 32, 18, 24, -25, 30, -14],\n [0, 0, 0, 0, 0, 0, 0, -35, -16, 33, 1, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, -17, 25, -4, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 10, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1034", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (9, 7) of the inverse. Round your answer to the nearest integer:\n[[26, -13, -32, -5, -28, -11, 18, -25, 9, 9, 24, 28],\n [7, 28, 11, 25, 12, -28, -2, -28, 16, -28, 26, 29],\n [-22, 33, 12, -24, 28, -6, -28, 30, 33, -1, -24, 31],\n [-26, -34, -21, 27, -29, -16, 24, -28, 22, -28, -6, 18],\n [18, -7, 17, -5, -32, -7, 8, -14, -24, -6, -31, 30],\n [34, -1, 12, 15, -20, 12, 3, -35, -20, -16, -4, -34],\n [23, 23, -31, 30, 3, 8, 5, 26, -10, 15, -24, 11],\n [13, -14, 18, 17, 2, -11, -22, -1, 2, 26, -32, -7],\n [-3, -29, -32, 29, 35, -27, -4, -8, 26, -34, -32, 34],\n [-28, 10, -24, -17, -8, -31, 7, -24, 33, -3, 17, -5],\n [-11, -29, -11, -7, -15, 20, -13, -30, -1, -31, 26, 4],\n [35, -29, -18, 12, -13, -17, -26, 14, -2, 15, 15, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 6, 23, 13, -13, -20, 11, 6, -11, 33, 7, -30],\n [-22, -10, -22, 20, -7, 21, 35, -31, 13, 25, 13, 13],\n [33, 32, -19, -35, 25, -26, -2, 25, 14, -3, 6, 20],\n [18, 30, 23, -35, 9, -11, -33, 35, 21, 32, -34, -30],\n [-2, 23, -14, 16, -22, 6, 35, 33, -21, 16, -1, 25],\n [34, 12, 11, 10, -14, -4, -22, -12, -18, -9, -18, 32],\n [-7, -5, -33, 31, 35, -5, -33, -18, 9, -24, 3, 14],\n [26, 19, -17, 10, 17, 32, -31, -1, -29, -20, -16, -32],\n [-33, 25, 14, 18, 20, -34, 33, -22, 9, 8, -4, 11],\n [-35, 26, -33, -11, -6, 22, -6, -21, 7, -13, 28, 23],\n [14, -14, -20, -9, -19, -34, 0, -13, 9, 15, 5, -25],\n [-25, -10, -7, -10, -13, -32, 25, -3, 19, 32, -28, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[24, -20, 10, 30, -13, -2, 28, 28, -8, -31, -1, -27],\n [0, 5, 24, -29, 26, -10, 3, -6, -34, 2, 33, 34],\n [0, 0, -7, -6, 8, -1, -10, 17, 17, -29, -23, 25],\n [0, 0, 0, -12, -6, -35, -12, -16, 18, -28, 32, -3],\n [0, 0, 0, 0, 16, 14, -20, 22, -1, 10, 18, 35],\n [0, 0, 0, 0, 0, -32, -29, 35, 2, 0, 20, -13],\n [0, 0, 0, 0, 0, 0, 23, 25, -23, 20, 23, 14],\n [0, 0, 0, 0, 0, 0, 0, 19, -32, -20, -9, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, -32, 33, -24, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 16, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "490", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-29, -33, -10, -29, 4, 10, -9, 35, 2, -16, 17, 18],\n [0, 33, 4, 17, 11, 18, -3, 29, 33, -13, 18, -33],\n [0, 0, -18, -33, -33, -22, -28, -4, -17, -30, 12, 20],\n [0, 0, 0, -5, 6, 4, 19, -15, 7, 22, 2, -21],\n [0, 0, 0, 0, 6, 6, 16, -8, -26, -34, -34, 27],\n [0, 0, 0, 0, 0, 17, 3, 1, 21, -7, 32, 2],\n [0, 0, 0, 0, 0, 0, -1, 17, 31, -5, -21, -30],\n [0, 0, 0, 0, 0, 0, 0, -17, -9, 14, 1, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, -8, 22, -26, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 15, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25199", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 6) of the inverse of matrix 1/839 * A where A =\n[[-21, -4, 20, 20, 30, 31, -11, -9, -27, 25, 0, -25],\n [0, -29, -23, 35, 11, -30, -32, 7, -11, -11, 5, -24],\n [0, 0, 20, 14, 8, -30, -5, 12, -30, 1, -15, 16],\n [0, 0, 0, -15, -9, -8, -32, 5, 17, 12, 3, 32],\n [0, 0, 0, 0, 14, -13, 20, -27, -12, -7, -29, -18],\n [0, 0, 0, 0, 0, -7, 9, -19, -19, -5, -26, 34],\n [0, 0, 0, 0, 0, 0, 26, 29, -16, 15, -4, 23],\n [0, 0, 0, 0, 0, 0, 0, 30, 24, -27, 16, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 13, 12, 29, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -33, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-227", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-15, -26, -26, 26, 29, 31, -24, -17, 7, -28, 16, -34],\n [3, 18, 4, -7, -21, -10, 12, 5, 32, -3, -24, 14],\n [17, 14, -6, -5, -34, 30, 17, 31, 20, -3, -5, 32],\n [-13, 9, -1, 29, -33, -26, -8, -32, 21, 32, -13, -13],\n [14, -35, -12, 8, 29, 9, 2, 20, 15, -6, -31, 33],\n [1, -15, 34, 34, -30, 31, 8, 19, 16, 29, 16, -5],\n [31, 31, -30, -27, -24, 30, 28, 7, 24, 31, -5, 4],\n [-14, -1, 29, 35, 14, 4, -25, 5, -32, -33, 33, -2],\n [17, 2, -32, 35, -18, 11, -9, -8, 21, -31, -16, 19],\n [-3, 28, -17, -34, 33, 25, 22, -18, 9, -13, 14, -32],\n [-12, -24, -7, -30, -12, -19, 21, -4, 17, -10, 35, -1],\n [-9, -28, -1, -18, -13, -20, -5, 25, -2, -35, 32, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[11, 7, 0, -19, 0, 1, -18, -5, -8, 29, -5, -9],\n [0, -24, -9, 25, -11, -26, -21, -17, 32, -21, -21, 15],\n [0, 0, -23, 34, 21, 18, 4, -5, 17, -23, -12, 20],\n [0, 0, 0, -8, 25, 32, -31, -19, -16, 4, -14, 17],\n [0, 0, 0, 0, -9, -34, 16, -7, -30, -16, -18, -14],\n [0, 0, 0, 0, 0, -28, -18, -14, 34, 18, -1, 9],\n [0, 0, 0, 0, 0, 0, 18, 26, 22, 9, -7, 12],\n [0, 0, 0, 0, 0, 0, 0, 9, -11, 21, -10, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, -9, 4, 0, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -9, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1190", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (5, 8) of the inverse. Round your answer to the nearest integer:\n[[8, 20, -22, 11, 23, 24, -3, 20, -34, -34, 24, -16],\n [0, -6, 0, 31, 21, -19, -12, 32, -3, 21, 9, 18],\n [0, 0, -28, 24, -21, -5, 28, -31, 6, -7, -22, 16],\n [0, 0, 0, 12, -10, -5, 0, -9, -32, -31, 15, 30],\n [0, 0, 0, 0, -25, -29, 34, -6, 1, 9, 31, 12],\n [0, 0, 0, 0, 0, 25, -8, -13, 33, 13, -6, -10],\n [0, 0, 0, 0, 0, 0, -22, -6, -2, -13, 29, 10],\n [0, 0, 0, 0, 0, 0, 0, 17, -34, 13, -23, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, -20, 19, -8, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -6, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-55", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[31, 0, 10, -11, 2, -18, 3, 14, -29, 18, 20, 0],\n [0, -14, 19, 2, 20, -11, 4, -1, -29, 2, 17, 14],\n [10, 19, 9, 14, 0, 9, -10, 18, -12, -8, -22, -2],\n [-11, 2, 14, -20, 3, -2, 12, -6, -10, 6, -15, -12],\n [2, 20, 0, 3, 7, 6, 14, 14, -25, 34, 32, 0],\n [-18, -11, 9, -2, 6, -19, 0, 6, -12, 13, -9, 2],\n [3, 4, -10, 12, 14, 0, 5, -6, 7, -4, 30, -14],\n [14, -1, 18, -6, 14, 6, -6, 25, 0, -8, 4, -12],\n [-29, -29, -12, -10, -25, -12, 7, 0, 28, -2, 13, 0],\n [18, 2, -8, 6, 34, 13, -4, -8, -2, 19, 21, 26],\n [20, 17, -22, -15, 32, -9, 30, 4, 13, 21, 14, 11],\n [0, 14, -2, -12, 0, 2, -14, -12, 0, 26, 11, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16408", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (5, 12) of the inverse. Round your answer to the nearest integer:\n[[35, -30, -6, 1, 16, 16, 26, 12, 12, 14, 6, 12],\n [-30, 29, -18, -10, -14, 6, 1, 6, 16, 5, -2, -3],\n [-6, -18, 30, 2, 14, 4, -22, -10, -27, -3, -20, -6],\n [1, -10, 2, -30, -8, -6, -3, 15, -16, 10, 22, -16],\n [16, -14, 14, -8, 12, 4, -7, -4, 15, -4, -24, 6],\n [16, 6, 4, -6, 4, 30, 8, 4, -18, 10, -16, 16],\n [26, 1, -22, -3, -7, 8, 30, 16, 10, -10, -9, 28],\n [12, 6, -10, 15, -4, 4, 16, -29, 2, 20, 7, -19],\n [12, 16, -27, -16, 15, -18, 10, 2, -21, 27, -30, 4],\n [14, 5, -3, 10, -4, 10, -10, 20, 27, -18, -12, -26],\n [6, -2, -20, 22, -24, -16, -9, 7, -30, -12, 26, 8],\n [12, -3, -6, -16, 6, 16, 28, -19, 4, -26, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-9, 5, 16, 16, 0, 14, -15, 11, -16, -4, -30, -2],\n [0, -2, -20, 8, -1, 23, 22, -9, 5, -6, -3, 12],\n [0, 0, -4, 0, -29, -11, -25, -33, 33, 19, 8, 8],\n [0, 0, 0, 31, 7, 22, 21, -20, 24, 19, 10, 7],\n [0, 0, 0, 0, 22, 30, -3, -32, -3, -23, -31, -28],\n [0, 0, 0, 0, 0, 25, -5, 9, -12, 27, 9, -8],\n [0, 0, 0, 0, 0, 0, -6, -27, 22, -23, 6, -17],\n [0, 0, 0, 0, 0, 0, 0, 4, -13, 23, -30, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 11, 26, -26, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 3, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52404", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (10, 4) of the inverse. Round your answer to the nearest integer:\n[[-8, -35, 25, -33, 12, -22, -22, 6, 13, 4, -13, 30],\n [0, 27, -14, 19, -19, 19, 21, 20, 3, -34, 24, -6],\n [0, 0, -15, 34, -23, -26, -23, 34, 27, -8, 13, -30],\n [0, 0, 0, 6, -8, -7, 18, -16, -3, 35, -27, -25],\n [0, 0, 0, 0, -11, -9, -21, 5, -15, 21, -35, 8],\n [0, 0, 0, 0, 0, -18, -22, 30, -12, 26, 30, -12],\n [0, 0, 0, 0, 0, 0, -6, 31, -35, -12, -12, -33],\n [0, 0, 0, 0, 0, 0, 0, 30, 18, -27, -16, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, -21, -3, -33, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 14, -35, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-28, 18, -34, -32, 10, -3, -26, 25, 21, 16, 16, -4],\n [0, -8, -10, 3, -18, -25, 26, -34, -1, 6, -22, -27],\n [0, 0, 21, 35, 29, -16, 21, 18, 10, 2, 11, -28],\n [0, 0, 0, -2, 8, -29, -15, 8, -11, 11, -34, 28],\n [0, 0, 0, 0, -13, -28, -1, -13, 10, 35, -34, 2],\n [0, 0, 0, 0, 0, -26, -10, 23, -35, -21, 32, 4],\n [0, 0, 0, 0, 0, 0, -29, 25, -27, 17, 10, 30],\n [0, 0, 0, 0, 0, 0, 0, -35, -15, 33, 31, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 31, -27, 20, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -23, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32334", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (7, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[16, -35, -3, -19, -4, 4, 6, -5, 3, -9, 17, 12],\n [0, 21, -30, 5, -32, -27, 31, -9, 31, 10, 17, 20],\n [0, 0, -22, 21, -7, -33, -21, -22, -25, -10, 29, -11],\n [0, 0, 0, 31, 18, -29, -25, -13, -16, 22, 8, 21],\n [0, 0, 0, 0, -7, 9, -27, -30, -3, -7, -4, -15],\n [0, 0, 0, 0, 0, -13, -19, -23, -30, 27, 7, 6],\n [0, 0, 0, 0, 0, 0, 27, -21, 27, 10, -18, -26],\n [0, 0, 0, 0, 0, 0, 0, 7, -7, 6, 23, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, -35, -35, -12, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -14, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (12, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, 13, 4, -12, 34, 30, -2, -18, -12, -35, 9, -11],\n [-26, 5, -29, 15, -10, -4, 14, 4, -3, -21, -13, -23],\n [-14, 28, -33, -17, 13, 15, 3, 34, -22, -8, -5, 21],\n [9, -30, 6, -33, -27, -33, -9, 15, -22, 13, -32, 12],\n [-25, 25, 16, -3, 8, -4, -34, -29, 15, 26, -24, 31],\n [-14, 3, -22, -20, 35, -18, 11, 15, 3, -19, 24, -30],\n [10, 33, -3, 19, -3, 33, -16, -13, 1, 10, -9, 27],\n [-32, 22, -21, 22, 15, 24, 33, -2, 30, -7, -31, -34],\n [-33, 5, -14, 26, 12, -31, -32, -3, 14, -28, 12, -23],\n [-10, 15, -1, 11, 28, -9, 10, -2, 27, 7, -12, -19],\n [8, 30, 25, 4, -33, -13, -29, 20, 26, -9, 7, 18],\n [3, 6, -6, 6, 13, -21, 7, -1, 6, -4, 12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-137", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-12, 32, -1, 0, 30, 4, 34, -29, 16, 7, -31, -12],\n [6, -2, -10, 0, -19, 33, -30, -2, 17, 1, -16, 22],\n [23, -25, 4, 20, -15, 33, 10, 31, -4, -32, -10, -5],\n [25, -19, 17, 10, -28, -6, -18, 21, -28, -10, -15, 12],\n [15, 26, 35, 7, -34, -15, 26, -32, 17, -10, -25, 13],\n [6, -8, 4, 11, 14, 9, -22, -7, 4, 17, -9, 18],\n [4, 28, 7, 23, -10, 22, -28, 34, 24, 14, 34, 2],\n [-30, -23, -4, 1, -35, -35, 19, -12, -25, -10, -8, -26],\n [17, 12, -10, 21, 28, 5, 5, 0, 8, 7, -13, 7],\n [-14, -18, 27, 29, -22, 15, 11, -21, -19, 24, -20, 29],\n [-21, 34, -4, 1, -30, -25, -11, 29, -30, -5, -20, 33],\n [9, -25, -31, -24, -26, -33, -22, 15, -11, -17, 24, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[18, 26, 12, -16, 1, -22, 12, -14, -12, 15, -2, -2],\n [26, 35, -1, -28, 7, 8, 14, 6, 3, -8, 17, 10],\n [12, -1, 29, -10, 0, -18, 8, 18, -14, 4, -4, -24],\n [-16, -28, -10, 21, -14, 18, 14, -1, 12, -3, 16, -17],\n [1, 7, 0, -14, -1, 16, -8, 14, 7, -23, -8, 13],\n [-22, 8, -18, 18, 16, -12, 28, 2, -12, -18, 18, -10],\n [12, 14, 8, 14, -8, 28, 6, -10, -8, 19, -1, -31],\n [-14, 6, 18, -1, 14, 2, -10, 24, 0, -20, 10, -22],\n [-12, 3, -14, 12, 7, -12, -8, 0, -23, 0, -7, 16],\n [15, -8, 4, -3, -23, -18, 19, -20, 0, 2, -10, 6],\n [-2, 17, -4, 16, -8, 18, -1, 10, -7, -10, 21, 12],\n [-2, 10, -24, -17, 13, -10, -31, -22, 16, 6, 12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4635", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-24, -2, -2, 10, -6, -18, -34, 19, 0, 30, 9, -11],\n [0, 23, 29, -4, -26, 17, -28, 28, -3, -20, -1, -27],\n [0, 0, 20, 7, 0, 35, -9, -28, -15, -23, -34, -32],\n [0, 0, 0, -19, -30, 7, 31, 30, 23, -13, 3, -3],\n [0, 0, 0, 0, -30, -13, 15, -34, 1, -13, -32, -23],\n [0, 0, 0, 0, 0, -13, 3, 9, -17, 26, -5, 28],\n [0, 0, 0, 0, 0, 0, 15, -22, 5, 24, -4, -17],\n [0, 0, 0, 0, 0, 0, 0, -9, -32, -19, 30, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, -29, 5, 35, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27, -21, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8640", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (8, 12) of the inverse. Round your answer to the nearest integer:\n[[2, -11, -6, -9, 24, 20, -25, -11, -14, -7, 20, 10],\n [0, -30, 9, -13, -3, 22, -32, -6, -8, -33, 11, -16],\n [0, 0, -16, 20, -23, -6, -20, 24, -25, -8, 30, -3],\n [0, 0, 0, 15, -35, 2, 10, 28, 29, -20, -31, -31],\n [0, 0, 0, 0, 27, 11, -17, 5, 1, -25, 10, 29],\n [0, 0, 0, 0, 0, 6, -29, 3, 28, 3, -20, 21],\n [0, 0, 0, 0, 0, 0, -2, -27, -17, -4, -24, -8],\n [0, 0, 0, 0, 0, 0, 0, -23, 18, 8, -26, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 12, 1, -25, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-351", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 9, -25, 29, -1, -4, 14, -3, 33, -3, 30, -3],\n [0, -23, -29, -1, -17, -2, -10, 34, 17, 18, -13, 27],\n [0, 0, -3, 23, 29, -3, 35, 25, -20, 28, 24, -22],\n [0, 0, 0, 33, -25, 35, -26, -18, -33, -6, 15, -23],\n [0, 0, 0, 0, -14, 9, -4, -1, 21, 16, 19, 28],\n [0, 0, 0, 0, 0, 9, 4, 33, -4, 10, -19, 19],\n [0, 0, 0, 0, 0, 0, -35, -8, 30, 35, -30, 24],\n [0, 0, 0, 0, 0, 0, 0, 1, 35, -4, -27, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, -28, -25, -21, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 33, -20, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "975933", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[5, -27, 12, -13, -3, -3, 33, 27, 17, -15, 28, -4],\n [0, 5, 10, -14, -18, -11, 31, -17, -15, 14, -12, 25],\n [0, 0, 14, 21, 33, -22, -12, -26, 33, 9, 18, -25],\n [0, 0, 0, 12, 12, 5, 22, 3, -26, 17, 24, 33],\n [0, 0, 0, 0, 8, 9, -19, 17, 0, -18, -24, 34],\n [0, 0, 0, 0, 0, 32, 1, 11, -30, -14, -7, -7],\n [0, 0, 0, 0, 0, 0, 4, -9, 28, -23, -25, -11],\n [0, 0, 0, 0, 0, 0, 0, -12, -17, -17, -3, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 11, 30, -15, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 17, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "945", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[13, -2, 17, 24, 30, -8, 20, 16, -25, 7, 12, 22],\n [0, -22, 18, -34, 6, -29, -27, -3, 32, 28, 27, -28],\n [0, 0, -24, 22, 13, 8, -25, -20, 30, 2, 7, 31],\n [0, 0, 0, -5, -12, 29, 20, 27, -10, 22, -9, 33],\n [0, 0, 0, 0, -11, 32, 7, 15, -12, -27, -14, -9],\n [0, 0, 0, 0, 0, 9, 3, -6, 28, -13, -13, -4],\n [0, 0, 0, 0, 0, 0, 16, 19, 9, 10, 14, 15],\n [0, 0, 0, 0, 0, 0, 0, -3, 23, 16, -29, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, -3, 12, 8, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -13, -20, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37310", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-9, -16, -5, -34, 25, 23, -5, 20, 33, 0, -6, -13],\n [3, 34, 1, 30, 23, 33, -22, 15, -26, 13, 17, 17],\n [10, 23, 29, 18, 22, 3, 21, 33, -12, 15, -35, -25],\n [35, 35, -31, 23, -24, 16, 29, -28, 18, -3, 6, 30],\n [32, -1, -14, 3, -31, -28, 26, 15, -2, 5, -16, -9],\n [35, -20, -29, -15, 9, -9, -34, 35, -23, -17, 18, 22],\n [-26, -33, -19, -26, 7, 15, 14, -35, -16, 27, 6, 18],\n [21, 10, -22, 18, -32, 27, -15, -35, 24, -13, -20, -22],\n [-34, -29, 34, -24, -12, -14, 10, -6, -32, 2, 8, -11],\n [32, 20, -32, 28, 9, -23, -17, -27, 32, 24, 26, -3],\n [-5, 26, 9, 14, -23, 0, -26, 14, 10, 24, -14, 24],\n [-2, -34, 17, -8, 25, 8, -29, -4, 25, -7, -9, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[17, -9, -21, -34, -21, 8, 8, -25, 31, -2, 16, 32],\n [0, 12, -21, -25, 6, 13, -21, -25, 13, -26, -20, -25],\n [0, 0, 13, -15, -23, -12, 14, 14, 32, 35, -18, 27],\n [0, 0, 0, -19, -28, -33, 3, -5, 27, 12, 22, 9],\n [0, 0, 0, 0, 13, -5, -15, 20, -25, -33, -29, 2],\n [0, 0, 0, 0, 0, 9, -13, -18, 26, 20, -31, 32],\n [0, 0, 0, 0, 0, 0, 28, -32, -23, -7, -15, -28],\n [0, 0, 0, 0, 0, 0, 0, 9, -4, -5, -35, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 34, -25, -7, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 32, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-14, 17, -31, 26, -22, -28, -1, 31, -20, 25, 34, 1],\n [0, 29, 19, -5, -24, 27, -14, -32, -14, 23, 9, 23],\n [0, 0, -1, 15, -25, 20, -19, 25, 16, 20, 26, 15],\n [0, 0, 0, -9, 12, 18, 8, 17, 23, -23, -20, 8],\n [0, 0, 0, 0, -29, -18, 31, -23, 13, -8, -20, -12],\n [0, 0, 0, 0, 0, -28, -2, 28, 12, 34, 5, -18],\n [0, 0, 0, 0, 0, 0, -10, -28, 1, -18, 8, -7],\n [0, 0, 0, 0, 0, 0, 0, -24, -3, -1, 5, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 27, -30, 9, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -23, -32, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28093", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[0, -24, 22, 31, -17, 3, 22, -26, -18, 11, 15, 3],\n [29, 0, 33, -31, -33, 4, 15, -19, -25, 10, 27, 0],\n [-17, 5, -34, -9, -8, 25, 1, -1, -17, 23, 17, 31],\n [-18, -1, 14, 4, 21, 6, -1, 31, 24, -12, -35, 14],\n [19, 20, -14, -14, 29, 33, -10, 25, 17, -2, -24, -33],\n [-26, 33, -34, 34, -30, 33, 10, -12, 1, -20, 16, 14],\n [-7, 19, 19, 3, 21, -17, -30, 14, -1, 7, 20, 0],\n [-21, 1, 18, -28, -23, 33, 28, 15, -12, 31, -28, -10],\n [10, 11, -16, 9, -7, 9, -25, -35, -27, -35, 33, 19],\n [-12, -6, 3, 4, 23, 17, -13, -33, -22, -5, -30, -35],\n [19, -18, 34, -2, -19, -5, -34, -7, -20, 33, 34, -1],\n [22, -32, -28, -3, 18, -29, -11, -17, 22, 24, 31, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[29, 23, -25, 10, 35, -30, -29, 25, 24, -5, -13, -35],\n [5, 0, 21, -1, 14, 17, 31, 16, 6, -15, -6, 27],\n [2, 6, -10, -30, -29, -16, -30, 14, -9, 12, -3, 18],\n [-35, -10, 28, 24, -21, -14, -10, -27, -3, 24, 23, -25],\n [-17, -15, 6, -34, -25, 15, 27, -32, -28, 11, -27, 6],\n [6, -35, -31, 26, -19, -1, 28, -2, 13, 34, 33, -24],\n [-22, -26, -6, 4, -9, 29, 25, 17, -16, -12, -9, -2],\n [-13, -20, 14, -12, 28, 23, 1, 21, -25, -8, -14, -28],\n [22, -33, -17, 31, -14, -23, -3, -21, 33, -25, -2, 25],\n [31, 12, -35, -14, 17, 6, -4, -2, -25, -28, -22, 2],\n [26, -7, -16, 9, 28, -21, -5, -11, -34, 5, -34, 17],\n [30, -3, -11, -35, -15, 16, 24, 12, 31, -31, -9, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-242", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-22, -30, -22, -17, -35, 26, -7, 4, -29, 8, 34, -23],\n [0, -14, -31, -27, 34, 17, 33, -5, 10, -33, -18, 19],\n [0, 0, -22, -18, 25, 32, 4, 25, 8, 2, 5, -33],\n [0, 0, 0, 19, 0, 31, 0, 33, 3, -22, -19, -28],\n [0, 0, 0, 0, 15, -19, -11, 25, -2, 9, -7, -24],\n [0, 0, 0, 0, 0, 15, -5, -22, 22, -27, 10, -5],\n [0, 0, 0, 0, 0, 0, -21, -2, 20, 1, 18, 12],\n [0, 0, 0, 0, 0, 0, 0, 29, 25, -4, -20, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, -26, -11, 24, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 30, -25, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6759", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[2, 4, 10, -8, -18, -16, -16, 10, -5, -6, -12, 4],\n [4, -16, -13, 2, 16, -27, 23, 7, -26, 6, 6, -10],\n [10, -13, -9, 2, -4, -2, 8, -4, -13, -10, 26, 6],\n [-8, 2, 2, 9, -12, 0, 13, -1, 4, 22, 20, -10],\n [-18, 16, -4, -12, -23, 26, 4, 14, -1, -16, 1, -28],\n [-16, -27, -2, 0, 26, -5, 11, 4, 2, 9, -1, -17],\n [-16, 23, 8, 13, 4, 11, 13, 8, -9, -12, 18, 10],\n [10, 7, -4, -1, 14, 4, 8, 16, -18, -6, 1, -4],\n [-5, -26, -13, 4, -1, 2, -9, -18, 34, 16, 5, -15],\n [-6, 6, -10, 22, -16, 9, -12, -6, 16, 9, 8, 33],\n [-12, 6, 26, 20, 1, -1, 18, 1, 5, 8, -2, 0],\n [4, -10, 6, -10, -28, -17, 10, -4, -15, 33, 0, -22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-108", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[17, -30, 2, 30, -29, -4, 11, -5, 1, 18, -16, 35],\n [0, -2, -14, 34, 18, 6, 10, -8, 13, -9, 3, 20],\n [0, 0, 1, -12, -12, -6, -9, -6, -32, -9, 31, -30],\n [0, 0, 0, 31, -21, 13, -1, -19, 34, -21, -24, -3],\n [0, 0, 0, 0, -23, 30, -18, -28, 20, -30, 9, -6],\n [0, 0, 0, 0, 0, 4, 12, -20, 22, 32, 31, 31],\n [0, 0, 0, 0, 0, 0, 15, 3, -26, 0, 13, 15],\n [0, 0, 0, 0, 0, 0, 0, -2, 9, -25, 16, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, -35, 25, 12, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27, -30, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "317", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (11, 9) rounded to the nearest integer?\n[[14, -27, 25, 12, -22, -9, -10, -21, -25, -22, -32, 23],\n [0, 14, -4, 23, 31, 1, 13, -13, 0, 14, -35, 14],\n [-22, 22, -21, 23, -34, 27, -26, -8, 22, 0, -1, 16],\n [29, 32, 24, -9, -15, -5, 32, 8, -12, -25, 1, -24],\n [26, 17, -26, 18, -6, -21, 35, -4, 4, 35, -30, 8],\n [26, 12, 34, -9, 14, 5, 6, 32, -21, 17, -11, 24],\n [-27, 18, -4, 27, 33, 1, -15, 28, -35, 35, 34, 4],\n [-22, -30, 23, -27, 26, -2, -27, -14, 6, -6, 34, -7],\n [2, -31, -29, -25, -9, 27, -24, 23, 22, 2, -3, -1],\n [19, 23, 8, 12, -21, 19, 6, -11, -34, 5, 8, 14],\n [35, 8, 23, 21, 4, 24, -21, 24, 30, 3, 11, -23],\n [-15, -22, -14, -20, -35, -2, -30, -3, -26, 15, -11, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "396", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -5, -18, 26, -2, 24, -12, -16, -8, 31, 8, 16],\n [-5, 23, 23, -18, -12, 16, 27, -10, 7, -20, -10, 24],\n [-18, 23, 35, 18, -7, 10, -8, -12, 6, -32, 5, -2],\n [26, -18, 18, -5, -6, -16, -4, -28, -2, 8, 28, -20],\n [-2, -12, -7, -6, -12, -20, -23, 19, 12, -16, 12, -12],\n [24, 16, 10, -16, -20, 35, -19, 14, 32, 12, -3, -6],\n [-12, 27, -8, -4, -23, -19, 5, -14, -2, 1, 15, -12],\n [-16, -10, -12, -28, 19, 14, -14, 29, -20, 19, 14, 3],\n [-8, 7, 6, -2, 12, 32, -2, -20, 27, 22, 14, -13],\n [31, -20, -32, 8, -16, 12, 1, 19, 22, -24, 15, 30],\n [8, -10, 5, 28, 12, -3, 15, 14, 14, 15, 35, -14],\n [16, 24, -2, -20, -12, -6, -12, 3, -13, 30, -14, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[15, -26, 2, -19, -3, -23, 8, 11, 0, 16, 18, 6],\n [-26, -25, 10, 22, -4, -9, -25, -26, -6, -6, -16, -7],\n [2, 10, -8, -9, -3, -16, 4, 10, -12, -18, 3, 14],\n [-19, 22, -9, -20, -14, -2, -6, -8, 10, 6, 5, 2],\n [-3, -4, -3, -14, -22, -6, 16, 2, -6, -2, 10, 4],\n [-23, -9, -16, -2, -6, -7, -16, 6, 26, -26, 4, 29],\n [8, -25, 4, -6, 16, -16, -9, 0, 4, 25, -6, -1],\n [11, -26, 10, -8, 2, 6, 0, -2, -20, -20, -34, 5],\n [0, -6, -12, 10, -6, 26, 4, -20, 8, 20, 1, -8],\n [16, -6, -18, 6, -2, -26, 25, -20, 20, -35, -8, 2],\n [18, -16, 3, 5, 10, 4, -6, -34, 1, -8, 26, 4],\n [6, -7, 14, 2, 4, 29, -1, 5, -8, 2, 4, -31]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-364", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[11, -7, -15, -11, 17, 20, 25, -4, -28, -34, -9, 0],\n [0, 5, -23, -30, 23, -16, -17, -24, -33, -31, 33, 7],\n [0, 0, -29, -1, 17, -19, 35, -16, -2, -6, 4, -23],\n [0, 0, 0, -18, -10, -2, -15, -8, -31, -28, -2, 19],\n [0, 0, 0, 0, -10, 5, 35, 35, 32, 27, 32, 19],\n [0, 0, 0, 0, 0, -7, 15, 22, -6, 28, 15, -32],\n [0, 0, 0, 0, 0, 0, 11, 10, -34, 3, -15, 6],\n [0, 0, 0, 0, 0, 0, 0, -15, -32, -23, -5, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 12, 27, -13, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -26, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-80847", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-16, 16, -8, -2, 7, 22, 13, 24, -16, -16, 8, 8],\n [16, -30, 6, 20, -12, 6, -14, 30, 9, 8, 12, 2],\n [-8, 6, 7, -12, -21, 9, -3, -6, -6, 27, -22, 14],\n [-2, 20, -12, -19, 26, 14, 25, 4, -13, 0, 19, 8],\n [7, -12, -21, 26, 7, -8, 2, 2, 2, 0, -9, 5],\n [22, 6, 9, 14, -8, 22, -5, 8, 11, -4, -14, -8],\n [13, -14, -3, 25, 2, -5, 24, 0, -14, -14, -8, 9],\n [24, 30, -6, 4, 2, 8, 0, -35, 27, 23, -8, -8],\n [-16, 9, -6, -13, 2, 11, -14, 27, -25, -10, -25, -24],\n [-16, 8, 27, 0, 0, -4, -14, 23, -10, 9, 3, -13],\n [8, 12, -22, 19, -9, -14, -8, -8, -25, 3, -4, -23],\n [8, 2, 14, 8, 5, -8, 9, -8, -24, -13, -23, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3079", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[9, 1, -9, 10, -28, -24, 29, 28, -4, 10, 30, 0],\n [10, -14, -20, -8, 12, 0, 3, 0, 22, 12, 5, 15],\n [0, 13, 22, -8, -20, -13, 32, 2, -9, -6, 28, -14],\n [34, -14, 27, -12, 14, -6, -29, 22, -4, -1, -14, -10],\n [1, 0, 10, -26, -31, 25, -24, -16, -26, -10, -24, -28],\n [-16, 11, -28, -32, 29, 1, 16, -28, -3, -1, -11, 27],\n [4, 26, -8, 17, 15, 31, 30, 21, -29, -13, 8, 26],\n [-28, -23, -6, -16, -8, -17, -34, 9, 9, 26, 16, 16],\n [9, -24, -4, -19, 20, -15, -3, 19, -33, 19, -18, -26],\n [-4, -4, 3, -27, -24, -30, 22, 8, 20, -28, 22, 24],\n [-32, -15, -28, 20, -1, -15, -10, 14, -30, -31, -10, -9],\n [20, 27, 24, 1, -15, 17, 17, -3, -34, 10, 19, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1449", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[32, 14, 7, -16, -14, 17, -1, 9, -31, -32, -21, 33],\n [0, 11, -24, 2, 3, 9, 14, -1, 25, -31, 9, 2],\n [0, 0, -21, 2, 12, -32, -28, -24, -17, 28, -32, -34],\n [0, 0, 0, -27, -15, 20, 29, 30, 26, 23, 8, -27],\n [0, 0, 0, 0, 22, 19, 20, -13, -9, 17, -23, 5],\n [0, 0, 0, 0, 0, 13, 25, -26, 29, 5, -32, 1],\n [0, 0, 0, 0, 0, 0, 12, -23, 11, -15, -27, 32],\n [0, 0, 0, 0, 0, 0, 0, 28, -29, -28, -22, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 15, -19, -32, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 13, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "626", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (12, 10) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-32, -25, 22, 3, -22, -4, -9, 10, -34, 27, 9, 2],\n [-33, 3, 34, 21, -15, 33, 25, -10, 9, -21, 32, 9],\n [-11, -2, -31, -33, 19, 25, -31, 32, -16, 0, 34, 20],\n [-30, 19, 25, -31, -7, 32, 22, 22, 16, -17, -18, 34],\n [-5, -35, -30, 1, -34, 22, 1, 12, 8, 8, -9, 1],\n [-6, 29, -21, -12, -25, 14, -6, -18, -3, -33, 30, -25],\n [-13, 20, 29, 16, -29, -1, -20, 15, 17, 31, 16, 35],\n [19, 1, -29, -13, -35, -24, -21, 22, -9, 13, 27, 15],\n [-12, 21, 9, 14, -3, -10, 1, -24, 11, -7, 30, -30],\n [-26, -34, 13, -20, 34, -22, 27, -33, 5, -28, 10, 1],\n [30, 1, 1, -33, 24, 1, -3, 29, 9, 12, 28, 24],\n [-17, 23, 6, -21, 15, -1, 24, -25, -29, -6, 10, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[30, 9, -35, -17, 19, 11, -13, 2, -20, -22, 32, -30],\n [-32, 33, -1, -10, -27, 13, 33, -11, 9, -6, 24, -4],\n [-5, 14, 25, -19, 15, -21, -24, -25, 31, -11, 2, 13],\n [-14, 31, -12, 26, -21, 9, 5, -30, 14, 6, 30, 24],\n [-28, -27, 21, -9, 4, -8, -11, -26, -5, -31, -8, -23],\n [35, 32, -15, -19, 17, -34, -3, -2, -28, 14, -35, 9],\n [-4, 26, 32, 0, -21, 13, -18, -25, -21, -25, 19, 23],\n [32, 27, 21, -10, -21, -25, 22, 30, 5, -21, 20, 15],\n [14, -17, 8, -35, 3, -13, 8, -15, -8, -25, -12, -24],\n [24, 31, -3, 30, 6, 8, 21, -20, 26, -26, 27, -13],\n [14, -32, -13, -2, 18, -22, -32, 10, 1, 29, 26, 31],\n [23, 19, 0, -13, -4, 12, 3, -25, 25, -33, -21, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-188", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[9, 14, 30, -3, 13, -19, 5, -17, -25, 24, -15, 8],\n [0, -23, 10, 17, 21, 19, -25, -21, 4, -21, -23, -7],\n [0, 0, 23, 12, 22, 6, -26, -20, 13, 18, 26, 30],\n [0, 0, 0, -19, -10, 25, -7, 26, 35, -28, 16, 25],\n [0, 0, 0, 0, -7, 22, 15, 34, -28, -14, 8, 1],\n [0, 0, 0, 0, 0, 30, 5, -20, 14, 0, 11, 25],\n [0, 0, 0, 0, 0, 0, -25, -3, -24, -32, 15, -33],\n [0, 0, 0, 0, 0, 0, 0, -24, 7, 19, 5, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 35, 15, 33, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33930", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[13, -2, 23, -7, -11, 24, 34, -9, 32, 32, 7, 1],\n [14, -8, 0, 31, 24, -19, 26, 11, 13, -13, 33, 25],\n [3, -13, 13, 28, -13, -20, -3, 15, 14, 30, -6, -1],\n [23, -9, 0, -6, 18, 0, 25, -3, 29, -34, -24, 35],\n [-33, -29, 9, -29, 24, -20, 25, 23, -8, 31, 0, 12],\n [-12, 26, -14, 34, -21, 34, 10, 21, -21, -22, 30, 26],\n [-9, 8, 8, -11, 7, 34, 26, 26, -11, -20, -28, -8],\n [35, 22, -6, -33, 9, 23, 33, 20, -32, -11, 11, 5],\n [-31, 3, 34, -9, -12, 15, -9, 4, -21, 10, -5, 3],\n [2, -34, -4, 12, 19, 35, 10, -4, 9, 13, -24, 2],\n [-34, 35, 4, 26, -28, -17, 26, 18, 1, -21, -11, 28],\n [-24, 31, -27, -15, -4, -30, -20, 15, 7, -3, -29, -24]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-15, 30, -17, -16, -33, -1, -21, -18, -14, 21, 23, 23],\n [0, -25, -34, -26, -19, 11, 31, 2, 15, -14, 23, -26],\n [0, 0, -5, -10, -23, -20, 0, 0, 9, -11, -12, -17],\n [0, 0, 0, 26, 7, -19, 24, -11, -2, 5, -22, 21],\n [0, 0, 0, 0, -6, -7, 30, -24, -15, -2, 2, 34],\n [0, 0, 0, 0, 0, 19, -7, -4, -24, -12, 6, 29],\n [0, 0, 0, 0, 0, 0, -34, 21, 28, 4, -25, 15],\n [0, 0, 0, 0, 0, 0, 0, 24, 31, -20, -10, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 28, 12, 29, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 13, -26, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35060", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, -10, -28, 34, -2, 16, 8, 30, -11, 12, -27, -20],\n [0, -11, 8, -32, 8, 0, 5, -19, 33, -17, -20, 25],\n [0, 0, -31, 28, -19, 25, 18, 7, 1, 31, -2, 30],\n [0, 0, 0, 24, 18, 16, 24, 13, 9, 17, 16, 28],\n [0, 0, 0, 0, 31, -11, 28, -12, 29, 16, 15, 35],\n [0, 0, 0, 0, 0, 18, -24, -8, 14, -17, 18, 26],\n [0, 0, 0, 0, 0, 0, 22, -25, -13, -24, 31, -1],\n [0, 0, 0, 0, 0, 0, 0, 15, -18, -7, -3, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 33, 10, 10, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 32, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39932", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[19, -16, -13, -26, 12, 9, -2, 25, 28, 7, 28, 4],\n [0, -14, -19, 6, -29, 28, 16, -11, 22, -14, 19, 14],\n [0, 0, 7, -1, 22, -6, 13, 33, 3, 25, 34, 3],\n [0, 0, 0, -9, -13, 10, -15, 4, 30, 12, 13, 6],\n [0, 0, 0, 0, -21, -10, -33, -18, -16, 23, -26, 12],\n [0, 0, 0, 0, 0, 26, -18, 12, 8, 6, -4, 0],\n [0, 0, 0, 0, 0, 0, 13, 3, 22, -20, -7, 29],\n [0, 0, 0, 0, 0, 0, 0, -34, -19, 12, -17, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 7, -2, 28, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 6, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18558", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[16, -15, 4, -20, -16, -31, -21, 4, 8, 21, 4, 27],\n [0, 4, -15, 30, -17, -22, -16, 21, -16, -5, -7, 20],\n [0, 0, -27, 25, 22, 34, -35, 30, 9, 5, -11, -6],\n [0, 0, 0, 23, -22, -13, 12, 24, 11, -26, 10, -28],\n [0, 0, 0, 0, -25, 16, -6, 10, -35, 16, -21, -8],\n [0, 0, 0, 0, 0, 2, 2, 16, 10, 17, -6, -32],\n [0, 0, 0, 0, 0, 0, -27, -17, 8, -29, -5, 31],\n [0, 0, 0, 0, 0, 0, 0, -26, -1, 12, 27, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 29, -26, 3, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 31, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "509940", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-14, -11, -32, -1, -16, 12, 16, 2, 12, 9, -3, 23],\n [0, 8, -1, 22, -12, -5, -4, -3, -25, 11, 31, -28],\n [0, 0, -28, -10, -17, 23, -27, -29, 32, -30, 25, -20],\n [0, 0, 0, 30, -5, -7, 23, 35, -8, 24, -30, -30],\n [0, 0, 0, 0, 30, 20, -15, 27, 0, 5, 9, 17],\n [0, 0, 0, 0, 0, -17, -8, 30, 34, 6, 18, 31],\n [0, 0, 0, 0, 0, 0, -20, -17, -5, -33, 19, -25],\n [0, 0, 0, 0, 0, 0, 0, 23, 5, -25, 35, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 9, 11, 20, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -13, -18, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46462", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[18, -12, 4, -26, 14, -3, -6, 16, 8, 34, 0, -32],\n [-12, 11, -26, 0, -23, 16, 10, 12, 15, -4, -8, 6],\n [4, -26, -24, -7, 6, 8, -3, 11, -10, 1, 6, 14],\n [-26, 0, -7, 19, 5, -10, 4, 7, 10, 5, 18, 18],\n [14, -23, 6, 5, 23, -14, -2, -14, -14, 10, 13, 9],\n [-3, 16, 8, -10, -14, -14, 9, -23, -12, -24, 22, 30],\n [-6, 10, -3, 4, -2, 9, -27, 24, -3, 28, 16, -3],\n [16, 12, 11, 7, -14, -23, 24, -10, -9, -19, 20, 0],\n [8, 15, -10, 10, -14, -12, -3, -9, -27, 0, 26, 16],\n [34, -4, 1, 5, 10, -24, 28, -19, 0, -11, 14, -21],\n [0, -8, 6, 18, 13, 22, 16, 20, 26, 14, -2, -15],\n [-32, 6, 14, 18, 9, 30, -3, 0, 16, -21, -15, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-465", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (4, 9) of the inverse. Round your answer to the nearest integer:\n[[10, 11, 23, -24, 21, 29, -18, 32, 34, 22, 15, 26],\n [26, -1, -9, 20, -7, 7, -19, 1, 4, 21, -30, 23],\n [23, 35, 7, -21, -21, -26, 32, -3, -27, -9, 26, -25],\n [-21, 35, -28, 33, 30, -34, -19, -27, 35, -32, -5, -33],\n [5, -29, 30, 14, 24, 35, 11, 21, -14, -14, -18, 26],\n [-24, -7, -33, 17, -10, 16, 5, -23, 4, 15, -34, 0],\n [-22, -10, 30, -25, 14, 35, -1, -7, 2, -3, -30, -18],\n [-5, -31, 4, 11, 27, 7, -34, -16, -12, -1, 19, 16],\n [9, 11, 15, -7, 32, 14, -22, -8, 22, -3, 15, -35],\n [32, -7, -1, -18, 8, 19, 0, -17, 13, -15, 17, 34],\n [-35, -35, -9, -17, 16, 34, 27, 31, -34, 1, 17, 3],\n [-5, -17, 6, 15, 32, -2, 18, 22, -21, -7, 21, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 35, -9, -35, -14, -14, 17, 30, 34, 29, 19, 8],\n [1, 2, 32, -31, -13, 24, 6, -12, 6, 12, -30, 31],\n [-20, -7, 22, -33, -14, 29, -5, -31, 2, -16, 29, 28],\n [32, -6, 32, -29, 25, 16, -5, -19, -17, -29, -13, 30],\n [18, 7, -25, -7, -1, 25, -8, 22, -29, -19, 30, -14],\n [-8, 21, -34, 25, 9, -15, 20, 24, 31, 0, 5, -17],\n [12, -29, -25, 25, -32, 20, -30, 26, -6, 23, 7, 25],\n [20, 22, 23, 29, 24, 17, -25, 13, 6, 26, 30, -16],\n [-19, 8, -20, 22, -15, 17, -26, -30, -19, -24, 6, 24],\n [-3, 0, -13, -33, 31, 26, 10, -27, -14, 14, 18, 17],\n [-3, 5, -15, -10, -26, 28, -13, 31, -26, -35, -8, 3],\n [22, 2, 29, -34, 34, -18, 16, 18, -18, -14, 11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[6, 3, -17, -16, 32, -9, 29, 10, 28, 28, 21, 14],\n [-35, -33, -32, -9, 1, -13, -9, -34, -26, 8, -9, 1],\n [13, -7, -28, 24, 29, 18, -11, -29, -14, -21, -33, 19],\n [-28, 12, 29, 16, 2, -14, 21, -23, 0, 18, 11, 11],\n [34, 2, 12, 31, -14, -14, 26, -35, 27, 6, 31, -34],\n [25, 25, -26, 0, 21, -20, -23, -2, -14, -17, -18, 12],\n [-26, -9, -22, -24, -27, -1, -22, -12, 31, 10, -10, 10],\n [35, -7, -31, -6, -24, 25, -22, -5, 7, 26, 16, 31],\n [9, -13, -31, 22, 4, -24, -19, -21, 7, 31, -22, 23],\n [-1, -6, 33, -23, -15, 2, 20, 34, 32, -12, -9, -28],\n [28, 21, -31, -17, 16, 9, 1, -21, 22, -9, -28, 12],\n [-10, -27, -21, -24, -3, -32, -31, -20, 17, 9, 32, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-42", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-23, -33, -31, -21, -3, 5, -2, -19, 5, 22, -29, 8],\n [1, 8, 1, -21, -33, 30, 24, 27, -19, -6, 1, 8],\n [30, 5, 24, 34, -23, 20, -12, -33, 28, -7, -20, -32],\n [35, 18, -16, 21, 31, 20, 28, 31, -21, 34, -15, -9],\n [30, -20, -35, 30, 30, -32, 30, -32, 9, -35, 21, 31],\n [-21, 31, -22, -26, 7, -28, -35, 9, 7, -25, 5, 29],\n [4, 16, 31, 9, -27, 34, 9, -17, -33, 8, -23, -10],\n [-16, 28, -13, -5, 34, 15, -30, -19, 29, 8, 25, -20],\n [32, 31, -29, 24, -13, 32, -16, 0, 32, -10, -1, 17],\n [-16, -26, 34, -33, 10, 31, -32, 4, 3, -19, -7, -32],\n [29, -19, 28, 11, -18, 35, -10, -12, -3, -7, 10, -10],\n [5, -11, -21, -2, 15, -9, -32, -16, 12, 17, 27, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-82", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, 30, 14, -23, -9, -10, 17, -2, 21, -24, 29, -27],\n [9, 8, 12, -17, 18, 0, -21, -27, -27, 10, -5, 19],\n [34, 22, -21, 4, -26, -35, -12, 28, 12, 14, -33, 34],\n [28, -11, 20, 5, 23, -3, -24, -35, 32, 33, 23, -6],\n [-3, 4, -14, -11, -32, -24, -32, -13, 34, 22, -1, 22],\n [-30, -29, -15, -21, 30, 31, -24, 13, 26, -3, 25, -23],\n [-23, 23, -8, -12, -6, -32, -23, -35, 8, 13, -12, -2],\n [3, 6, -29, -13, -15, 7, 24, -12, 31, -8, 30, -32],\n [0, 21, 21, -17, -5, 6, 24, -6, 12, -6, 5, -4],\n [23, 12, 29, -15, 0, 31, -20, 22, -29, -8, 14, -24],\n [-11, -6, -25, 24, 6, 19, 0, 13, 10, 34, -1, -22],\n [1, 4, 16, 5, -31, -15, 19, 13, 25, -30, 15, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[26, -21, -9, -10, -11, -10, -24, 8, 22, -8, 6, 16],\n [-21, -17, 14, -22, -24, -6, 12, -20, 12, -1, -9, -3],\n [-9, 14, -23, 8, 0, 8, 17, 4, 18, 18, -29, 0],\n [-10, -22, 8, -7, 8, -2, -23, 12, -6, -6, -2, -2],\n [-11, -24, 0, 8, 29, 32, 6, -6, -20, -12, 23, 23],\n [-10, -6, 8, -2, 32, 0, -20, 2, -11, -8, -24, 24],\n [-24, 12, 17, -23, 6, -20, 23, 10, -12, 9, -18, 28],\n [8, -20, 4, 12, -6, 2, 10, -6, -6, -2, 27, 8],\n [22, 12, 18, -6, -20, -11, -12, -6, -2, 10, 7, -5],\n [-8, -1, 18, -6, -12, -8, 9, -2, 10, 15, 1, 0],\n [6, -9, -29, -2, 23, -24, -18, 27, 7, 1, 28, -3],\n [16, -3, 0, -2, 23, 24, 28, 8, -5, 0, -3, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-117", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (9, 8) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-34, 22, -3, 29, 27, -5, 32, -23, -9, 21, -22, 16],\n [0, -27, 3, -29, 21, 19, -29, -20, 11, 27, -3, -15],\n [0, 0, -20, 9, 35, -4, 7, -6, -26, -21, -23, 22],\n [0, 0, 0, 34, 9, -4, 17, -5, 8, 29, -11, -26],\n [0, 0, 0, 0, 27, -21, -28, 2, -8, -34, -33, -11],\n [0, 0, 0, 0, 0, 16, -6, -25, -27, -16, -32, 33],\n [0, 0, 0, 0, 0, 0, 11, 30, 35, -12, 10, -28],\n [0, 0, 0, 0, 0, 0, 0, -20, -27, 0, 19, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 5, -23, 21, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -26, 35, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[7, -30, -22, -4, 27, -27, 10, 31, -4, -35, -20, -4],\n [0, 11, -31, -22, 33, -25, -9, 3, -29, -34, 13, 6],\n [0, 0, -35, -7, 15, -1, -1, 1, 11, -18, -30, -8],\n [0, 0, 0, 35, 2, 19, 8, -13, 23, -7, 12, 18],\n [0, 0, 0, 0, 34, -26, -17, 23, -12, -18, -4, -17],\n [0, 0, 0, 0, 0, -30, 19, -34, -30, -6, 19, -25],\n [0, 0, 0, 0, 0, 0, -20, 10, 0, -26, 30, -19],\n [0, 0, 0, 0, 0, 0, 0, 10, 10, -34, -9, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 16, 21, -2, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 23, -30, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-493", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[17, -27, 21, -30, 12, 23, 31, -14, -15, -21, 13, 14],\n [11, 33, 5, -14, 26, -26, -17, 7, 29, -9, -28, 18],\n [-8, 8, -12, 29, -28, -34, -18, 25, 6, 4, -32, 28],\n [3, -26, -2, -9, 9, -26, 1, -33, -21, 26, -27, 31],\n [-32, -7, -7, -5, 24, -14, 30, 8, -1, -24, -14, -4],\n [-27, 28, 23, 28, 12, 17, -4, 18, 5, 31, 19, -1],\n [22, 33, -35, -27, 13, 32, 10, 1, -17, -16, 3, -21],\n [-15, 18, -26, 13, -35, -4, -22, -8, 4, 16, -9, -21],\n [25, 26, -35, -32, 3, -9, -5, 15, 6, 27, -6, -29],\n [18, 23, 32, 30, -7, 23, -2, 17, 4, 22, -7, 34],\n [34, 13, -30, -29, 0, 34, -35, -14, 6, -4, -4, -30],\n [-30, -25, -7, -3, -35, 1, 1, -10, 5, 6, 24, -33]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-23, -25, 21, 33, 29, -4, -23, -19, 30, -15, 34, 18],\n [-21, -21, -27, 35, -15, -27, 30, 35, -34, 20, -24, 20],\n [15, 34, 23, 35, -25, -33, -2, -17, -29, -25, 27, 31],\n [20, 7, 20, 9, 24, -3, -8, 21, 16, -32, -19, -1],\n [6, 24, -10, 12, 28, -19, -29, 29, 16, 5, -20, 30],\n [20, -9, -18, 27, -10, -14, 22, -35, 10, -9, 8, -3],\n [-3, 18, -11, -30, 12, 24, 26, -21, 23, 2, -21, -5],\n [29, -16, -7, -20, -3, 19, -17, 14, -2, 28, -12, -4],\n [-33, -23, -24, 26, 9, -12, -12, -21, 14, 31, 9, 29],\n [-16, -15, -24, -17, -34, -3, 1, -26, -4, -6, -22, -31],\n [0, 22, -23, -18, -28, 33, 12, -33, 34, -19, 15, 21],\n [7, 6, -7, 19, 34, 7, 24, 5, 13, -9, -33, 32]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "242", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[6, 18, -35, -15, 31, 11, 23, -35, -22, 4, 31, -27],\n [0, -11, 28, 24, -3, -31, 16, -3, -20, -33, -31, 26],\n [0, 0, -18, -24, 7, 14, 4, -1, 21, 20, -8, 26],\n [0, 0, 0, 29, -1, 22, -27, 3, -15, 24, 7, 27],\n [0, 0, 0, 0, -11, 22, -26, -30, 14, -16, 10, -25],\n [0, 0, 0, 0, 0, -8, 2, -3, 18, 24, -32, 18],\n [0, 0, 0, 0, 0, 0, -15, 8, 25, -12, -1, -13],\n [0, 0, 0, 0, 0, 0, 0, 26, -33, -20, -30, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, -8, 1, 25, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -31, 28, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "292528", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[34, 10, -4, 0, -6, -33, 1, -32, 32, 7, -29, 7],\n [0, 30, 10, 33, -33, -1, -21, -9, 33, 17, 31, 3],\n [0, 0, -32, -20, -29, -9, 31, -33, -4, 12, 32, -26],\n [0, 0, 0, 7, -14, 28, -6, 5, 3, -11, -25, -14],\n [0, 0, 0, 0, -34, -33, 8, 0, 1, -13, 17, 26],\n [0, 0, 0, 0, 0, 2, 15, 22, -12, 6, 35, -16],\n [0, 0, 0, 0, 0, 0, -4, -9, 14, 30, 2, 20],\n [0, 0, 0, 0, 0, 0, 0, 23, 14, 32, 16, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, -17, -28, -18, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -29, 4, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "306", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[28, 11, 6, -9, -13, 35, 9, -4, 3, 18, 8, 28],\n [0, -30, -28, 30, 4, 27, 6, 26, -29, -35, 7, -23],\n [0, 0, 2, 9, 15, -21, 23, 30, -22, -22, 5, -12],\n [0, 0, 0, 10, -20, -14, -4, 5, -14, 17, -13, -1],\n [0, 0, 0, 0, 31, 19, -5, 18, 0, -1, -22, -14],\n [0, 0, 0, 0, 0, 13, 35, -27, 7, 26, -16, -17],\n [0, 0, 0, 0, 0, 0, 23, 35, -22, 17, 18, 8],\n [0, 0, 0, 0, 0, 0, 0, -6, -28, -18, 24, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 30, 33, -35, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 25, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "988350", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, -30, -6, 9, -7, 16, -7, 32, -25, -16, 21, 8],\n [0, -3, 23, 32, 13, -21, -33, 31, -25, 19, -28, 1],\n [0, 0, -14, 22, 10, -13, -2, 14, 11, 13, -33, -6],\n [0, 0, 0, 16, 31, -11, -34, 22, 18, -20, 27, 7],\n [0, 0, 0, 0, -18, -29, 26, 25, 26, 26, -23, 23],\n [0, 0, 0, 0, 0, -23, 33, -17, 18, 33, 25, 13],\n [0, 0, 0, 0, 0, 0, 12, -32, -25, 7, -22, -4],\n [0, 0, 0, 0, 0, 0, 0, -6, -10, -25, -33, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 8, -29, 17, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -18, -18, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-43126", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-21, -33, -35, -23, 26, -33, -20, -4, -8, 12, 12, -9],\n [0, -1, -17, -19, -27, 10, -24, -3, -7, -23, 31, 22],\n [0, 0, -26, -5, 17, 8, -7, 13, 21, 1, 12, 23],\n [0, 0, 0, 24, 34, -17, 17, -7, 26, -9, 4, 0],\n [0, 0, 0, 0, 19, 22, 3, 5, 14, 23, 20, 17],\n [0, 0, 0, 0, 0, 4, 0, -23, 10, -35, 24, -34],\n [0, 0, 0, 0, 0, 0, 23, -32, -20, -25, -14, 29],\n [0, 0, 0, 0, 0, 0, 0, -32, 8, 29, -30, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, -2, -24, -15, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -15, -20, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1482", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 10, 3, 12, -4, 4, 1, 18, 12, 3, 2, 18],\n [10, 31, -11, -8, -16, 10, 14, -1, -24, -4, -34, -10],\n [3, -11, -17, -16, -20, 4, 10, 10, -8, -30, 4, 28],\n [12, -8, -16, -20, 16, 18, 29, 22, -2, 4, 8, 10],\n [-4, -16, -20, 16, -32, -16, -18, 9, 10, 9, -4, 28],\n [4, 10, 4, 18, -16, -33, 10, 7, 2, -17, 18, 24],\n [1, 14, 10, 29, -18, 10, 17, 5, 10, 28, -15, -15],\n [18, -1, 10, 22, 9, 7, 5, -22, 0, 12, -12, 5],\n [12, -24, -8, -2, 10, 2, 10, 0, -16, -8, -15, -2],\n [3, -4, -30, 4, 9, -17, 28, 12, -8, -6, 16, 25],\n [2, -34, 4, 8, -4, 18, -15, -12, -15, 16, -15, 1],\n [18, -10, 28, 10, 28, 24, -15, 5, -2, 25, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-11, -24, 29, -20, 19, 2, 7, -28, 17, 25, 34, 10],\n [-27, 31, -13, -5, -2, -1, 12, -15, 31, 2, 17, -1],\n [-22, 22, 32, 2, -21, 18, 29, -26, -25, 0, 21, 2],\n [32, 1, -18, 3, 0, 4, -29, -17, 1, -28, 0, 35],\n [5, 7, 1, 29, 18, -14, 11, 9, -11, -16, -6, 15],\n [35, -33, 34, -29, -7, 19, -34, -10, 9, 18, 2, -27],\n [34, 18, 11, 12, -12, -34, -5, -15, 28, 13, 11, -35],\n [-2, -4, 27, 27, 16, 3, 12, -33, -22, -10, -1, -32],\n [9, -10, 17, 28, -10, -7, 25, -22, 17, 23, 33, -6],\n [-14, -30, -31, 5, 11, -13, 17, 4, 25, -22, -14, 32],\n [-33, 31, 2, -29, -23, 19, -34, 1, 14, -16, 13, -25],\n [14, 5, -32, 7, -5, -34, -24, -6, 8, 0, -11, 35]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[14, -14, 0, -33, -9, -29, 1, 19, 8, 24, 23, 16],\n [-32, -34, -19, -6, 12, -34, 30, -9, -15, -31, 29, -11],\n [-11, 12, -25, -17, -18, -29, -32, -15, 5, -30, 27, -18],\n [-9, 10, 10, 9, 7, 14, -15, -3, -6, -35, 33, -3],\n [-18, -24, -24, 28, -7, -17, -34, -24, 8, 0, -19, -29],\n [-18, -23, 24, -24, 12, 15, 31, 24, -26, -13, -32, -11],\n [29, 25, 33, 33, 11, -9, 26, 35, 13, 25, -6, -5],\n [-20, 29, -25, 26, 2, 23, -17, -27, 33, -13, 19, -16],\n [-23, 21, -16, 11, -29, -2, 20, 17, 17, 27, -6, 32],\n [-32, 1, 3, 0, -21, 0, -17, -20, 7, -30, -22, -8],\n [-30, -17, -30, -31, 30, 12, 34, -22, 9, 4, -6, -14],\n [-33, -7, 12, -28, 13, -29, -12, -31, 28, -31, 13, 34]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-21, 11, -1, 0, -10, 8, 9, 24, 18, 0, 6, -9],\n [11, 13, 10, -2, -4, -22, -22, -5, -8, 0, -22, 21],\n [-1, 10, -5, -12, 8, -2, 6, -20, -4, 0, 8, -20],\n [0, -2, -12, 11, -7, -2, 18, -12, -4, -16, 24, -27],\n [-10, -4, 8, -7, -26, -3, 20, 10, -22, -17, -6, -23],\n [8, -22, -2, -2, -3, -30, 5, -14, 2, 6, -12, 4],\n [9, -22, 6, 18, 20, 5, -2, -13, 12, -16, -2, 31],\n [24, -5, -20, -12, 10, -14, -13, 18, -28, -7, -10, -16],\n [18, -8, -4, -4, -22, 2, 12, -28, -9, 8, -10, 14],\n [0, 0, 0, -16, -17, 6, -16, -7, 8, -22, 18, 2],\n [6, -22, 8, 24, -6, -12, -2, -10, -10, 18, 28, -2],\n [-9, 21, -20, -27, -23, 4, 31, -16, 14, 2, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4929", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[10, 14, 8, 22, 8, -6, -2, -12, 24, 6, -11, 7],\n [14, -14, -12, 7, -7, -6, -17, 16, 5, -16, 24, 18],\n [8, -12, 35, 6, 30, 24, 8, 2, 21, 4, 16, 6],\n [22, 7, 6, -11, -7, -20, -20, -6, 18, 6, -18, -13],\n [8, -7, 30, -7, 29, -4, -12, 23, 17, -5, -8, 4],\n [-6, -6, 24, -20, -4, -23, -10, 2, -22, -12, -12, -18],\n [-2, -17, 8, -20, -12, -10, 34, 8, 20, -7, 2, -12],\n [-12, 16, 2, -6, 23, 2, 8, -10, 17, 6, 8, -10],\n [24, 5, 21, 18, 17, -22, 20, 17, -10, 29, 6, 14],\n [6, -16, 4, 6, -5, -12, -7, 6, 29, 31, -21, 16],\n [-11, 24, 16, -18, -8, -12, 2, 8, 6, -21, 31, -10],\n [7, 18, 6, -13, 4, -18, -12, -10, 14, 16, -10, 14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 5) of the inverse of matrix 1/839 * A where A =\n[[-18, -7, -26, 3, -33, 12, 6, 11, -10, -4, -9, 34],\n [0, -18, -14, 27, 14, -35, -33, 20, -29, -9, -21, -4],\n [0, 0, -4, 17, -8, 34, 0, 26, -26, -22, -11, 29],\n [0, 0, 0, -13, -34, -21, 8, 8, 27, 1, -31, -4],\n [0, 0, 0, 0, -16, -34, 18, -10, -34, 30, -8, -21],\n [0, 0, 0, 0, 0, 4, 23, -10, -20, -34, 27, -11],\n [0, 0, 0, 0, 0, 0, -3, -26, 17, 35, 4, -12],\n [0, 0, 0, 0, 0, 0, 0, -9, -7, 4, -29, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, -34, -24, 17, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-731", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[21, -16, 23, 32, -10, -23, -15, 19, 6, -13, 34, 8],\n [0, 29, 15, -9, 1, 4, -9, 29, 24, 20, 16, 17],\n [0, 0, -1, 13, -22, 23, -31, -4, -14, 25, -15, -3],\n [0, 0, 0, -33, 21, 20, 26, -18, 20, 12, -31, -22],\n [0, 0, 0, 0, 29, -4, -18, -18, 5, 34, 15, 0],\n [0, 0, 0, 0, 0, 6, 27, 5, 25, -6, -23, -29],\n [0, 0, 0, 0, 0, 0, -32, 3, 5, 5, 5, -8],\n [0, 0, 0, 0, 0, 0, 0, -21, -13, -19, 22, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, -32, 29, -26, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 17, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82821", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[17, -28, 23, -17, 8, 8, -2, 17, -33, -34, 24, 10],\n [0, -29, 25, -1, -1, 33, 13, -34, -2, -23, 28, -1],\n [0, 0, 8, -29, 3, -23, -32, -17, -5, 7, 28, -34],\n [0, 0, 0, -21, 7, -22, -16, -13, 18, 26, 26, 28],\n [0, 0, 0, 0, -24, -16, -11, -8, -20, 15, 4, -15],\n [0, 0, 0, 0, 0, -18, -30, 23, -30, -21, 25, -6],\n [0, 0, 0, 0, 0, 0, 22, -9, 22, 15, 11, 21],\n [0, 0, 0, 0, 0, 0, 0, -28, -23, -35, 27, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 6, 23, 26, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 0, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1599", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[0, -4, -14, 6, 6, -1, 4, 18, -6, 25, -5, -28],\n [-4, 12, 34, 14, 6, -20, -5, 26, -14, 12, 30, 2],\n [-14, 34, -31, 24, -12, 5, -6, 2, 12, -2, -3, -9],\n [6, 14, 24, 35, -7, -19, 14, -3, -2, -16, -14, 18],\n [6, 6, -12, -7, -23, -22, 7, 27, -4, -15, -18, -4],\n [-1, -20, 5, -19, -22, -9, 14, -10, -3, 1, -10, -20],\n [4, -5, -6, 14, 7, 14, 3, -6, -7, 6, 2, -3],\n [18, 26, 2, -3, 27, -10, -6, -13, 6, 3, 28, 12],\n [-6, -14, 12, -2, -4, -3, -7, 6, -15, -18, -10, 8],\n [25, 12, -2, -16, -15, 1, 6, 3, -18, -24, 0, 12],\n [-5, 30, -3, -14, -18, -10, 2, 28, -10, 0, -19, -6],\n [-28, 2, -9, 18, -4, -20, -3, 12, 8, 12, -6, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16416", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (12, 5) of the inverse. Round your answer to the nearest integer:\n[[17, -30, -26, -20, -14, 30, 6, -31, 1, 15, -17, -32],\n [0, 19, -29, 25, 32, -10, 23, 3, -2, -11, 0, 30],\n [0, 0, -23, -19, 2, 7, 5, 35, -34, -35, -17, -20],\n [0, 0, 0, 15, 13, -13, -34, -4, 18, -16, 31, -18],\n [0, 0, 0, 0, 2, 22, 5, -30, -32, 8, -32, -8],\n [0, 0, 0, 0, 0, -17, -20, -33, -30, 18, -10, -2],\n [0, 0, 0, 0, 0, 0, -30, -13, 21, -27, -26, 34],\n [0, 0, 0, 0, 0, 0, 0, 2, -19, -22, 10, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 31, 4, -35, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -17, -21, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[22, -9, 12, 5, -25, 7, -33, 13, 13, 8, -30, 12],\n [0, -9, 14, -13, 30, -7, -22, -7, -31, 23, -18, 35],\n [0, 0, 8, 2, -33, -8, 18, 9, 7, -3, -23, 5],\n [0, 0, 0, 30, 8, 7, -32, -17, -2, 26, -31, -25],\n [0, 0, 0, 0, -18, -29, 11, -21, 26, -13, 0, -19],\n [0, 0, 0, 0, 0, 35, -35, 14, 27, 14, 1, -21],\n [0, 0, 0, 0, 0, 0, -24, -22, 25, 25, -27, -12],\n [0, 0, 0, 0, 0, 0, 0, -3, 25, -25, -33, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, -4, 16, 26, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -19, 35, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-729", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, -4, 25, -30, 26, -1, -25, -22, 9, -10, 4, -2],\n [0, -14, 5, 23, -4, -1, 34, -32, -28, 17, -5, -14],\n [0, 0, -20, -18, -20, -6, -24, -22, -30, -12, -23, 16],\n [0, 0, 0, 3, 12, -10, -8, 29, -23, 9, -33, 14],\n [0, 0, 0, 0, 27, 16, -28, 22, 13, -32, -2, -4],\n [0, 0, 0, 0, 0, 24, 32, -33, 31, -33, 28, 12],\n [0, 0, 0, 0, 0, 0, -16, -26, -8, 32, 16, -34],\n [0, 0, 0, 0, 0, 0, 0, -28, -20, -22, -3, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 12, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 22, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "391537", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 1, -19, -10, 7, 22, -27, -15, 29, 27, -9, 0],\n [23, 10, -6, -19, 16, 11, 1, -22, 0, -1, 22, 14],\n [-30, 26, 26, 2, -27, -23, -13, -3, 18, 9, 12, 32],\n [25, 16, 10, 8, 13, 1, 5, -14, 6, 22, 16, 17],\n [13, -23, 26, 0, 16, 5, 1, -17, 22, -12, 27, 19],\n [-32, -11, 25, -5, -15, -31, 32, -31, -20, -24, 29, 30],\n [7, -11, 10, -35, -4, 25, -7, 12, -13, 33, 17, 35],\n [-10, 35, -15, 24, 19, 32, -24, -28, -19, 7, -27, -19],\n [-20, 15, -1, 16, -24, 31, 33, -23, -23, -8, 11, 8],\n [27, 33, -16, 0, 9, 21, -34, 6, 14, -5, 12, -10],\n [-11, -1, -2, 9, -13, -20, -32, 18, 32, 17, -22, -33],\n [6, 31, 14, -16, 19, 30, 17, -10, -17, 27, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (6, 7) rounded to the nearest integer?\n[[12, 0, 12, -2, 20, -4, 8, 0, 10, 10, 32, 30],\n [0, 23, 0, -6, -14, -7, 14, 30, 14, 2, -12, 20],\n [12, 0, 16, -6, 20, 12, -17, 10, 20, -10, -2, 23],\n [-2, -6, -6, 5, 14, 8, -14, -5, 14, 6, -5, 8],\n [20, -14, 20, 14, 4, -20, -17, 18, -8, 0, 31, 0],\n [-4, -7, 12, 8, -20, 6, -3, -4, 12, 10, -5, 3],\n [8, 14, -17, -14, -17, -3, 4, 4, -8, -26, -4, -8],\n [0, 30, 10, -5, 18, -4, 4, -15, 16, 6, -7, -10],\n [10, 14, 20, 14, -8, 12, -8, 16, -8, -14, 5, -8],\n [10, 2, -10, 6, 0, 10, -26, 6, -14, -23, -22, 12],\n [32, -12, -2, -5, 31, -5, -4, -7, 5, -22, 24, 9],\n [30, 20, 23, 8, 0, 3, -8, -10, -8, 12, 9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-13, 33, -22, -21, -21, -1, -25, 1, -15, -21, 9, -28],\n [0, -4, 35, -11, 10, -26, 14, 20, -35, -27, 12, -10],\n [0, 0, 9, -18, 23, 21, 31, -8, -21, -1, 6, -11],\n [0, 0, 0, 25, -25, 21, 7, 11, 6, -32, 26, -11],\n [0, 0, 0, 0, -3, 8, 35, -6, 31, -8, 4, -5],\n [0, 0, 0, 0, 0, 10, -9, -27, -25, 35, -31, 23],\n [0, 0, 0, 0, 0, 0, -25, -1, -24, -24, 14, 15],\n [0, 0, 0, 0, 0, 0, 0, -28, 15, 13, 27, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 15, 15, -2, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 5, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4010470", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (2, 9) rounded to the nearest integer?\n[[18, -30, 34, 13, 23, 21, 25, 20, 5, -22, 1, 5],\n [0, 6, 0, 20, 35, -10, -22, 3, 24, -8, 8, 9],\n [0, 0, 34, 34, -33, -29, -2, 29, -9, 18, 7, -12],\n [0, 0, 0, 8, -21, 13, 7, -30, 14, 10, 4, -6],\n [0, 0, 0, 0, -19, -28, 10, 21, -8, -5, 15, -7],\n [0, 0, 0, 0, 0, 20, -35, -29, -24, -15, 0, -3],\n [0, 0, 0, 0, 0, 0, 23, -13, -16, -5, 31, 17],\n [0, 0, 0, 0, 0, 0, 0, 18, -20, 24, -24, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, -18, 7, 19, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 25, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5632", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[1, -26, -15, -1, 14, -2, 12, 18, 32, -26, -5, -25],\n [0, -31, -14, 3, 5, -25, 22, -25, 12, 17, 21, 4],\n [0, 0, 25, 16, -8, 30, 6, 33, -1, -27, -29, 21],\n [0, 0, 0, -4, -12, 3, -2, 3, 4, -21, 13, 24],\n [0, 0, 0, 0, -21, -30, 25, -28, 14, -18, 31, -12],\n [0, 0, 0, 0, 0, 3, -7, -35, -35, 1, -24, 32],\n [0, 0, 0, 0, 0, 0, -11, 6, -11, -11, -11, -19],\n [0, 0, 0, 0, 0, 0, 0, -35, 26, -3, 11, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 33, -19, -35, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 29, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "701", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[19, -33, 30, 30, -35, 29, -5, -18, 10, -10, -12, 5],\n [0, -28, 32, 10, 24, 10, -35, 26, 10, -17, -33, 22],\n [0, 0, 18, -18, 33, 23, 8, 13, 20, -16, -12, 4],\n [0, 0, 0, 23, -22, 7, -25, -5, -19, 17, 10, -11],\n [0, 0, 0, 0, -24, 19, 7, 2, -31, 18, -19, -19],\n [0, 0, 0, 0, 0, -32, 34, -32, -22, 24, 15, -23],\n [0, 0, 0, 0, 0, 0, 20, 11, -29, 33, 29, -17],\n [0, 0, 0, 0, 0, 0, 0, -22, -20, -3, -31, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, -19, 6, 26, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -3, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -31, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1075", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (4, 10) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-30, 8, -5, -1, -1, -17, -3, 23, 11, 35, 32, -34],\n [0, -2, 17, -11, -14, 1, -35, -4, 12, -29, 31, 30],\n [0, 0, -23, 8, 26, 32, 11, -6, -1, 15, 17, -26],\n [0, 0, 0, -31, -4, 3, -8, 35, 15, -34, 12, -9],\n [0, 0, 0, 0, -27, -3, -13, 34, 24, -19, -34, 3],\n [0, 0, 0, 0, 0, -18, -5, -24, -4, 32, -13, 22],\n [0, 0, 0, 0, 0, 0, 26, -28, 12, -27, -15, 2],\n [0, 0, 0, 0, 0, 0, 0, -32, -33, 26, 11, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 35, 25, 21, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 14, -6, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[14, 9, -1, 26, 21, 10, 33, -6, 14, -21, 0, 3],\n [24, -9, 18, -34, 34, -32, 11, 12, 21, 29, 22, 15],\n [11, 34, -2, 1, 19, 8, 32, 7, -26, 30, -20, -1],\n [4, 26, -2, 6, -32, 27, -13, -25, -13, 25, 33, 16],\n [25, -31, -19, -2, -20, -32, 16, -16, 12, 15, 9, 13],\n [20, -33, 6, 35, 6, -7, -19, -8, 24, 11, -25, 29],\n [24, 25, 7, 3, -35, -27, -27, -33, -7, 6, 7, -12],\n [-33, -28, 9, -10, 15, 19, -3, -1, -25, 13, -11, -26],\n [9, -30, -8, -23, 28, -6, -31, 35, 19, 16, -8, -12],\n [13, 12, -5, -12, 35, -16, -34, 22, 18, 3, -17, 34],\n [-32, -16, -33, 26, 33, 32, -17, -20, -14, -15, 20, 24],\n [-2, 33, 30, -23, -15, 24, 32, 10, -20, 19, -25, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-115", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[14, 16, 26, 5, -25, -29, -20, -7, -31, 28, -21, -30],\n [13, 15, 6, 29, -31, -12, 1, 17, -30, 3, 26, 24],\n [5, -26, 34, -29, -31, -9, -1, 19, -19, -29, 25, 29],\n [-21, 22, 13, 16, -10, 7, 17, 20, 32, -3, -22, -19],\n [3, 12, -30, -14, 1, 7, 9, 29, -32, 32, 21, -2],\n [-6, 3, 3, -19, -24, -30, -7, -22, -35, 3, -30, 8],\n [5, -4, -31, 11, -19, -3, 6, -13, 34, 14, -7, 28],\n [-32, -29, 26, 23, -15, -20, 34, -23, -28, 25, -33, 10],\n [26, -13, -28, -16, -6, 18, -16, -34, -19, -21, 29, 33],\n [33, 32, 7, -24, -14, 34, -16, -21, -28, 1, -8, -25],\n [34, -9, 6, -28, 23, 24, 26, -17, 7, 24, 15, 28],\n [30, 34, 12, -18, -16, 31, 4, -18, -24, -10, -3, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2680", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (8, 1) rounded to the nearest integer?\n[[22, 21, -27, -26, 8, 17, -9, 16, 28, 18, -23, -5],\n [13, -9, -23, 10, 15, 7, -17, -7, 31, -17, -23, 2],\n [-1, -3, 9, 21, 13, 30, 3, 11, -3, 14, 30, -3],\n [13, 35, -26, -8, 8, -23, -7, 4, -27, -7, -32, -17],\n [12, 31, 6, 22, 23, -20, 24, 31, -19, 28, -3, 35],\n [-14, -29, -31, -23, -26, -22, 35, -5, -32, 12, 27, -32],\n [21, -1, -22, -12, -13, 17, -9, -28, -3, -19, 22, 26],\n [-6, 10, -19, 31, 21, -30, 20, 34, 14, 31, -1, -17],\n [-21, 1, -5, 19, 35, -35, 18, -2, -9, 7, -20, -11],\n [33, -33, 32, 23, 25, -21, 25, -24, 27, -12, 35, -12],\n [26, -23, -26, 29, -31, 11, -28, 15, 1, 7, 21, 8],\n [29, 13, 3, -6, 30, 15, 10, -28, -30, 23, -31, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (7, 8) of the inverse. Round your answer to the nearest integer:\n[[-33, -4, 26, -6, 13, -24, 14, -18, 11, 27, 8, -15],\n [12, 30, -4, 9, 15, 17, -8, 26, -7, 25, -28, 10],\n [-5, 30, 26, -18, 19, 1, -6, -15, -23, -17, -32, -15],\n [-12, 9, -23, -14, 13, 12, -19, -16, -4, 14, 26, -21],\n [6, -25, 1, 32, 2, 25, 25, -21, -8, 31, -15, -7],\n [25, -20, 7, -12, -5, -23, -11, -30, 7, 15, 5, -1],\n [8, -22, 20, 22, 7, 23, 19, 1, -2, 10, 12, 4],\n [-16, 6, 28, -13, 15, -24, 15, -33, -29, 1, -16, 22],\n [-17, -9, 0, 24, -13, -6, 3, 30, -2, -27, 14, -35],\n [-34, 33, -1, 9, -26, 27, -10, -33, 10, 3, 14, 24],\n [-17, -26, -32, 3, 7, 1, -18, -7, 10, 14, -19, -13],\n [-30, -1, 1, 13, -33, 4, 24, -1, 4, 23, -32, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[19, -31, 29, -5, 24, 7, -27, 22, -20, 34, -2, -1],\n [0, 14, -24, -6, 8, -34, -27, 35, -24, -2, 13, 15],\n [0, 0, -10, 33, 13, 15, 5, -25, 11, -22, -20, 8],\n [0, 0, 0, -10, -33, 13, 5, -17, -24, 19, -34, -8],\n [0, 0, 0, 0, -28, -8, 6, -33, 24, 15, -17, -32],\n [0, 0, 0, 0, 0, 19, -16, -32, 1, -14, 8, 25],\n [0, 0, 0, 0, 0, 0, 12, 0, -21, -29, -5, 25],\n [0, 0, 0, 0, 0, 0, 0, 8, 31, -16, 10, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, -19, -11, -24, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -28, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1963328", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[9, 0, -4, -10, -3, 7, -30, 16, 24, 23, 8, -12],\n [0, 31, 4, -16, -11, -4, 35, 16, -15, 13, -13, 28],\n [0, 0, -31, 29, 28, 7, 12, -34, 30, 31, -3, -13],\n [0, 0, 0, 32, 7, 18, 29, 10, -24, 19, 22, -27],\n [0, 0, 0, 0, -14, -11, -27, -1, 17, 10, 10, 27],\n [0, 0, 0, 0, 0, 28, 29, 20, -18, -25, 28, -2],\n [0, 0, 0, 0, 0, 0, 31, 29, -32, -26, 35, 33],\n [0, 0, 0, 0, 0, 0, 0, -33, -6, -30, 35, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, -3, 29, -12, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -27, -5, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3637", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-22, -2, -11, -6, -10, -24, 13, -2, 0, 19, -2, -10],\n [-2, 28, -26, -14, 0, -4, -12, 2, 12, 8, 2, 8],\n [-11, -26, 18, 18, 2, -8, 18, -16, -10, -20, -15, -2],\n [-6, -14, 18, -31, 10, -10, 10, 16, 24, 19, -16, 0],\n [-10, 0, 2, 10, 33, 14, -19, 2, 20, 4, 12, -18],\n [-24, -4, -8, -10, 14, -5, 6, -8, -16, 6, 12, 16],\n [13, -12, 18, 10, -19, 6, 25, 2, -13, -1, 4, 8],\n [-2, 2, -16, 16, 2, -8, 2, -27, -14, -8, 4, -23],\n [0, 12, -10, 24, 20, -16, -13, -14, -23, 18, 5, -14],\n [19, 8, -20, 19, 4, 6, -1, -8, 18, 8, 14, 32],\n [-2, 2, -15, -16, 12, 12, 4, 4, 5, 14, -20, -10],\n [-10, 8, -2, 0, -18, 16, 8, -23, -14, 32, -10, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "386", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, 5, -16, 23, -35, 11, 11, -31, -32, 30, 12, 18],\n [0, -14, -34, 19, -20, -24, 20, 14, 30, -25, -18, 15],\n [0, 0, -10, -30, 20, 11, -17, -33, -23, 5, 5, -29],\n [0, 0, 0, 11, -21, 20, 14, -19, -2, 6, -7, -30],\n [0, 0, 0, 0, -13, 18, -28, -24, 9, 21, 29, 32],\n [0, 0, 0, 0, 0, -4, 4, -32, -29, 20, 21, 10],\n [0, 0, 0, 0, 0, 0, -6, 31, 18, -11, 6, 25],\n [0, 0, 0, 0, 0, 0, 0, -2, -28, 20, -25, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, -30, -12, 0, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 14, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4207892", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, 3, 16, -29, -14, 26, -9, -4, 1, -14, 15, -12],\n [3, -19, 6, -8, -18, -12, 0, 10, -14, 3, 27, 18],\n [16, 6, -16, 1, -13, -19, 0, -2, -4, 7, 7, -15],\n [-29, -8, 1, 9, -8, 10, -8, -33, -2, 8, 10, -5],\n [-14, -18, -13, -8, 30, 10, 20, 24, 4, 0, 16, 19],\n [26, -12, -19, 10, 10, -12, 6, -16, 20, 28, 16, -2],\n [-9, 0, 0, -8, 20, 6, -32, -8, 14, 18, 18, -24],\n [-4, 10, -2, -33, 24, -16, -8, 18, 12, -22, -5, -2],\n [1, -14, -4, -2, 4, 20, 14, 12, 4, 1, 6, -4],\n [-14, 3, 7, 8, 0, 28, 18, -22, 1, -17, 1, -15],\n [15, 27, 7, 10, 16, 16, 18, -5, 6, 1, 3, 18],\n [-12, 18, -15, -5, 19, -2, -24, -2, -4, -15, 18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "703", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-29, -14, -5, 23, 4, -33, 6, -19, -32, -28, -12, 5],\n [0, -8, -2, -32, -18, -2, -8, 2, 33, -7, 0, 7],\n [0, 0, 3, -22, 9, 9, -26, -29, -20, -22, -10, 6],\n [0, 0, 0, -34, -32, 26, 7, 10, -22, 7, -35, -8],\n [0, 0, 0, 0, 24, 20, 22, 8, 13, 12, -13, 14],\n [0, 0, 0, 0, 0, -19, -35, 17, -32, -11, -29, 27],\n [0, 0, 0, 0, 0, 0, 13, -10, 8, -3, 25, -27],\n [0, 0, 0, 0, 0, 0, 0, -16, -31, -23, -13, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 30, -8, -1, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 3, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9729", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[17, -14, -1, -8, 28, 8, 0, -16, -1, -6, 16, -20],\n [-14, 30, -13, 4, 2, 12, -12, 1, 1, -30, 9, -14],\n [-1, -13, 30, 8, 3, 16, -20, -12, 9, 35, 14, 4],\n [-8, 4, 8, -12, -34, 14, -22, 8, 20, -30, 2, -10],\n [28, 2, 3, -34, 7, -30, 8, 7, -20, -12, 8, 4],\n [8, 12, 16, 14, -30, 19, -6, 21, 18, 23, 0, 23],\n [0, -12, -20, -22, 8, -6, 1, -25, 24, 2, 1, -4],\n [-16, 1, -12, 8, 7, 21, -25, 33, -4, 28, -10, 18],\n [-1, 1, 9, 20, -20, 18, 24, -4, -22, -2, -10, 12],\n [-6, -30, 35, -30, -12, 23, 2, 28, -2, -8, 8, -30],\n [16, 9, 14, 2, 8, 0, 1, -10, -10, 8, 27, 18],\n [-20, -14, 4, -10, 4, 23, -4, 18, 12, -30, 18, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -6, 12, 5, 10, -26, 16, 22, 10, -19, 32, 5],\n [-6, -32, 7, 24, -22, -4, 10, 17, -32, 11, 1, 20],\n [12, 7, -35, 12, -4, -24, -18, 10, 2, -14, 0, 16],\n [5, 24, 12, 32, -12, -16, 6, -2, -30, 9, 15, 18],\n [10, -22, -4, -12, 20, -5, -28, 14, 0, 12, 10, -7],\n [-26, -4, -24, -16, -5, 16, -12, 10, 27, 20, 12, -1],\n [16, 10, -18, 6, -28, -12, 29, 27, -18, 17, 2, -5],\n [22, 17, 10, -2, 14, 10, 27, -3, 30, -6, -6, -22],\n [10, -32, 2, -30, 0, 27, -18, 30, -26, -8, -3, 20],\n [-19, 11, -14, 9, 12, 20, 17, -6, -8, -31, 12, -13],\n [32, 1, 0, 15, 10, 12, 2, -6, -3, 12, -13, 2],\n [5, 20, 16, 18, -7, -1, -5, -22, 20, -13, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2156", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[14, -19, 3, 6, -13, 33, 28, -27, -28, 28, 4, -21],\n [0, -20, -8, 24, -8, -12, -33, -13, 14, 25, -33, -2],\n [0, 0, -12, 1, -2, 13, -15, -21, -23, -20, 25, -7],\n [0, 0, 0, -21, -25, -25, -8, 29, 23, 16, 23, -22],\n [0, 0, 0, 0, 35, 31, -19, -15, -20, 14, -11, 6],\n [0, 0, 0, 0, 0, 25, 34, -35, -5, -5, 1, -22],\n [0, 0, 0, 0, 0, 0, -5, 14, 27, 23, -4, 26],\n [0, 0, 0, 0, 0, 0, 0, 23, 10, -27, 7, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, -9, -8, -18, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -21, 25, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3822", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[29, 34, -28, 20, 12, 6, -2, -4, -14, 1, -18, 14],\n [34, 23, 12, -14, -14, -11, -14, -8, 12, 4, -16, 20],\n [-28, 12, -34, 11, -4, -22, -22, -15, 14, 2, -27, -5],\n [20, -14, 11, 4, 13, -3, 14, 27, -2, 14, -26, -6],\n [12, -14, -4, 13, -1, 30, -14, 10, 12, 14, 16, -2],\n [6, -11, -22, -3, 30, 30, -6, -3, 23, 2, 23, 16],\n [-2, -14, -22, 14, -14, -6, 14, 5, -8, 24, -32, -4],\n [-4, -8, -15, 27, 10, -3, 5, -9, 2, 0, -22, -2],\n [-14, 12, 14, -2, 12, 23, -8, 2, 16, 6, -16, -14],\n [1, 4, 2, 14, 14, 2, 24, 0, 6, 29, 18, -18],\n [-18, -16, -27, -26, 16, 23, -32, -22, -16, 18, -7, 10],\n [14, 20, -5, -6, -2, 16, -4, -2, -14, -18, 10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-153", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, 19, 2, -10, -1, 25, -14, -6, -18, -10, 10, 8],\n [19, 10, -8, 21, -16, -8, -10, 26, 14, 6, 22, -16],\n [2, -8, -13, 12, 0, 20, -14, -18, 6, 1, -32, -1],\n [-10, 21, 12, -10, 12, 7, 10, 7, -8, -22, -28, 10],\n [-1, -16, 0, 12, -26, 26, 0, -15, -2, -8, -12, 11],\n [25, -8, 20, 7, 26, -12, 22, -12, -16, 4, -3, -20],\n [-14, -10, -14, 10, 0, 22, 17, -18, 7, 28, 25, -6],\n [-6, 26, -18, 7, -15, -12, -18, -19, 2, 18, 16, 4],\n [-18, 14, 6, -8, -2, -16, 7, 2, 24, 12, -6, 3],\n [-10, 6, 1, -22, -8, 4, 28, 18, 12, -3, 17, 0],\n [10, 22, -32, -28, -12, -3, 25, 16, -6, 17, -16, 28],\n [8, -16, -1, 10, 11, -20, -6, 4, 3, 0, 28, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "260", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-13, -2, 1, -31, 6, -11, 10, -9, -29, 24, -24, -29],\n [0, -28, -32, -8, 10, 25, 4, -2, -9, -10, -25, -35],\n [0, 0, 24, 32, -34, 18, -27, 33, -26, -33, -5, -32],\n [0, 0, 0, -23, 25, 9, 32, -12, 24, 24, -31, -4],\n [0, 0, 0, 0, 35, 6, -16, -25, -34, -5, -26, 23],\n [0, 0, 0, 0, 0, 3, -26, 1, -13, -16, -2, -32],\n [0, 0, 0, 0, 0, 0, 10, -5, 30, 14, -15, -15],\n [0, 0, 0, 0, 0, 0, 0, -26, 3, -25, -6, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, -1, -35, -20, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 5, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-209", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (7, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[21, -23, -17, 3, 17, 23, 1, -25, -20, -35, -14, 22],\n [12, 11, 18, -17, 28, 30, -20, 3, -15, 9, 29, -13],\n [6, -26, -24, 5, 20, -30, 1, -10, 28, -34, -35, -33],\n [-33, -7, -14, -22, 21, 27, 9, -4, -32, -30, 2, -14],\n [3, -16, -28, -9, -12, 29, -26, 25, 34, -22, 26, 35],\n [-24, -23, 20, -5, 32, -22, 31, 1, 29, -24, 33, -23],\n [-29, 22, 19, 14, 1, 8, -25, -27, -25, 8, 35, -4],\n [-15, 35, 6, -12, -9, 9, -30, -29, -26, -33, -14, -5],\n [6, 10, -32, 30, 11, 16, 0, -33, 19, 10, -25, 23],\n [27, -9, 27, 31, -5, -8, -14, -33, 19, -5, 26, 9],\n [-18, -7, 33, -2, 14, 11, 28, 34, 3, -32, 12, 28],\n [32, 21, -34, -9, -23, -17, -15, -25, -1, 5, 23, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[8, 29, 9, 0, 3, 21, -5, -11, -15, -28, -28, -18],\n [0, 3, -24, 18, 33, -16, 6, 1, -9, 35, -20, -21],\n [0, 0, -35, -18, 20, 29, 5, -26, 21, -5, -15, -35],\n [0, 0, 0, 10, -25, 20, -7, -33, -17, 32, -1, 9],\n [0, 0, 0, 0, -20, -10, 35, -31, -35, -6, -12, -16],\n [0, 0, 0, 0, 0, -25, 9, -23, 12, 19, -32, -6],\n [0, 0, 0, 0, 0, 0, -20, -25, 16, 15, -26, -2],\n [0, 0, 0, 0, 0, 0, 0, 5, 25, 17, -29, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 31, 9, -9, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -17, -6, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "148971", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[14, -18, 13, 5, -12, -6, -21, -20, -18, -35, -25, 3],\n [-27, 3, -19, -1, -3, 17, 28, -9, -14, 6, 17, 29],\n [10, -22, -5, -23, -31, -8, -32, -7, -4, 7, -22, 27],\n [-33, 35, 10, -2, 8, -22, -18, 9, 9, -11, 18, -34],\n [-3, 8, 7, 23, 4, 20, -34, -30, 18, 34, -13, 22],\n [-29, -31, 11, 12, -33, -5, -13, 13, 1, -17, -4, 26],\n [-16, 24, -25, -2, 17, 13, 29, 3, 32, 18, 32, -13],\n [27, 21, 0, 16, -17, -15, 8, -4, -3, 24, 33, -30],\n [-35, -21, 21, -35, -17, -14, -10, -30, 24, 19, 30, 11],\n [10, 14, -15, -10, -32, 32, 17, -7, -12, 25, 30, 20],\n [-26, 33, 18, -16, 31, 2, -20, 18, -33, 28, -8, 22],\n [-6, 6, 29, -10, 19, 21, -23, 5, 12, 9, -29, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (7, 9) rounded to the nearest integer?\n[[11, -19, -4, -11, 2, 21, -27, 32, 34, 9, 29, -27],\n [0, 30, 33, -6, -25, -18, -2, 12, -30, -11, -11, -17],\n [0, 0, 2, 18, -9, -3, 14, -20, 15, -10, 14, -5],\n [0, 0, 0, -28, 34, -20, 13, -30, 25, 18, 18, 8],\n [0, 0, 0, 0, -1, -10, 35, 30, -7, 9, -15, 32],\n [0, 0, 0, 0, 0, 26, 9, -4, 16, -11, 5, 9],\n [0, 0, 0, 0, 0, 0, 12, -30, -10, -17, 14, 7],\n [0, 0, 0, 0, 0, 0, 0, -22, 0, -21, -20, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, -13, -16, 31, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -33, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-54", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[18, 10, -11, -17, -27, -6, 9, 19, -25, -1, -19, 22],\n [-8, -34, -15, 6, 31, -17, -31, -2, 15, 6, 7, -3],\n [31, -15, -17, 27, 31, -25, -11, 27, 3, 24, 9, -35],\n [11, 14, 35, -19, -5, -9, -5, -18, 35, 12, -10, -7],\n [20, 22, 32, -5, 10, -23, 29, -2, -5, 6, 25, 26],\n [-21, -9, 6, 28, 3, -35, -27, 32, -5, 13, 4, -33],\n [-19, -2, 6, -4, 3, 18, 7, 30, -25, -28, -1, -9],\n [-19, -34, -14, 25, -34, -19, 31, -14, -3, 19, 34, 18],\n [6, 4, -19, -3, 3, -11, 22, 10, -30, -2, -24, 12],\n [14, -15, 10, 3, 23, -27, -17, -29, 17, -15, 19, 5],\n [3, -9, 5, 25, -12, 29, 24, 14, 22, -26, -25, 22],\n [0, 29, -6, -29, -24, 1, -27, 11, -32, 32, 21, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4491", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[6, 8, 2, -27, 8, -22, -1, -14, 10, -32, 15, 4],\n [8, -21, 6, 25, -10, 19, -1, 27, 5, -12, 0, 14],\n [2, 6, 1, 14, -27, -2, -2, 33, -7, -27, -3, -4],\n [-27, 25, 14, -30, -10, -14, -20, -4, 5, 10, 18, -24],\n [8, -10, -27, -10, 26, 22, 2, -6, 0, 26, -26, 18],\n [-22, 19, -2, -14, 22, 26, -6, -22, -4, -23, 10, -4],\n [-1, -1, -2, -20, 2, -6, -25, 9, 2, -18, 21, 24],\n [-14, 27, 33, -4, -6, -22, 9, -17, -20, -30, 10, -26],\n [10, 5, -7, 5, 0, -4, 2, -20, 20, 18, 16, 14],\n [-32, -12, -27, 10, 26, -23, -18, -30, 18, 9, -13, -34],\n [15, 0, -3, 18, -26, 10, 21, 10, 16, -13, 17, 10],\n [4, 14, -4, -24, 18, -4, 24, -26, 14, -34, 10, 23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7212", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-30, -34, -13, 19, 9, -14, 0, -34, -19, 11, -25, -14],\n [-27, -34, 34, 9, 24, -25, 6, 17, 1, -31, -11, 34],\n [8, 31, 20, -10, -19, -21, 31, -7, 28, -7, 19, -5],\n [4, 27, 1, 34, -35, 3, -15, -8, 27, 17, -16, 13],\n [27, 12, 9, -1, -32, 16, 8, 0, -15, 33, -22, -24],\n [34, 0, -24, 29, 34, -1, 33, 6, -20, 25, -28, -5],\n [25, 21, 10, 6, -14, 22, 19, -19, 30, 10, -2, 2],\n [-20, 26, -32, 22, -26, 30, 23, 0, -33, 2, 0, 24],\n [31, -32, -24, -25, -25, 21, 7, 11, -15, -13, 25, 11],\n [29, 2, -29, -22, 29, 2, 14, -6, -2, -10, 17, -19],\n [-17, 26, -23, 8, -8, 10, 22, 0, 3, -17, 1, 29],\n [15, 12, -16, 9, -10, 3, -33, -3, -12, 15, -14, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-206", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-16, -13, 23, 14, -4, 16, 23, 21, -5, 18, -32, -16],\n [0, -10, -17, 3, -17, 11, 0, 1, 0, 15, -22, 2],\n [0, 0, -25, -14, -32, 21, -10, -31, 27, 21, -24, 16],\n [0, 0, 0, 3, -6, -8, 7, 33, 5, -9, 5, -3],\n [0, 0, 0, 0, 35, 27, -11, 24, -4, -13, 0, 5],\n [0, 0, 0, 0, 0, -11, -13, -9, 1, -7, 35, 13],\n [0, 0, 0, 0, 0, 0, -29, 7, 15, 25, 8, -35],\n [0, 0, 0, 0, 0, 0, 0, -4, -20, -18, -18, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 5, -19, 10, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 7, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-36310", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-11, -4, -17, 24, -25, 11, 7, -30, 25, 31, 26, -17],\n [-4, -5, 34, -32, -1, -23, 3, 22, -33, -19, 22, 10],\n [-7, -29, 15, 32, 28, -25, -1, 23, -8, -30, -20, -1],\n [-30, -21, -27, 10, -28, -3, -10, -19, -25, -10, 32, 3],\n [30, 32, 16, -25, 14, 16, 14, 26, 19, -3, 17, -23],\n [21, 16, -33, -21, 32, -8, 3, 20, -6, 12, 18, 30],\n [28, 21, 19, 24, 32, 0, -7, 6, 13, -20, -3, -25],\n [15, 26, 32, -2, 2, 23, 7, 14, -6, -16, -21, -32],\n [-9, 0, -2, 12, 22, -15, 6, 17, -15, -11, 25, -9],\n [-32, 24, -17, -19, 25, -2, 15, -19, 33, 3, 35, -22],\n [-20, -12, 14, -10, -19, -10, 8, 7, 21, -33, 35, 33],\n [-16, 4, -31, 26, -11, -27, -22, -25, -18, -30, -33, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2675", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (1, 8) of the inverse. Round your answer to the nearest integer:\n[[25, 5, 24, -2, 31, 15, 0, -1, 27, 23, -22, 26],\n [-15, 5, 24, 21, -24, 21, 4, -26, 26, -23, 26, 31],\n [6, 29, 31, 10, 32, 1, 22, 26, 11, -5, -6, -10],\n [23, -23, -11, 20, 20, 18, 29, 17, 4, -15, -9, 35],\n [27, -8, 8, 6, 3, 22, 0, 17, 34, 20, 12, 8],\n [8, -29, 1, 30, 5, 3, 0, -28, 7, -21, 18, -30],\n [15, -23, -9, -2, 15, -8, 35, -1, -16, -34, -15, 6],\n [-14, 22, 0, -20, 1, -15, 29, 23, 31, -10, -1, -27],\n [-27, -13, 17, 13, 2, -33, -15, -5, 25, 9, 10, -21],\n [-20, -19, -10, 9, -14, 31, 31, 32, -4, -20, 24, -6],\n [1, -28, -5, -33, -31, 10, 7, 33, 30, 15, -20, 4],\n [13, 30, 9, -13, -35, -1, -14, -7, 26, -25, 15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-27, -29, -32, -1, -24, -20, 14, 18, 35, 25, -26, 1],\n [3, -6, 10, 11, 29, -13, -11, -20, -1, 28, 21, 13],\n [-1, 21, 19, 32, -31, -8, 10, -20, -29, 1, -19, -19],\n [-9, -15, -2, 22, 13, 28, -4, 17, 2, -14, -21, 14],\n [30, 28, 1, -14, 14, -22, 15, 23, -25, -29, 4, 7],\n [25, -2, -31, -12, -1, 5, 32, -33, 25, -32, 34, 14],\n [29, 32, 32, 20, 0, 31, 18, -7, 27, 26, -3, 30],\n [-6, -1, -6, -16, 15, 10, 18, -19, 16, -30, -28, 12],\n [-34, -27, -22, -15, 3, 18, 19, 29, -13, 7, 23, 14],\n [31, 14, 26, 18, 7, -9, 11, -11, -8, 28, -11, -5],\n [10, -2, -24, -9, 18, 9, -16, 13, -23, 5, 29, 21],\n [29, 6, 19, -2, -5, -32, 27, 25, -21, 20, 20, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "358", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[22, -20, -12, -15, -21, 4, -23, -25, 12, 21, 0, -14],\n [-20, -32, -23, 5, -12, -13, -20, -22, 9, 7, 13, 8],\n [-12, -23, 1, -14, -32, -8, -22, -8, 34, 10, -18, 0],\n [-15, 5, -14, 19, -8, -24, -10, -13, 12, -18, 18, 8],\n [-21, -12, -32, -8, 2, -6, 30, -2, 0, 25, 10, 4],\n [4, -13, -8, -24, -6, -16, -8, -12, 7, -8, -4, 19],\n [-23, -20, -22, -10, 30, -8, 28, 24, 32, -10, 18, 13],\n [-25, -22, -8, -13, -2, -12, 24, -7, 10, -16, 3, -8],\n [12, 9, 34, 12, 0, 7, 32, 10, 1, 2, 11, -16],\n [21, 7, 10, -18, 25, -8, -10, -16, 2, -7, -31, 28],\n [0, 13, -18, 18, 10, -4, 18, 3, 11, -31, 12, 8],\n [-14, 8, 0, 8, 4, 19, 13, -8, -16, 28, 8, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1544", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-26, -33, 8, -20, 2, 27, -27, 31, 14, -30, -9, 35],\n [20, -21, -12, 19, -12, -17, -8, 32, 12, 33, 14, 30],\n [16, -31, -18, 29, -7, 18, 4, -1, -16, 24, 23, -24],\n [34, 31, 2, 18, 0, 22, -16, 3, 30, 10, -11, 25],\n [28, -16, 31, 8, 20, 28, 20, 13, 1, -14, 3, 26],\n [22, 31, -18, 2, -15, -2, 18, -5, 31, 22, -33, -2],\n [-24, 23, 8, 8, 22, 14, 2, 12, -2, 8, 19, 24],\n [-4, -20, -5, 6, 2, -32, -4, 32, -35, 0, -29, 8],\n [-12, -3, -11, 22, -24, -25, 33, 8, 30, 16, 30, 14],\n [-24, 33, -3, 22, -26, 17, 13, -1, 13, -26, 21, 27],\n [27, 2, 25, 30, -2, -14, -19, -23, -21, 35, -23, 27],\n [-29, 34, 33, 1, -10, 11, -19, 19, -14, 3, 5, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1028", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 10) of the inverse of matrix 1/839 * A where A =\n[[-7, -16, 33, 22, -8, -5, 28, -9, -10, 14, -9, 2],\n [-17, -29, 5, -28, -16, -13, -8, -13, 14, -15, -11, -3],\n [32, 22, 12, 29, -4, 26, -22, 22, 10, 31, 29, -19],\n [3, 16, 19, 32, -17, -9, -18, 17, -22, -31, 1, 6],\n [12, -10, -9, 6, 1, -8, 5, 26, 33, -3, -5, 20],\n [-29, 21, -2, 31, 35, 10, -8, 9, 24, -29, 10, -27],\n [-21, 19, -27, -2, 21, -32, 2, -22, 5, 32, -33, -9],\n [-23, 32, -1, -17, 8, -4, 9, 33, -11, 15, 26, -28],\n [-18, 18, 8, 31, -2, -20, 19, 12, -6, 23, 0, -13],\n [21, 4, 13, -31, -2, -11, 4, -18, -34, -14, -25, 0],\n [-27, 32, -4, 20, 16, -22, 19, 16, -22, 27, -21, -35],\n [19, 18, -24, 22, -26, 13, -4, 14, -25, -29, -12, -20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 33, -19, 24, 27, -2, -20, 15, -27, -9, 12, -6],\n [-14, -14, -12, 2, -30, -19, 19, 24, 16, -12, 15, -21],\n [-8, -22, -25, -35, -19, 15, 18, 30, 30, -21, 22, -32],\n [29, -9, 8, 16, 10, 21, -25, 1, -20, 33, 28, -28],\n [-1, -31, -23, -31, -20, -16, 6, -8, 18, -25, 30, 32],\n [23, -31, -29, -14, 27, -34, -28, -33, -30, -35, 30, 21],\n [16, 1, 16, -27, -1, 9, 13, 4, -28, -21, 6, -24],\n [16, 20, 20, 22, 17, -6, 14, 6, -24, 29, 29, 23],\n [-2, -16, 27, 24, 29, 17, -6, 28, 26, -18, -26, -29],\n [34, -32, 4, -26, -10, 19, 34, -7, 3, 17, 15, -13],\n [20, 25, 1, -31, 33, -30, -16, 34, -8, -3, -22, -4],\n [0, -14, 29, -24, 18, -30, -22, -4, 24, 13, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 7) of the inverse of matrix 1/839 * A where A =\n[[31, -12, -18, -24, -14, 3, 17, 19, -17, 23, 30, -14],\n [0, 19, -32, 28, -31, 3, -11, -3, 4, -3, 7, -21],\n [0, 0, 13, 29, 2, -29, -21, 3, -4, 13, -6, 30],\n [0, 0, 0, 6, 8, -30, -13, 12, 21, 32, 24, 6],\n [0, 0, 0, 0, -1, 25, 16, -16, -28, -10, -35, 23],\n [0, 0, 0, 0, 0, -28, -14, -28, -10, -3, 7, -16],\n [0, 0, 0, 0, 0, 0, 15, -16, -11, 14, -28, 3],\n [0, 0, 0, 0, 0, 0, 0, 10, -10, -4, 11, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, -20, 33, 23, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -35, 29, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-280", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 6, 9, 1, -8, 13, -14, 15, 7, -16, 6, 2],\n [6, 5, 4, 5, -2, -16, 2, 11, 5, -27, -9, -21],\n [9, 4, -16, -4, 6, -12, -20, 24, -2, -8, 4, 4],\n [1, 5, -4, 17, 16, 6, -3, 7, -2, -12, 14, 15],\n [-8, -2, 6, 16, -14, -28, -11, 4, 12, -7, -19, 1],\n [13, -16, -12, 6, -28, -8, -12, 11, 4, -32, -6, 7],\n [-14, 2, -20, -3, -11, -12, -20, 12, 31, 6, 14, 20],\n [15, 11, 24, 7, 4, 11, 12, 31, 27, -3, 14, 5],\n [7, 5, -2, -2, 12, 4, 31, 27, 2, 18, -2, 24],\n [-16, -27, -8, -12, -7, -32, 6, -3, 18, 17, -19, -4],\n [6, -9, 4, 14, -19, -6, 14, 14, -2, -19, 30, 16],\n [2, -21, 4, 15, 1, 7, 20, 5, 24, -4, 16, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-64", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[20, 30, -14, 34, -4, 23, -4, -34, -23, 35, 23, -4],\n [0, 3, 17, 6, 16, -9, -6, -35, 24, -28, -32, 25],\n [0, 0, -18, 12, -24, 5, -1, -2, 12, 31, 23, 25],\n [0, 0, 0, -31, -13, 35, -5, -26, 11, -11, 14, -30],\n [0, 0, 0, 0, 1, -34, 8, 29, -26, 33, 25, -34],\n [0, 0, 0, 0, 0, -20, 20, -21, -12, 16, 2, 7],\n [0, 0, 0, 0, 0, 0, 31, -10, -29, -13, 19, -17],\n [0, 0, 0, 0, 0, 0, 0, 35, 25, -27, 5, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 30, 15, -17, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 13, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28165", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-15, 35, 31, -10, -8, -23, 23, 17, 29, 2, -27, 29],\n [-14, -10, 27, 25, 21, -15, -3, -24, 23, 10, -30, -16],\n [-3, -7, 17, 23, 18, 17, -1, -10, -13, 1, -9, 12],\n [12, -13, 2, 14, -6, 15, -18, 14, 28, 28, 6, 7],\n [-35, 9, 32, 1, 34, -5, 2, -14, 9, -1, -12, 26],\n [-19, 9, 28, 14, -13, -9, -16, -24, 2, 22, 34, 18],\n [30, 32, -34, 26, 25, -4, -30, 22, 29, -7, -28, 19],\n [7, 18, -23, -24, 33, -17, -21, -31, -17, -34, 0, -27],\n [-5, 11, 20, -22, 23, -13, 35, -15, 32, -12, -27, -18],\n [-15, -27, 9, -15, 8, 0, 0, -4, -9, 29, 8, -14],\n [6, 28, -24, 17, 13, -30, 30, 28, -13, -32, 7, 31],\n [-34, -17, -35, 35, 33, -29, 18, 2, -26, -12, -30, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[6, 5, -12, 1, 7, 32, -28, -27, 3, -35, -33, -27],\n [0, 17, 11, 11, 27, -25, 13, 5, 19, -33, -22, 31],\n [0, 0, 16, -4, -2, -18, 17, 1, -35, -7, -22, -12],\n [0, 0, 0, -27, 0, -17, -20, -27, 8, 17, 7, 5],\n [0, 0, 0, 0, 18, 14, -24, 19, 3, -27, -26, -21],\n [0, 0, 0, 0, 0, -3, -22, -33, 20, 34, -1, -19],\n [0, 0, 0, 0, 0, 0, 16, 3, 5, -8, -19, -34],\n [0, 0, 0, 0, 0, 0, 0, -29, -1, 25, 19, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 12, -29, 5, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -27, 24, -15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-773", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[2, 6, -2, -22, 6, -2, -30, 10, 12, 2, -8, -3],\n [6, 15, 20, 17, -15, 32, -28, -12, 4, 2, 15, -2],\n [-2, 20, -3, 27, -15, -22, -20, -5, -20, 30, -14, 20],\n [-22, 17, 27, 1, -7, 10, -28, -1, -6, 19, 18, 21],\n [6, -15, -15, -7, -13, 0, -16, 3, -32, -6, -17, 8],\n [-2, 32, -22, 10, 0, -3, -3, 19, 20, -22, -32, -6],\n [-30, -28, -20, -28, -16, -3, -15, 22, 6, -20, -2, 10],\n [10, -12, -5, -1, 3, 19, 22, -3, -18, -2, 22, -6],\n [12, 4, -20, -6, -32, 20, 6, -18, -12, -16, 20, 12],\n [2, 2, 30, 19, -6, -22, -20, -2, -16, 1, 10, 30],\n [-8, 15, -14, 18, -17, -32, -2, 22, 20, 10, 32, -18],\n [-3, -2, 20, 21, 8, -6, 10, -6, 12, 30, -18, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2006", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-31, 20, -20, 0, 22, -30, -3, 4, 11, 26, 26, 32],\n [20, 15, -20, 3, 4, 7, 21, -15, -6, 13, -12, -30],\n [-20, -20, 5, -23, 18, 11, -23, -3, 5, 10, 13, 8],\n [0, 3, -23, 23, 3, 15, 10, 18, -5, -17, 22, -10],\n [22, 4, 18, 3, 3, 0, -3, -18, 32, -16, 26, -16],\n [-30, 7, 11, 15, 0, -26, 12, 14, -2, 17, 10, 4],\n [-3, 21, -23, 10, -3, 12, -14, -6, -24, 10, -2, 22],\n [4, -15, -3, 18, -18, 14, -6, 27, -18, -4, -14, 0],\n [11, -6, 5, -5, 32, -2, -24, -18, -18, 20, -16, -14],\n [26, 13, 10, -17, -16, 17, 10, -4, 20, -9, -22, 1],\n [26, -12, 13, 22, 26, 10, -2, -14, -16, -22, -30, -22],\n [32, -30, 8, -10, -16, 4, 22, 0, -14, 1, -22, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1635", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-31, -32, -28, -34, -33, -6, -29, 8, -12, -29, -35, -6],\n [28, 22, 25, 34, 29, -5, 26, 4, 30, -25, 16, 25],\n [26, 2, 17, 21, 0, 18, -3, 3, -32, 10, -19, -5],\n [3, -14, 28, 31, -18, 17, 24, 0, 12, 35, 33, -5],\n [-34, -18, 20, -26, 10, 30, -26, 23, -14, -15, 13, -33],\n [1, 6, -8, 33, 19, 33, -5, 15, -9, -15, 32, -32],\n [33, -23, -4, 33, -5, 24, -21, -18, -18, -8, -28, -8],\n [26, 33, -18, -29, -17, -21, 20, -4, 7, -34, -15, 28],\n [1, -21, -7, -5, 3, 22, 3, -21, 20, -6, -11, 24],\n [11, 20, -11, 10, -33, -14, 0, -31, 4, 35, -9, 24],\n [27, 11, 15, 8, -9, 17, -31, -14, 3, -15, 21, 14],\n [4, 9, 11, -12, 20, 33, -21, -2, -7, -1, -11, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2256", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[19, 32, -10, 11, -32, 0, -34, 11, -20, 4, -16, -17],\n [0, -16, -31, 18, 14, 10, 1, 21, -21, -17, 19, 20],\n [0, 0, 11, -27, 0, -31, -7, 31, -11, 25, 11, 24],\n [0, 0, 0, -23, -10, -18, 3, 21, -12, -5, 11, 19],\n [0, 0, 0, 0, 19, 15, -8, -35, 10, 6, 21, 13],\n [0, 0, 0, 0, 0, -27, 20, 34, -14, -32, -31, -30],\n [0, 0, 0, 0, 0, 0, -5, -13, 22, -28, 30, -29],\n [0, 0, 0, 0, 0, 0, 0, 15, -35, -26, 33, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 8, -24, 1, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 11, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102975", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (7, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[33, -5, -2, 18, 4, -28, -7, -10, 23, -23, -26, -27],\n [-25, -27, -30, -6, -34, -17, -21, 21, 24, 26, -33, 10],\n [18, -26, 16, -29, -30, 21, -24, 5, 33, 25, -11, -32],\n [-7, 27, 0, 9, -31, -22, -35, -20, -30, 20, -12, -12],\n [-23, 26, -2, -7, -23, -27, -33, 23, -32, 9, 2, 12],\n [-24, 9, -15, 26, 22, 22, -6, -17, 6, 15, 23, -13],\n [8, -33, 17, 11, 7, -21, 26, -2, -4, 28, -33, 30],\n [32, -12, -6, 7, 29, -8, 16, -20, -15, 14, 5, -4],\n [29, 30, 24, -5, -18, -19, -28, -26, 24, 19, 24, -12],\n [-31, 32, 0, 29, -1, -12, -30, 16, 30, -22, 4, -2],\n [-35, -13, -35, 8, 11, -8, -8, 33, -16, 16, 12, -19],\n [28, -31, 24, 21, -16, 33, 31, -2, 14, -35, -34, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-23, 7, -9, 10, 10, 19, 14, -10, 1, 4, 0, -8],\n [7, 30, -28, 8, 9, 2, 20, 2, -8, -10, 10, -4],\n [-9, -28, -13, -2, 10, -10, 17, -10, 12, -17, -6, -2],\n [10, 8, -2, 34, 30, 15, 24, -3, -12, -5, -15, 6],\n [10, 9, 10, 30, -11, -21, -8, -18, -10, -26, -8, 3],\n [19, 2, -10, 15, -21, 20, -11, 17, 6, -4, 3, 10],\n [14, 20, 17, 24, -8, -11, -18, -22, 6, 18, 27, 0],\n [-10, 2, -10, -3, -18, 17, -22, -3, 8, 13, 0, -2],\n [1, -8, 12, -12, -10, 6, 6, 8, -14, -22, -1, 4],\n [4, -10, -17, -5, -26, -4, 18, 13, -22, -17, 26, 0],\n [0, 10, -6, -15, -8, 3, 27, 0, -1, 26, 34, 10],\n [-8, -4, -2, 6, 3, 10, 0, -2, 4, 0, 10, -28]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2135", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[21, -3, 31, -34, -10, -13, -3, -8, -33, 17, 25, 6],\n [31, 30, 11, 10, -5, 22, -21, -26, 6, 21, -22, 29],\n [-20, 6, -11, 12, -15, 17, -34, -31, -25, -34, -15, 7],\n [-8, 4, 5, -11, 19, 20, 8, -13, 34, -20, 31, -25],\n [-33, -13, -5, -15, -10, 16, 24, 27, 25, 2, -28, -9],\n [1, -2, -7, 23, -1, 12, 27, 30, 4, -20, 29, 22],\n [-1, 33, 25, -21, 31, -8, 21, -30, -32, -31, 5, -5],\n [-25, 28, 26, 0, -24, -35, -30, 30, 22, -16, -24, -26],\n [12, -28, -2, -33, 13, -17, 3, 23, 31, 34, -2, -18],\n [-14, 16, -25, 30, 24, -12, -29, 35, 16, -4, 16, -4],\n [8, -11, 15, 11, -3, 2, 0, 18, -11, 34, -9, -7],\n [15, -9, 35, -34, -27, -8, 10, -17, -21, -34, 13, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-18, -16, -16, -3, -26, -4, 4, 2, 16, -14, 2, -5],\n [-16, 11, 8, 10, -30, 6, -4, 12, 6, -27, 7, 5],\n [-16, 8, -13, 11, -19, 22, 12, 1, -5, 4, -5, -16],\n [-3, 10, 11, 30, -7, -2, -17, -1, -34, 18, -24, -4],\n [-26, -30, -19, -7, 24, -16, 13, -26, -2, 14, 1, -20],\n [-4, 6, 22, -2, -16, -23, 6, -14, -28, 13, 10, 14],\n [4, -4, 12, -17, 13, 6, 11, -26, -14, 28, 28, -24],\n [2, 12, 1, -1, -26, -14, -26, -4, 3, -30, -2, -7],\n [16, 6, -5, -34, -2, -28, -14, 3, 23, -26, 16, 4],\n [-14, -27, 4, 18, 14, 13, 28, -30, -26, -35, 8, -20],\n [2, 7, -5, -24, 1, 10, 28, -2, 16, 8, 22, 2],\n [-5, 5, -16, -4, -20, 14, -24, -7, 4, -20, 2, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1904", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[15, -1, -16, -16, -4, 27, -23, 35, -9, 4, 34, 23],\n [0, -6, -1, 19, 33, -33, 6, 3, 8, 30, 19, -5],\n [0, 0, 13, -7, -28, 13, -20, 24, 4, -3, -33, -23],\n [0, 0, 0, -25, -3, 4, 3, 10, 6, -35, 31, 33],\n [0, 0, 0, 0, -16, -34, -28, 30, 7, 31, 8, -34],\n [0, 0, 0, 0, 0, 25, 30, -20, -4, 2, -20, 19],\n [0, 0, 0, 0, 0, 0, -22, 33, -12, -4, 22, 20],\n [0, 0, 0, 0, 0, 0, 0, 5, 2, 16, 14, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, -3, -32, 29, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 24, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1401387", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-26, 2, 13, 10, -29, 12, 6, -24, 4, -8, -7, 16],\n [2, -2, 14, 1, 8, -20, 0, -8, 6, -2, 7, -10],\n [13, 14, 3, -2, 0, 0, -12, 0, 2, -12, -22, 11],\n [10, 1, -2, -18, -26, 18, -15, 0, -6, -17, -18, 18],\n [-29, 8, 0, -26, 17, 20, 4, -21, 11, 8, 20, -28],\n [12, -20, 0, 18, 20, 20, -6, 10, 0, -27, 6, -16],\n [6, 0, -12, -15, 4, -6, 24, -21, 25, 2, 22, -3],\n [-24, -8, 0, 0, -21, 10, -21, 24, 14, -26, 10, 0],\n [4, 6, 2, -6, 11, 0, 25, 14, 23, 12, 4, 20],\n [-8, -2, -12, -17, 8, -27, 2, -26, 12, 3, -11, -15],\n [-7, 7, -22, -18, 20, 6, 22, 10, 4, -11, 11, -16],\n [16, -10, 11, 18, -28, -16, -3, 0, 20, -15, -16, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-32, 32, -16, 27, -8, -15, 3, 10, 21, -29, -17, -31],\n [19, 9, 5, 6, -4, 10, -32, -30, 31, -34, -15, -22],\n [-7, -20, 14, -32, 21, -20, -25, 27, 20, -7, 11, 2],\n [2, 18, 33, -11, -27, -15, 19, 30, 34, -16, -33, 8],\n [5, -11, 15, -21, -8, 23, 32, 9, 29, -7, -8, -1],\n [-23, 15, 33, -22, 32, 30, -33, -32, 9, 35, -21, 16],\n [32, 23, -19, -19, -30, 15, 8, 12, -33, -24, 18, 16],\n [-2, 29, -31, 34, -21, 26, 16, -15, 28, -2, 18, -28],\n [-31, -15, 35, 19, -9, 19, -15, -2, -19, -30, -35, -27],\n [6, 2, -35, -8, 10, -23, 30, -16, 30, -18, 33, -10],\n [32, -32, 9, 21, -25, 30, -27, 26, 6, -20, 1, -7],\n [-4, -27, -25, -13, -11, -29, -3, 19, -30, -32, -19, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1641", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-34, -2, -13, 14, -3, 6, 4, -18, 16, 4, 20, -10],\n [-2, -17, 0, 4, 5, -10, -20, -2, 12, 28, -8, -6],\n [-13, 0, -18, 12, 10, 5, 18, -11, 18, 26, -14, 35],\n [14, 4, 12, -20, -10, 14, 18, -6, -4, 0, 2, 4],\n [-3, 5, 10, -10, -19, -9, -15, 4, 10, 2, -8, 10],\n [6, -10, 5, 14, -9, 20, 10, -26, 2, 9, 20, -11],\n [4, -20, 18, 18, -15, 10, 21, -5, -14, -2, 0, -15],\n [-18, -2, -11, -6, 4, -26, -5, -4, 8, -1, -4, 28],\n [16, 12, 18, -4, 10, 2, -14, 8, 2, 2, 4, -24],\n [4, 28, 26, 0, 2, 9, -2, -1, 2, -14, -6, 14],\n [20, -8, -14, 2, -8, 20, 0, -4, 4, -6, -23, -28],\n [-10, -6, 35, 4, 10, -11, -15, 28, -24, 14, -28, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3559", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-33, 6, 7, -4, 6, -12, -6, 0, -4, 23, -30, 2],\n [6, 33, 16, 7, 2, 5, 4, 22, 2, 2, 4, -34],\n [7, 16, 5, -9, -27, -18, -8, 16, 2, 4, 20, 2],\n [-4, 7, -9, 23, -5, -15, 4, 23, -24, -18, 10, -1],\n [6, 2, -27, -5, 7, 17, 0, 0, 28, -9, 11, 24],\n [-12, 5, -18, -15, 17, -34, 24, -2, 8, 0, 2, 21],\n [-6, 4, -8, 4, 0, 24, -10, -12, -2, 5, 2, 12],\n [0, 22, 16, 23, 0, -2, -12, -12, 18, 30, -30, -16],\n [-4, 2, 2, -24, 28, 8, -2, 18, -10, -14, 12, -20],\n [23, 2, 4, -18, -9, 0, 5, 30, -14, 7, 6, -3],\n [-30, 4, 20, 10, 11, 2, 2, -30, 12, 6, -23, 14],\n [2, -34, 2, -1, 24, 21, 12, -16, -20, -3, 14, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "618", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-5, 4, 29, -20, 11, -29, -19, -19, 25, -33, 9, 23],\n [22, -4, 31, -35, -28, -6, 19, 20, -30, -4, 31, 32],\n [-8, -23, 31, 2, -12, -24, -27, -35, -16, 20, -4, 33],\n [17, -8, -29, -28, -13, -29, -12, 12, 26, -28, 9, 5],\n [-17, -17, -26, -1, -26, 8, -24, 22, -12, -29, 30, -16],\n [-21, -17, -25, -34, 5, 34, 12, 5, -15, 29, -21, 17],\n [14, -17, -19, 24, -18, 24, -10, -2, 25, 22, 27, 22],\n [19, -16, 24, 25, 6, 13, -19, -16, 31, -14, 4, 17],\n [24, -1, -4, 13, 21, 25, 11, -26, -5, -17, 12, 24],\n [-30, 21, 29, 1, 14, -11, -30, 19, 25, -12, -6, 15],\n [7, -10, -35, 11, -17, 0, 28, 26, -31, 12, -9, 34],\n [23, -35, 7, -35, 0, -8, -27, 16, -14, 7, -31, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (12, 4) rounded to the nearest integer?\n[[3, 17, 18, 10, -18, -29, 33, 6, 16, 30, -35, -19],\n [11, -11, 22, -3, 10, 0, 4, -32, 4, -34, -24, 16],\n [9, -17, -17, 10, 1, -24, 0, 29, 22, -29, 27, -24],\n [-4, 25, -11, 5, -29, 10, 12, 26, -3, 33, 30, 21],\n [-2, 3, 26, 20, -11, 1, 20, 3, 33, 9, 30, -16],\n [-26, -30, -3, -10, 25, 0, 26, -13, 6, -6, 28, -11],\n [-19, -30, -25, -35, -20, 31, -9, -9, -34, 12, -11, 0],\n [2, 4, -24, -7, 35, -7, 1, 30, 26, -7, 32, 33],\n [-31, 16, -26, -1, 27, 19, -19, 9, 29, 20, 34, 16],\n [25, 25, -1, -23, 15, -35, -13, -2, 28, -25, 29, -14],\n [5, -11, -29, -10, 15, -12, -26, -23, -18, -25, 22, -4],\n [-15, 5, 24, 10, 20, -28, -19, 0, -31, 20, 23, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (6, 5) rounded to the nearest integer?\n[[9, 15, 22, 35, 3, 21, -7, -23, 8, 4, 7, 14],\n [20, 26, 19, -6, -8, 32, 5, -24, 2, 17, -13, 6],\n [31, -25, -26, -5, 8, 1, -11, -15, -21, -25, 9, -28],\n [-10, -15, 16, 14, -12, -10, 5, 15, -20, 5, 16, 21],\n [15, 23, 32, 4, -20, -1, -10, 23, -33, -31, 4, 19],\n [12, 35, 17, -9, 0, 0, 3, 21, 0, -29, -15, -21],\n [10, 11, 23, 25, 5, 18, -13, -24, -28, -14, 14, -2],\n [-23, -16, -28, 34, -11, -22, 23, 15, 17, -20, 31, 2],\n [9, -20, -11, 16, 10, -28, 20, -23, 27, -21, 17, 19],\n [-31, 3, -23, 31, -17, -5, 17, 30, -31, -6, 13, 22],\n [-18, 0, 2, 14, 13, -8, 20, -3, -34, -34, -4, -24],\n [3, 15, -30, -21, 11, 9, 9, -21, -26, -24, -1, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 6) of the inverse of matrix 1/839 * A where A =\n[[-26, -8, -4, -12, -13, -9, 14, -6, 0, 6, 4, 4],\n [-8, -28, 16, 22, -20, -3, 2, 16, 6, 14, -12, -11],\n [-4, 16, -4, -16, -13, -26, 2, -20, 2, -26, -3, -18],\n [-12, 22, -16, 33, -16, 18, -7, -20, 8, 3, -18, 2],\n [-13, -20, -13, -16, 4, -6, -2, 20, -14, 4, -10, 8],\n [-9, -3, -26, 18, -6, -7, 2, 4, 12, -26, 6, -14],\n [14, 2, 2, -7, -2, 2, -35, -23, -6, 0, -16, 20],\n [-6, 16, -20, -20, 20, 4, -23, 16, -14, -13, -6, 5],\n [0, 6, 2, 8, -14, 12, -6, -14, 33, 8, -23, -18],\n [6, 14, -26, 3, 4, -26, 0, -13, 8, -8, -12, 2],\n [4, -12, -3, -18, -10, 6, -16, -6, -23, -12, 4, 12],\n [4, -11, -18, 2, 8, -14, 20, 5, -18, 2, 12, -15]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-26, 12, 22, 9, -23, 24, 0, -12, -8, 14, 9, 8],\n [12, -21, -8, 18, -13, -16, -24, 22, 12, -15, 16, -6],\n [22, -8, 7, 2, -5, -4, 3, 0, 28, -10, -28, 6],\n [9, 18, 2, 16, -22, -9, -5, -29, 20, 8, 1, -32],\n [-23, -13, -5, -22, -4, 1, -13, -16, -8, -28, -13, -14],\n [24, -16, -4, -9, 1, 24, -16, 3, -14, 20, 23, -30],\n [0, -24, 3, -5, -13, -16, -2, 0, 21, 0, 2, -21],\n [-12, 22, 0, -29, -16, 3, 0, -26, -9, 18, 14, -8],\n [-8, 12, 28, 20, -8, -14, 21, -9, 30, 10, -6, 4],\n [14, -15, -10, 8, -28, 20, 0, 18, 10, -2, 14, -14],\n [9, 16, -28, 1, -13, 23, 2, 14, -6, 14, 18, -31],\n [8, -6, 6, -32, -14, -30, -21, -8, 4, -14, -31, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-105", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-18, 2, 30, -18, 4, 2, -10, -2, -10, 23, 0, 24],\n [2, -8, 5, 15, 12, 20, -3, 18, 28, -16, 9, 4],\n [30, 5, 23, 30, 17, -2, 13, -8, 2, 5, -15, 8],\n [-18, 15, 30, -26, -10, -2, 27, -18, 7, -18, 15, 9],\n [4, 12, 17, -10, -21, -15, 22, 0, 6, 10, 28, -14],\n [2, 20, -2, -2, -15, -19, 18, 3, 9, 13, -26, 16],\n [-10, -3, 13, 27, 22, 18, -25, 2, 0, -14, 13, 9],\n [-2, 18, -8, -18, 0, 3, 2, 28, -2, -30, -5, -13],\n [-10, 28, 2, 7, 6, 9, 0, -2, -32, -21, 10, 0],\n [23, -16, 5, -18, 10, 13, -14, -30, -21, -33, 20, -6],\n [0, 9, -15, 15, 28, -26, 13, -5, 10, 20, -9, -3],\n [24, 4, 8, 9, -14, 16, 9, -13, 0, -6, -3, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "227", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[8, -2, 2, -24, 13, 2, -30, 24, 27, 12, 18, -2],\n [-2, 23, -6, -24, -31, -15, 8, -18, -24, -20, 14, 4],\n [2, -6, 12, 16, -12, 24, -20, 1, -18, 0, 15, -23],\n [-24, -24, 16, 5, -2, 5, -8, 17, -5, 15, 16, -10],\n [13, -31, -12, -2, 28, -12, -30, -10, 12, -13, -11, -10],\n [2, -15, 24, 5, -12, -28, -12, -2, -1, -14, 24, -6],\n [-30, 8, -20, -8, -30, -12, -35, -10, -6, -3, -20, 6],\n [24, -18, 1, 17, -10, -2, -10, -17, -1, -24, 14, -22],\n [27, -24, -18, -5, 12, -1, -6, -1, 30, -18, 10, 6],\n [12, -20, 0, 15, -13, -14, -3, -24, -18, 21, -3, 3],\n [18, 14, 15, 16, -11, 24, -20, 14, 10, -3, -11, 16],\n [-2, 4, -23, -10, -10, -6, 6, -22, 6, 3, 16, -35]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3725", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-23, 0, 2, 24, 0, -22, 0, -3, 12, 0, 14, 21],\n [0, 33, 9, 1, 3, 14, 6, 16, -8, -6, 2, -26],\n [2, 9, 9, -18, 12, 10, -12, 2, -22, -6, -20, -20],\n [24, 1, -18, -27, 21, 12, -18, -6, 6, 16, -22, 14],\n [0, 3, 12, 21, 24, 2, 34, -10, 20, 4, -10, -2],\n [-22, 14, 10, 12, 2, -9, 4, -25, 0, -10, -4, 18],\n [0, 6, -12, -18, 34, 4, -16, -22, -24, 14, 2, -2],\n [-3, 16, 2, -6, -10, -25, -22, 7, 10, 7, -12, 16],\n [12, -8, -22, 6, 20, 0, -24, 10, -2, 4, -19, -5],\n [0, -6, -6, 16, 4, -10, 14, 7, 4, 1, -7, 5],\n [14, 2, -20, -22, -10, -4, 2, -12, -19, -7, -4, 6],\n [21, -26, -20, 14, -2, 18, -2, 16, -5, 5, 6, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-94", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 11, 32, -19, -9, 15, 23, 23, -12, 18, -23, -22],\n [0, 34, 16, -15, -6, 18, -17, 23, 11, 30, -35, 16],\n [0, 0, 12, -24, 19, -33, 30, -30, -14, 31, -15, 1],\n [0, 0, 0, 35, 1, 4, 27, 16, -4, -9, 6, 16],\n [0, 0, 0, 0, -11, 29, 21, -8, -18, 27, -18, -12],\n [0, 0, 0, 0, 0, -16, 30, 32, 10, -17, -29, 6],\n [0, 0, 0, 0, 0, 0, -32, -21, 7, -6, 3, 7],\n [0, 0, 0, 0, 0, 0, 0, -11, 35, -4, 12, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 14, -4, -26, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 19, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24015", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-28, -25, -16, 8, 23, -19, -24, -15, 31, -32, 18, -9],\n [32, -2, -35, 23, 16, 9, -18, 14, -2, 18, 18, 16],\n [-6, -32, 17, -12, 14, 9, 25, -29, 9, -2, -26, -25],\n [9, 13, 4, 15, 35, -8, 26, -21, 2, 13, -35, 14],\n [-22, -23, -14, 21, 5, 1, -31, -5, 29, 21, -21, -7],\n [18, 5, -2, -1, 19, -3, 6, -28, -6, 6, -11, -22],\n [29, -6, -23, -24, -12, 34, 2, 16, 34, -1, -8, -31],\n [6, -16, -14, 15, 11, 3, -8, 32, 11, -15, 12, 14],\n [13, 26, -1, -31, 1, 5, 4, 22, -34, 14, 12, -12],\n [-3, 34, 6, -10, -20, -15, -34, 23, -28, -29, -15, -18],\n [-35, -28, -34, -14, -16, -1, 24, -5, 5, 31, -12, -21],\n [2, 2, 30, -31, -34, -34, 2, 1, -26, -12, -12, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, -4, -17, -13, -9, -32, -1, -2, -24, 6, -23, -30],\n [-4, -11, -4, -4, -5, 16, -1, 24, -25, 13, -16, -8],\n [-17, -4, 10, -21, -22, 11, 8, -8, -12, 19, -2, -16],\n [-13, -4, -21, -22, 22, -2, -20, -10, 0, 14, 17, 10],\n [-9, -5, -22, 22, 0, -24, 15, -20, 2, -20, 0, 28],\n [-32, 16, 11, -2, -24, -27, 1, 12, -5, -10, 6, 9],\n [-1, -1, 8, -20, 15, 1, 29, -14, -2, -4, -21, -24],\n [-2, 24, -8, -10, -20, 12, -14, -12, 1, -4, -18, -25],\n [-24, -25, -12, 0, 2, -5, -2, 1, -12, 23, -22, -10],\n [6, 13, 19, 14, -20, -10, -4, -4, 23, 0, 3, 12],\n [-23, -16, -2, 17, 0, 6, -21, -18, -22, 3, -14, -16],\n [-30, -8, -16, 10, 28, 9, -24, -25, -10, 12, -16, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6241", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-17, 6, 6, 4, -2, 2, 12, 15, -5, -10, -4, 4],\n [6, -14, 2, 1, -22, -24, -3, -14, -8, 31, 2, -2],\n [6, 2, 35, 17, 8, -14, 4, -21, 5, -24, -9, -11],\n [4, 1, 17, -12, 1, -5, 25, 11, -26, -24, 10, -6],\n [-2, -22, 8, 1, -20, 2, 28, -34, -30, 18, -8, -5],\n [2, -24, -14, -5, 2, -28, 4, 0, 9, 4, -13, -15],\n [12, -3, 4, 25, 28, 4, 2, -7, 12, 12, 15, -16],\n [15, -14, -21, 11, -34, 0, -7, 23, -3, 8, -2, -18],\n [-5, -8, 5, -26, -30, 9, 12, -3, -4, -2, 8, 2],\n [-10, 31, -24, -24, 18, 4, 12, 8, -2, -11, -20, 22],\n [-4, 2, -9, 10, -8, -13, 15, -2, 8, -20, -3, 32],\n [4, -2, -11, -6, -5, -15, -16, -18, 2, 22, 32, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1382", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[27, -10, -9, 3, -31, 0, -35, 16, -28, -35, -29, 2],\n [0, 24, 31, -29, -28, -2, 4, 6, -4, 33, -23, 19],\n [0, 0, -29, -26, 1, 12, 29, 6, -23, -13, 21, -17],\n [0, 0, 0, -20, -1, 22, 12, 12, -13, -10, 19, -13],\n [0, 0, 0, 0, 9, 35, -24, -14, -19, 12, 35, 14],\n [0, 0, 0, 0, 0, -2, -27, 3, 31, -13, 4, -32],\n [0, 0, 0, 0, 0, 0, -16, -25, -4, 3, 9, 21],\n [0, 0, 0, 0, 0, 0, 0, -26, -34, 6, -29, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, 26, 4, -20, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 13, -28, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84967", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-1, -9, -30, 28, 1, 11, 8, 35, 30, 7, 21, 11],\n [0, -16, 31, 21, -35, 20, -28, 12, 22, 28, 35, 21],\n [0, 0, -33, 27, -25, 22, 10, -24, -28, 9, -21, 13],\n [0, 0, 0, -5, -16, -34, -30, -10, 1, 35, 23, 30],\n [0, 0, 0, 0, -24, -4, -18, 26, -20, -31, -12, 13],\n [0, 0, 0, 0, 0, 32, -32, -20, 4, 13, 6, -25],\n [0, 0, 0, 0, 0, 0, -24, 15, -12, -10, 17, -15],\n [0, 0, 0, 0, 0, 0, 0, 29, 6, 2, -4, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, 29, 15, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 24, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-846", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[8, -18, 8, 10, -16, 14, 8, -10, 6, -22, 4, 2],\n [-18, 2, -6, 0, 22, 12, -2, -20, -3, 17, -3, -19],\n [8, -6, 11, -24, 19, 16, -25, 13, -25, 10, 22, 7],\n [10, 0, -24, 23, 26, 4, 3, 12, -20, 24, 0, -15],\n [-16, 22, 19, 26, -2, 4, -14, -12, 8, -28, 0, -12],\n [14, 12, 16, 4, 4, -8, -1, -18, -32, 1, -31, -8],\n [8, -2, -25, 3, -14, -1, -28, -2, -10, 0, 1, 4],\n [-10, -20, 13, 12, -12, -18, -2, -5, -6, 12, 28, -8],\n [6, -3, -25, -20, 8, -32, -10, -6, 23, -8, -2, 18],\n [-22, 17, 10, 24, -28, 1, 0, 12, -8, -5, 23, -21],\n [4, -3, 22, 0, 0, -31, 1, 28, -2, 23, -21, -23],\n [2, -19, 7, -15, -12, -8, 4, -8, 18, -21, -23, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-45", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, -8, -19, 12, -12, -16, 19, -10, -7, -14, -16, -7],\n [21, -19, -26, 33, -35, 3, 10, -24, -16, -30, -18, -34],\n [-3, 18, -35, -14, 32, -15, -7, -16, 33, 15, -9, -18],\n [-14, 5, 1, -18, -15, -30, -8, -34, -25, -25, -10, 7],\n [20, -28, 27, 10, 23, -10, 29, 27, 17, 5, -25, -28],\n [-6, -11, 28, 24, -25, 12, 15, -4, -24, 6, -13, -21],\n [11, 6, 3, -23, 6, -13, 9, -14, 24, -9, 16, 33],\n [-25, 4, -30, 31, -4, 4, -16, -18, -34, -23, 20, 10],\n [26, 11, 23, 28, -24, -24, -24, -13, -18, -12, 11, 34],\n [4, 9, 31, 26, 22, 18, -27, -2, 24, -9, -9, 24],\n [-11, 4, 0, -11, 22, 25, 16, -30, -22, -29, -2, 0],\n [15, -5, 17, 25, -10, 14, -28, -13, -17, -14, 5, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (8, 3) of the inverse. Round your answer to the nearest integer:\n[[21, -5, -19, -19, -25, 24, -32, 22, -33, 0, 7, -16],\n [-31, 19, -10, 14, 16, 25, -21, 17, -2, -20, 11, 28],\n [34, 25, 5, 9, -34, 13, -17, 2, -19, -30, 18, 12],\n [8, 23, -2, -21, -14, -1, -34, 8, -16, 9, 26, 25],\n [20, 20, -34, -24, -13, -17, 18, 33, -15, 24, -16, -30],\n [23, -13, 18, -18, 6, 12, -23, -8, -22, 1, 11, 17],\n [5, 4, -14, -1, -27, -18, 17, -28, -17, 7, -4, -17],\n [-29, -12, -13, -29, 4, -13, -14, -14, -16, -15, -22, -14],\n [-3, -23, -21, -24, -30, -4, -12, -19, -11, 24, 27, -13],\n [9, 17, -9, 29, 9, 20, -35, 1, 7, 31, 11, -14],\n [-20, -25, -11, -19, 14, -21, -29, -14, -4, -21, -26, -31],\n [-30, -33, -5, 7, -3, -13, 7, -24, -26, -3, -23, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-53", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-30, -12, -9, 27, -12, 19, -26, -16, -14, 9, 16, -17],\n [0, 12, 34, 11, -23, -28, -31, 32, -1, -21, -1, -3],\n [0, 0, 24, -15, 31, -1, -35, -18, -30, -17, -5, 12],\n [0, 0, 0, -28, 34, 32, -24, -21, 15, 32, -26, -6],\n [0, 0, 0, 0, 23, 25, 34, 14, -29, 17, -29, -6],\n [0, 0, 0, 0, 0, 26, -7, 13, 9, 15, -16, -5],\n [0, 0, 0, 0, 0, 0, -35, 19, -30, 27, 20, 20],\n [0, 0, 0, 0, 0, 0, 0, 6, 28, 16, 4, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 28, 7, -4, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 28, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2767", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[31, -26, -30, 2, -18, -16, -30, -6, -20, -11, 15, -20],\n [0, 1, 28, 35, 24, 19, 16, 20, -19, -9, -33, -7],\n [0, 0, -22, 20, -14, -12, -25, -7, 2, 34, -27, 9],\n [0, 0, 0, -15, 24, 23, -15, -25, -16, -19, 15, 28],\n [0, 0, 0, 0, 20, -29, -23, 8, 4, 33, -8, 4],\n [0, 0, 0, 0, 0, 24, -26, -16, -6, -1, 23, 15],\n [0, 0, 0, 0, 0, 0, -8, -25, -1, -21, 18, 4],\n [0, 0, 0, 0, 0, 0, 0, 33, -35, -9, 0, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 20, 3, 14, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 28, -15, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "508577", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[19, 2, 15, -29, 3, -26, -22, -18, -24, -8, 6, 14],\n [2, 35, 8, -6, -14, 12, 7, -18, -12, 18, 11, 6],\n [15, 8, -30, 6, 20, 28, -4, 34, 14, -18, -10, -2],\n [-29, -6, 6, 33, -5, -22, 25, 6, 16, -12, 6, 10],\n [3, -14, 20, -5, -8, 1, 6, -29, 16, -1, -9, -14],\n [-26, 12, 28, -22, 1, -12, 30, -14, -2, -14, 4, 20],\n [-22, 7, -4, 25, 6, 30, -32, -12, 2, 20, 8, 2],\n [-18, -18, 34, 6, -29, -14, -12, -10, -14, -10, 9, -2],\n [-24, -12, 14, 16, 16, -2, 2, -14, -28, 3, 6, 26],\n [-8, 18, -18, -12, -1, -14, 20, -10, 3, -7, -12, 18],\n [6, 11, -10, 6, -9, 4, 8, 9, 6, -12, 17, 10],\n [14, 6, -2, 10, -14, 20, 2, -2, 26, 18, 10, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1184", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, 8, 24, 17, -19, 0, 30, -34, -16, -26, 33, 22],\n [11, 27, 3, 26, 24, -4, 27, 3, -18, -12, -34, -20],\n [15, 18, 20, 26, 35, 24, -16, 28, 32, 13, -10, 16],\n [25, -27, -31, -6, -32, -5, -22, -11, -8, -21, 31, -27],\n [30, -13, 12, -3, -8, 27, -28, 0, -34, -12, -14, -12],\n [33, 17, 22, -1, 19, -10, 10, -11, -25, -12, -12, -34],\n [-30, -11, -33, -31, -4, 12, 19, 0, 0, -11, 20, -8],\n [-1, -23, 24, -9, -30, 20, -9, 6, 2, 19, -17, -23],\n [32, -30, -7, 25, -21, -24, -15, -11, 2, 33, 13, -7],\n [26, 6, -14, 12, -8, -13, 17, -20, 24, 4, 3, 32],\n [-30, 11, -25, -26, -5, 35, -22, 23, -30, 22, -18, -3],\n [-6, -35, 21, 23, -10, 17, -18, -12, -18, 3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1218", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (8, 6) of the inverse. Round your answer to the nearest integer:\n[[34, 3, 1, 2, 35, -2, -8, 27, -6, 5, -28, -28],\n [-27, -11, -27, 28, -33, -9, 30, 23, 4, -12, -13, 5],\n [17, 13, 30, 25, 28, -2, -9, 28, 24, -1, 17, 35],\n [22, -23, 17, -19, 21, 24, -21, -17, -1, -18, -19, -11],\n [1, -13, -13, 10, -29, 26, -13, -15, 22, 14, -8, 30],\n [-27, -1, 25, 32, -13, -30, 33, -24, 23, 29, 3, 5],\n [-33, 6, 7, 30, -7, 11, -10, -21, 9, 25, -16, 13],\n [-9, 29, -27, 22, 15, 2, -17, 8, -25, 9, -29, -33],\n [26, -35, -21, 8, -25, -35, -33, -14, 7, -30, -14, 14],\n [-8, -7, -31, -1, -25, -35, -29, -33, -5, -33, -19, -18],\n [-19, 6, -9, 29, -6, -6, 33, 29, -32, -25, 22, -23],\n [-26, -18, 6, 8, 26, -12, -6, 29, 5, 31, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (8, 11) rounded to the nearest integer?\n[[27, -32, -35, -15, -28, 10, -24, -35, -14, -8, 28, 4],\n [0, 24, 5, 23, 32, 0, -3, 9, 14, 11, 8, 32],\n [0, 0, 10, -5, 26, -20, -24, 18, -27, -1, 17, 7],\n [0, 0, 0, -8, -7, 22, -12, -16, -9, -17, 2, 24],\n [0, 0, 0, 0, 20, 16, 5, 30, -14, 30, -8, 2],\n [0, 0, 0, 0, 0, 9, 17, -29, 3, 32, 27, 10],\n [0, 0, 0, 0, 0, 0, -30, -1, 2, 28, -4, -35],\n [0, 0, 0, 0, 0, 0, 0, 30, -18, -18, 27, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, -22, 35, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 35, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[12, 26, 20, -8, -15, 8, 34, 5, -1, 20, -19, -10],\n [27, -2, 35, -4, -32, -26, 20, -1, -3, -11, 11, -25],\n [-2, 0, -19, -24, -10, -23, 0, 33, 9, -24, 2, 31],\n [30, -16, 4, -2, -14, -21, 30, -1, -5, 17, 21, 29],\n [2, 2, -26, 10, -9, 6, -34, 22, -17, 26, -25, -22],\n [21, -3, 8, -18, -7, -6, -33, -4, -21, 13, 24, 10],\n [14, -30, -16, 13, -8, -10, 20, 12, -30, 17, 23, -3],\n [-24, 3, -34, 8, -17, -27, -5, -32, 27, 10, -4, -31],\n [3, -23, 32, -8, -23, 21, -12, -27, -29, -14, -33, -32],\n [6, -34, 17, 10, -30, 21, -33, -19, 24, 3, -8, 9],\n [-32, 3, -33, 29, -20, 10, 4, 19, 0, 24, 0, 0],\n [11, 12, -26, -14, -8, 0, -4, -23, -2, 27, 29, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-75", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-5, 12, -14, 35, 19, 4, -32, 7, 29, -34, -33, 20],\n [13, -9, 24, 31, 33, 1, 12, 30, 34, -9, -31, 16],\n [22, -11, 26, -20, 12, 35, 16, 31, -21, 31, 25, 30],\n [33, -12, 8, 35, -11, -16, 30, 30, -26, 14, 34, -25],\n [-6, -9, 6, 0, 9, -9, 20, 1, 34, 3, -28, 11],\n [31, 18, -27, 7, -24, 4, -33, -24, 1, -29, 34, 5],\n [-32, -32, 31, 2, -9, -25, 1, 22, -28, -4, 24, 29],\n [-26, -17, 3, 9, 12, -18, 35, -20, -30, 35, 13, -17],\n [29, -14, -5, -22, -6, 15, -4, 7, -19, 26, -19, 25],\n [-30, -27, -5, -6, 23, -26, 28, -3, -33, 17, 5, -21],\n [-26, 3, -12, -23, -25, -23, 4, 23, 18, 25, 23, -19],\n [-23, -23, -21, -25, -35, -1, 8, 22, -35, 16, 30, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[29, -33, 12, -21, 31, 26, -6, 7, -4, -1, 19, -21],\n [0, -13, -4, 14, 14, 4, 8, -24, 32, -14, 7, 6],\n [0, 0, -11, 15, 24, 1, -10, 8, 19, 14, -5, 34],\n [0, 0, 0, -17, -31, 33, 23, 18, -31, 13, -16, 18],\n [0, 0, 0, 0, -24, 3, 21, 35, -27, 26, -14, 0],\n [0, 0, 0, 0, 0, -3, 32, 25, -22, 2, 17, 25],\n [0, 0, 0, 0, 0, 0, 4, -30, 12, -18, -4, 0],\n [0, 0, 0, 0, 0, 0, 0, 22, 14, 34, 10, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, -29, -24, -28, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 9, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-383", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-27, -19, -28, 19, 5, -28, -23, 19, -16, 33, -11, -20],\n [0, 23, -1, -26, -17, -23, 33, -2, 7, 31, -26, -4],\n [0, 0, 2, -25, -21, -28, 13, 30, -6, 8, 18, -5],\n [0, 0, 0, 25, -32, 14, 17, -8, 2, -32, -20, 6],\n [0, 0, 0, 0, 32, -2, -25, -1, -8, -25, 2, -21],\n [0, 0, 0, 0, 0, -26, -19, -35, -25, 5, -33, -19],\n [0, 0, 0, 0, 0, 0, 21, 4, 32, 5, 4, 1],\n [0, 0, 0, 0, 0, 0, 0, 28, -5, -29, -17, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 18, -26, -4, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 20, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1347", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-30, -21, 2, 5, 20, -18, -1, 9, -7, 33, -4, -31],\n [8, 14, -15, -14, 25, 3, -31, -3, 35, -12, 3, -21],\n [34, -31, 12, -16, -15, -24, 30, -6, -29, 22, -18, 24],\n [-18, 12, -2, -30, 9, 24, 35, -12, 33, -19, 26, -3],\n [26, -30, -33, 18, -25, 10, -32, -29, -10, -1, -8, 5],\n [14, 3, -26, 35, -29, -11, 33, -6, -25, 35, 3, -10],\n [21, 19, -14, -24, 28, 30, 24, 26, 16, 26, 29, -21],\n [4, -29, 19, 1, -3, -7, -17, 33, -22, -27, -31, -1],\n [-8, 9, -34, -30, -5, -4, 23, -22, 23, -35, 19, -5],\n [23, -28, 30, -24, -5, 21, -28, -17, 17, -25, 21, 33],\n [23, -8, -34, -25, 28, -18, 11, 17, -31, -17, -31, 4],\n [12, -13, 19, -2, 22, -6, 25, 20, -31, -32, 33, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "376", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[14, -14, -12, -14, -2, 12, -32, 21, 27, -6, 29, -32],\n [-1, -3, 15, -24, 32, -34, -3, 9, 20, -8, -6, -2],\n [-35, 16, -23, 4, 29, -27, 34, 13, -11, -10, -10, 4],\n [-2, -28, -34, -20, 27, -18, 3, 6, -4, 26, -4, 33],\n [-14, -9, -35, -23, -30, -23, 31, 1, -28, -16, 26, -13],\n [32, -11, -4, 22, -11, 33, -26, 28, -5, -32, 21, 35],\n [-2, -15, -29, 22, -3, 6, 17, 19, 14, 2, 10, -21],\n [-28, 13, 17, 1, 2, -8, 25, -29, -29, 23, -15, -11],\n [31, -4, 12, 19, 30, -13, 9, -26, 19, 24, -27, -33],\n [-4, 18, -13, -22, 0, 12, 31, -26, 32, 16, 13, 8],\n [-31, -21, -28, 19, -16, -30, -35, 10, 6, 34, 13, -2],\n [21, -19, 27, 25, 23, -32, -3, -16, -15, 5, 8, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17479", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[28, 0, 6, -8, -23, 2, 17, 21, -4, 4, -22, -2],\n [0, 27, 24, -18, -23, 30, -8, 27, 8, 4, 11, 4],\n [6, 24, 21, -14, -25, -20, -7, -6, -4, 14, 10, 11],\n [-8, -18, -14, 5, -9, 10, 10, -15, 8, -24, -9, -1],\n [-23, -23, -25, -9, 14, -14, 2, 4, -15, 2, -6, 22],\n [2, 30, -20, 10, -14, 11, -19, 18, -2, 6, -18, 8],\n [17, -8, -7, 10, 2, -19, -35, -12, 14, 4, 25, 1],\n [21, 27, -6, -15, 4, 18, -12, 29, 2, -2, 16, -6],\n [-4, 8, -4, 8, -15, -2, 14, 2, 9, 20, 2, 28],\n [4, 4, 14, -24, 2, 6, 4, -2, 20, 21, 14, 10],\n [-22, 11, 10, -9, -6, -18, 25, 16, 2, 14, 34, 9],\n [-2, 4, 11, -1, 22, 8, 1, -6, 28, 10, 9, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1868", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-27, -6, -18, -6, 24, 19, -26, -23, 5, -34, -31, -3],\n [29, 1, 25, 22, -24, 5, -8, 0, 6, 18, 18, 2],\n [35, 33, 22, -27, 12, -18, -24, -9, 0, 13, -27, -2],\n [14, 14, -14, -31, -21, -18, -21, 30, -15, 25, -32, 12],\n [-35, -29, 25, 17, -1, -15, 24, -31, -33, 23, -26, 10],\n [14, 26, 23, -19, 20, 8, -17, -18, -10, -8, 13, -4],\n [-16, 10, 22, -20, -35, 10, -4, -22, -22, 29, -11, 6],\n [-23, 17, 32, 24, 32, 5, -30, -10, -14, -7, 4, 30],\n [0, -17, -20, -2, 27, -11, 33, -22, -15, 8, 16, 12],\n [26, -34, 6, 30, -8, -31, -28, 6, -10, 22, -25, -14],\n [18, 5, 4, -24, -20, 7, -10, -30, -17, -13, -11, -20],\n [-34, 22, -18, 8, 18, -27, -34, 19, -31, -16, -32, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (4, 12) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-19, -14, 2, 8, -12, -11, 8, -2, -8, -6, 16, 5],\n [-14, -23, -2, 20, -16, -14, 20, 3, -16, -29, -8, 6],\n [2, -2, 20, -7, -8, 0, 4, 8, -2, 33, -1, -9],\n [8, 20, -7, 20, -6, -14, -3, 10, -3, -4, -2, -2],\n [-12, -16, -8, -6, 31, -4, -4, -2, -18, -17, 18, 22],\n [-11, -14, 0, -14, -4, -15, 5, -12, -2, 10, 15, -29],\n [8, 20, 4, -3, -4, 5, -24, 20, 20, -14, -24, -18],\n [-2, 3, 8, 10, -2, -12, 20, 9, 6, 1, -7, 0],\n [-8, -16, -2, -3, -18, -2, 20, 6, 4, -16, -14, 26],\n [-6, -29, 33, -4, -17, 10, -14, 1, -16, 26, -6, 17],\n [16, -8, -1, -2, 18, 15, -24, -7, -14, -6, 4, -4],\n [5, 6, -9, -2, 22, -29, -18, 0, 26, 17, -4, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-23, 13, 20, 20, 16, 14, -23, 24, 12, -26, -8, -22],\n [13, 9, 6, -24, -3, 6, -24, -3, 16, 24, 6, -8],\n [20, 6, 32, 0, -19, 24, -12, 20, 6, 18, 4, -10],\n [20, -24, 0, -9, -12, 0, 23, -4, 10, -24, -22, 22],\n [16, -3, -19, -12, -28, -2, -7, -26, 10, -5, 30, -18],\n [14, 6, 24, 0, -2, 25, 14, -12, 9, -12, 17, -4],\n [-23, -24, -12, 23, -7, 14, 10, 22, -18, -3, 14, 1],\n [24, -3, 20, -4, -26, -12, 22, 22, 0, -15, -5, 18],\n [12, 16, 6, 10, 10, 9, -18, 0, 34, 8, 16, 18],\n [-26, 24, 18, -24, -5, -12, -3, -15, 8, 5, 0, 0],\n [-8, 6, 4, -22, 30, 17, 14, -5, 16, 0, -11, -1],\n [-22, -8, -10, 22, -18, -4, 1, 18, 18, 0, -1, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-45", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[30, 27, -24, 8, 18, -10, 18, -5, -14, 12, -28, -8],\n [32, -12, -11, 11, -19, 30, -28, 26, 1, -31, 10, -32],\n [23, 34, -7, -28, 12, 25, 17, 28, -20, -11, 28, 24],\n [34, 31, -9, -19, -1, 33, 26, -9, 8, 27, 20, -28],\n [21, 25, -33, 11, -22, 9, 3, 31, -12, 26, -34, 33],\n [32, -34, 26, -25, -19, -24, -15, 20, -5, -5, 33, 4],\n [-34, -25, 16, -12, 12, 26, -34, -19, 24, 19, 13, 19],\n [6, -16, 28, -8, 0, -9, -30, -8, -23, 11, -25, 3],\n [-12, 9, 12, 6, 23, -7, 32, 10, 22, -24, -4, -28],\n [-25, -10, 5, 24, -17, 12, -19, 27, -26, -2, 15, 9],\n [-8, -18, 0, -31, -33, -30, 24, 8, 30, 30, 33, 16],\n [-35, -31, 32, 30, -31, 23, -10, -22, 5, 16, 6, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-110", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (8, 1) of the inverse. Round your answer to the nearest integer:\n[[-21, 0, -14, -13, 10, 7, 33, 21, -3, -18, 0, -30],\n [0, -18, 16, 10, 3, -8, 5, 10, -12, -10, 6, -10],\n [-14, 16, 7, 20, -6, -8, -22, 20, 13, 0, -18, -18],\n [-13, 10, 20, 34, 28, -18, -16, 2, 28, 2, -4, -10],\n [10, 3, -6, 28, -33, -11, 16, -11, 16, 16, -8, 1],\n [7, -8, -8, -18, -11, 28, -10, 10, 14, 32, 20, -28],\n [33, 5, -22, -16, 16, -10, -5, 4, 24, 4, -25, 14],\n [21, 10, 20, 2, -11, 10, 4, -4, 10, -34, -18, 23],\n [-3, -12, 13, 28, 16, 14, 24, 10, -8, 11, 19, 6],\n [-18, -10, 0, 2, 16, 32, 4, -34, 11, 19, 14, -20],\n [0, 6, -18, -4, -8, 20, -25, -18, 19, 14, -24, 20],\n [-30, -10, -18, -10, 1, -28, 14, 23, 6, -20, 20, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, 14, -7, 3, -35, 29, 14, -18, 13, 1, 34, -1],\n [0, 29, 7, 30, -1, -2, 6, -28, -30, 4, 32, -13],\n [0, 0, 22, 0, -2, -15, 9, 22, -21, 9, -19, 14],\n [0, 0, 0, -26, 30, 17, -25, 20, -2, 7, 32, -33],\n [0, 0, 0, 0, 9, 17, 14, 12, 33, 29, -31, -8],\n [0, 0, 0, 0, 0, -26, -8, 0, 25, -34, 15, -2],\n [0, 0, 0, 0, 0, 0, -31, 28, 17, -7, -35, -6],\n [0, 0, 0, 0, 0, 0, 0, -1, -23, -17, 12, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 31, -10, 15, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 34, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "314137", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[12, 20, 26, -12, -8, -8, 16, 8, 19, 14, -1, -18],\n [20, 24, -22, -26, -15, 21, -14, 0, 12, -17, -16, 20],\n [26, -22, -29, 23, 0, 8, 16, 19, 4, -8, 9, -6],\n [-12, -26, 23, 17, 9, 6, -6, -14, -12, -21, 20, -4],\n [-8, -15, 0, 9, -19, -4, 14, 14, 4, 6, 6, 30],\n [-8, 21, 8, 6, -4, -9, 6, 19, -2, 28, 34, 19],\n [16, -14, 16, -6, 14, 6, -23, 23, 24, 26, -6, 18],\n [8, 0, 19, -14, 14, 19, 23, -34, 24, -17, 15, -4],\n [19, 12, 4, -12, 4, -2, 24, 24, -35, -17, -18, 2],\n [14, -17, -8, -21, 6, 28, 26, -17, -17, -22, -6, -2],\n [-1, -16, 9, 20, 6, 34, -6, 15, -18, -6, 21, 8],\n [-18, 20, -6, -4, 30, 19, 18, -4, 2, -2, 8, -21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-45", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[31, -13, -26, -31, -34, -11, 24, 31, 17, -19, 5, -3],\n [0, 34, -30, -23, -33, -22, 31, 0, 10, -35, -16, -17],\n [0, 0, 24, -8, -10, -9, -25, -8, 34, 9, 7, -21],\n [0, 0, 0, 3, 25, 14, -1, 12, 8, 34, -26, 7],\n [0, 0, 0, 0, 3, 32, 25, 23, 23, -8, -18, -29],\n [0, 0, 0, 0, 0, 21, 13, -30, 18, 28, 19, -34],\n [0, 0, 0, 0, 0, 0, -9, -34, 21, 12, -13, -4],\n [0, 0, 0, 0, 0, 0, 0, -21, 33, -12, 9, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 6, 27, 14, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 18, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128883", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-4, -30, -8, -17, 8, -24, 3, 21, 0, -15, -18, -19],\n [-12, 12, -21, 4, 22, 4, 33, 3, -31, -22, 29, -1],\n [9, -9, -13, -31, 6, 17, 20, -33, -9, 10, -14, 27],\n [25, 12, -23, -7, -23, 11, -11, 16, -23, 3, -8, 8],\n [35, 6, -11, 31, 3, 0, 18, -16, 29, 8, 29, -35],\n [7, 17, 24, -9, 12, 31, 16, 9, -7, -18, -23, -22],\n [-35, -15, -9, -14, 26, -16, -3, -7, -30, 23, -23, -2],\n [6, -24, -15, -30, -9, -30, -19, 35, 24, -34, 6, -21],\n [-5, 24, 31, 29, 17, 4, 20, 23, 27, 34, 27, 21],\n [-12, -26, 1, 31, 14, 18, 3, -29, -14, -20, 7, -14],\n [-22, 13, -21, -12, 32, -15, -9, -17, -18, -30, -16, -32],\n [32, -19, 17, 12, -25, 22, 12, -35, -13, -33, -24, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2059", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-17, -30, -28, -15, 19, -14, -4, 22, 4, 8, -4, -24],\n [-30, 22, -12, 0, 7, 8, -30, 25, -10, -3, -3, 9],\n [-28, -12, -17, 12, 14, 8, 6, 0, -2, 17, 13, 34],\n [-15, 0, 12, 29, 17, -6, 4, 24, -16, 22, -29, 0],\n [19, 7, 14, 17, -19, 13, -17, 12, -28, 26, 4, 26],\n [-14, 8, 8, -6, 13, -13, 12, 27, 27, 6, 12, 9],\n [-4, -30, 6, 4, -17, 12, 23, 1, -14, 1, -21, -14],\n [22, 25, 0, 24, 12, 27, 1, -13, -2, -10, 2, 32],\n [4, -10, -2, -16, -28, 27, -14, -2, 20, -2, 22, 22],\n [8, -3, 17, 22, 26, 6, 1, -10, -2, -6, 16, -26],\n [-4, -3, 13, -29, 4, 12, -21, 2, 22, 16, -23, -17],\n [-24, 9, 34, 0, 26, 9, -14, 32, 22, -26, -17, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[24, 18, 9, -32, 0, -25, -35, 34, -20, 19, 17, 28],\n [0, 27, 30, 16, -32, 30, 4, 4, 3, -27, 8, -7],\n [0, 0, 3, 8, -21, 26, 4, -9, -18, -23, 5, 16],\n [0, 0, 0, -34, 10, -28, 26, -17, -20, -3, 34, 9],\n [0, 0, 0, 0, 35, -13, -28, -30, 5, 19, -35, -35],\n [0, 0, 0, 0, 0, -21, -1, 3, 13, -17, -32, 14],\n [0, 0, 0, 0, 0, 0, 9, 25, -24, -12, -27, 20],\n [0, 0, 0, 0, 0, 0, 0, -21, -18, -15, 11, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, -7, -24, 33, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -31, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "328", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[23, -12, -20, 16, 25, 15, -31, 34, 5, 23, 24, -31],\n [29, 4, 6, 5, 27, -8, 7, -11, 20, -29, 13, 25],\n [-17, 7, 18, -11, -12, 9, 28, 32, 26, -27, -22, -15],\n [0, -20, -6, -12, -27, -34, 35, 17, 7, 30, 32, -31],\n [25, 24, 23, 24, 35, 3, -11, -29, -32, -22, -6, -29],\n [23, 35, 11, -34, -25, -27, -30, -14, -22, -20, -30, -33],\n [16, 17, -1, -2, -21, 25, -23, 28, 11, -24, -3, 23],\n [8, 10, 23, -30, 4, 21, -31, -16, 7, 26, -22, 31],\n [-3, -4, 14, -28, -16, -12, 4, -18, 33, -19, -3, -19],\n [-13, -31, -29, 29, -28, 32, 10, 7, -23, 14, 15, 9],\n [-8, 0, -22, -7, -32, -16, 3, -3, -19, 10, -9, -1],\n [-30, 2, 21, 29, -4, -28, 25, -14, -23, 22, 34, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-103", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (3, 12) rounded to the nearest integer?\n[[23, 3, -15, 7, 31, 14, 21, -31, 17, -35, -30, 31],\n [-19, 4, -35, 35, -23, 9, 21, -21, -7, 12, 25, -13],\n [32, 14, 16, 21, 4, -14, -4, 1, 30, 25, 5, -9],\n [7, -18, -7, -7, -21, 31, -33, 1, -17, 3, 7, -16],\n [4, -17, -12, 24, -29, -35, 24, 30, 12, 13, -29, 12],\n [-5, 15, 24, 24, 31, 21, -12, -13, 35, -4, 35, 13],\n [10, 4, 17, 26, -33, -34, 18, 15, 10, -17, -14, -17],\n [-15, -9, -15, 19, -7, -3, -26, -15, -19, 22, 27, 26],\n [-30, -26, 10, 35, -25, 7, 22, 2, -13, 10, -4, 31],\n [-27, -32, 14, 33, -21, 23, -16, 32, 18, -23, -27, -24],\n [-12, -8, -29, 12, -21, -19, 15, 4, 31, -2, -30, -28],\n [-9, 34, -30, 10, 9, 4, -32, 4, -12, 28, 14, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-17, 23, -17, 2, -15, 1, 21, 11, -5, 2, -33, -27],\n [11, 25, -27, 11, -5, 4, 13, 16, 6, -30, -21, -8],\n [14, 28, -26, 3, -16, -32, 10, -9, 13, -30, 17, 0],\n [-14, 25, -4, 16, 16, 17, -6, -7, 24, -5, -5, -6],\n [-13, -8, 4, -4, 32, -13, -22, 33, -28, 21, 12, -34],\n [-2, 18, 16, -24, 19, 33, 10, -3, -8, -25, 19, 1],\n [-13, 3, 21, -19, -21, 35, 2, -8, 31, 29, -33, -14],\n [-14, -31, 33, 13, -31, 31, -33, -27, -27, -10, -25, 22],\n [5, -4, -17, 19, 35, -22, -19, -24, 21, -27, -23, 31],\n [-3, 33, 3, -1, -21, 1, -20, 12, -31, -20, 13, -32],\n [-27, -23, 32, 11, 14, -34, 16, -12, -25, 11, 28, 24],\n [6, -1, 35, 26, -21, -1, 20, 23, 34, 2, -32, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "375", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[11, 17, 24, 14, -22, -22, 18, 29, 19, 2, -19, 17],\n [0, 4, 7, 11, 17, -27, 27, -9, -11, 23, -25, 32],\n [0, 0, -16, -19, -13, -32, -25, 30, -20, 1, 9, -4],\n [0, 0, 0, 16, 32, 20, -23, 27, 9, -20, 20, 29],\n [0, 0, 0, 0, 4, 7, 16, -20, 7, 15, 29, 24],\n [0, 0, 0, 0, 0, -22, -35, 17, 35, -4, -32, -20],\n [0, 0, 0, 0, 0, 0, 21, -21, -16, 6, 5, -21],\n [0, 0, 0, 0, 0, 0, 0, 25, 12, -11, 25, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 33, -16, -18, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 21, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24010", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (6, 7) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -9, 19, -8, -9, -18, -35, 30, -18, 13, 8, 19],\n [0, -2, -11, 22, 24, 9, -32, 20, -11, 20, 0, -2],\n [0, 0, 2, 9, -14, 31, 26, -32, 12, -28, -4, 33],\n [0, 0, 0, -17, 23, 21, -15, -25, 0, 5, 4, -25],\n [0, 0, 0, 0, 24, 1, -18, 16, -28, 28, 3, -7],\n [0, 0, 0, 0, 0, 30, 14, 20, -23, -35, -21, 17],\n [0, 0, 0, 0, 0, 0, -13, -12, 0, 19, -7, 35],\n [0, 0, 0, 0, 0, 0, 0, -28, -32, 1, 12, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 31, -33, -26, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -19, 29, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[34, -22, 24, 30, -18, -28, 34, -8, -11, 35, -1, -20],\n [0, -18, -17, -34, 19, 32, -28, -6, -10, 26, 35, -3],\n [0, 0, -2, 0, -7, 32, -1, -8, -14, 22, 15, -10],\n [0, 0, 0, 10, 35, -29, 1, 32, -13, -4, 18, 19],\n [0, 0, 0, 0, 11, -1, 11, 12, -10, -7, 23, -21],\n [0, 0, 0, 0, 0, -33, -3, -8, 25, 21, 22, -12],\n [0, 0, 0, 0, 0, 0, 7, 11, 25, -9, 28, 14],\n [0, 0, 0, 0, 0, 0, 0, -27, 13, 17, 10, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 27, -34, 16, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 7, -26, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "638118", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[15, 11, -32, -35, 18, -13, 0, -1, 35, 19, 4, 13],\n [25, -17, 10, 32, 25, 34, 21, -22, -5, 16, -21, 25],\n [-18, -14, 32, -15, -25, 21, -22, -24, -24, -28, -34, -8],\n [12, -14, -23, 32, -31, -28, 4, -9, 20, -17, 4, 0],\n [28, -6, -32, -8, -23, -16, 2, -12, -2, -25, 31, 18],\n [5, 30, 23, 32, 22, -23, -11, -7, 34, 9, 35, 29],\n [19, 24, 26, -19, -34, 26, 11, -13, 2, 28, -26, -8],\n [-33, 0, 1, 31, 4, 6, 26, 10, 34, 16, 24, 29],\n [14, -12, 32, 33, -30, 15, -34, 24, -12, -4, 18, 24],\n [7, -32, 18, 3, -34, 30, -25, -17, 26, 13, 22, 22],\n [-23, 24, 1, -2, -26, 5, 29, -21, -35, 25, 7, 30],\n [34, -10, -26, 31, -17, -10, 7, -5, -14, 29, 5, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-35, 29, 21, -3, 8, 12, -35, -19, 9, 9, 19, 16],\n [-31, -9, 7, 5, 31, -16, 23, 23, -12, -10, -31, -7],\n [-10, 12, -4, 25, 0, 4, -17, -33, 25, -20, 24, -25],\n [-3, -28, 35, -20, 25, -10, -20, -8, 19, -10, -32, -15],\n [13, 10, -33, 14, 23, 1, 30, -29, 8, -13, -16, -10],\n [26, 18, 13, -33, -30, -28, 29, 6, -16, 29, 19, -16],\n [27, 20, 15, 13, -28, -2, -17, -27, 30, -2, -35, 30],\n [-14, 11, -33, -1, 0, -12, -26, 35, -15, 22, 9, 32],\n [-25, -18, -20, 20, 29, 28, -22, 16, 3, -22, -32, -28],\n [23, -3, 12, -10, 12, 11, 22, -32, 9, -17, -16, 18],\n [26, 15, -26, -6, 2, -2, -9, -16, -20, -5, 23, 2],\n [16, 30, 33, -3, 5, 6, 33, 31, -33, -3, 2, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-187", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (10, 7) of the inverse of matrix 1/839 * A where A =\n[[-19, 8, 2, 5, 4, -30, 1, 23, 13, 22, -21, 4],\n [0, 16, 31, 33, 7, -30, -12, 8, -25, 28, -3, -12],\n [0, 0, 3, 16, -30, 17, -1, -26, -34, -28, 11, 31],\n [0, 0, 0, 17, -35, -16, 30, -28, 26, 15, 4, 26],\n [0, 0, 0, 0, -35, 10, 3, 32, 13, -30, 5, 10],\n [0, 0, 0, 0, 0, 33, -9, 4, -35, 27, 12, 0],\n [0, 0, 0, 0, 0, 0, -16, 23, -28, 24, -16, -25],\n [0, 0, 0, 0, 0, 0, 0, 10, -24, -30, -14, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 30, 20, 34, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -26, -27, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[18, -35, -16, 5, -23, 8, 1, 24, -27, 27, 18, 14],\n [-4, 26, -24, 5, 8, 14, 24, -17, 16, -16, -35, -6],\n [35, -14, 12, 27, 33, -34, 0, -5, -22, 5, 25, 24],\n [-23, -32, -14, 27, 17, -16, -18, 3, 28, -14, -7, 29],\n [-14, -32, -29, -16, 2, 34, -5, 15, -30, -13, 22, -13],\n [19, -21, -29, -3, 25, 0, -19, 33, 9, 10, 32, 25],\n [-27, 23, 0, -34, -25, -12, 19, -7, -33, -18, -15, 8],\n [-2, 6, 31, 20, -28, 24, 22, -33, -23, 7, 12, -27],\n [32, 10, 15, -6, 18, 30, 2, 9, 34, 2, 21, 19],\n [-19, -31, -24, -2, 25, -33, 15, -18, -14, -32, 23, -13],\n [-7, 11, 17, 35, 18, -20, 5, 23, 7, 20, 9, -11],\n [-10, 28, 1, -21, -4, 22, 24, -28, 17, 34, 9, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[28, -24, 21, 12, -16, 6, 24, -7, 3, 14, 20, 14],\n [-24, -10, -22, -25, -20, -16, -1, 2, 5, 4, -8, 3],\n [21, -22, -1, 15, -12, 14, 0, -2, -22, 10, 20, -12],\n [12, -25, 15, 8, -18, -14, -12, 11, -2, 10, -10, 10],\n [-16, -20, -12, -18, -31, 5, 10, 17, -10, 16, -2, -10],\n [6, -16, 14, -14, 5, 1, -18, 0, -22, -22, -2, 4],\n [24, -1, 0, -12, 10, -18, 35, 14, -9, 18, 21, 3],\n [-7, 2, -2, 11, 17, 0, 14, 9, 8, -30, -2, 0],\n [3, 5, -22, -2, -10, -22, -9, 8, -9, 12, 12, -30],\n [14, 4, 10, 10, 16, -22, 18, -30, 12, -23, -14, 31],\n [20, -8, 20, -10, -2, -2, 21, -2, 12, -14, 34, -9],\n [14, 3, -12, 10, -10, 4, 3, 0, -30, 31, -9, 28]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5458", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[31, -24, -32, -25, 30, 22, -19, -17, -20, -17, 30, 14],\n [0, -1, -26, -1, 14, 15, 23, 4, 4, -7, -23, 24],\n [0, 0, 10, 34, -12, -14, 14, -4, 19, -14, 21, -19],\n [0, 0, 0, 31, -16, 15, 28, -27, -5, 10, 10, -4],\n [0, 0, 0, 0, 24, -23, -27, -20, 25, 16, 33, -30],\n [0, 0, 0, 0, 0, 21, -28, -30, 13, 4, -5, 35],\n [0, 0, 0, 0, 0, 0, 29, -33, -31, 17, 1, -24],\n [0, 0, 0, 0, 0, 0, 0, 29, 5, 23, 25, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, -21, -17, -4, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -25, 31, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5290", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (11, 7) of the inverse. Round your answer to the nearest integer:\n[[25, -14, 14, -24, -17, -30, 20, -32, -11, -17, 18, -26],\n [-18, -33, 1, 26, 31, -2, -29, -11, 33, -16, -35, -20],\n [-7, 23, -11, -21, -1, 34, -3, -5, 15, -33, -35, 22],\n [-2, 4, -6, 4, 34, -22, 21, -24, 16, 35, -31, -13],\n [25, 2, -31, 32, -26, 17, 27, -16, 26, -24, 21, 17],\n [-8, -1, 33, 21, -34, -20, 19, 35, 12, -20, 30, -9],\n [-32, 6, -10, 31, 33, 33, 19, -3, -30, 22, -5, 4],\n [32, -35, -25, -27, -28, -28, -15, -31, 11, 18, 14, 8],\n [2, 7, -34, -9, 3, -17, -24, -27, 11, 18, 23, 15],\n [20, 26, 20, -10, 21, 22, 1, -21, -13, 11, 15, -5],\n [-6, 9, -23, -29, -6, -31, 6, -14, -14, 29, -14, -28],\n [-19, 12, -9, 27, -22, -31, 6, 32, -15, -11, -16, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -35, -19, 2, 5, -25, 20, 29, 9, -24, 24, -24],\n [0, -29, -30, -1, -35, 4, 4, -11, -29, 20, -3, -35],\n [0, 0, 18, -7, 34, -27, -16, 23, 11, 22, 33, -18],\n [0, 0, 0, 16, 25, -3, -16, 32, 14, -6, -19, -5],\n [0, 0, 0, 0, -22, -7, -30, -12, -8, 20, -33, -32],\n [0, 0, 0, 0, 0, 12, 14, 22, 1, 21, -13, 28],\n [0, 0, 0, 0, 0, 0, 5, 9, 29, -22, 27, -26],\n [0, 0, 0, 0, 0, 0, 0, 23, 26, 32, 14, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, -28, 16, 34, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -17, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[31, 34, 18, 14, 27, 6, -27, 27, -3, -30, 26, -22],\n [0, 20, 7, -32, 31, -19, -3, 18, 33, -7, -8, -25],\n [0, 0, -1, 9, 34, 28, 33, -32, 15, 26, -9, 26],\n [0, 0, 0, 21, -19, 1, 3, -29, -20, -27, -19, -19],\n [0, 0, 0, 0, -35, 34, -2, 24, -10, -1, 3, 35],\n [0, 0, 0, 0, 0, 19, -17, 26, 7, -4, 22, -12],\n [0, 0, 0, 0, 0, 0, 17, -7, 1, 25, -5, 14],\n [0, 0, 0, 0, 0, 0, 0, 12, -15, 35, -31, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 24, 6, 17, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 1, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-11, 6, 22, 2, -9, -7, -3, -4, 18, -21, -17, 8],\n [6, -3, -11, 19, 28, -28, 9, -14, -32, 12, -16, -18],\n [22, -11, -35, 19, 15, -7, -12, 6, 2, -10, -3, -6],\n [2, 19, 19, -13, 9, -6, -6, 12, 22, -4, 5, -3],\n [-9, 28, 15, 9, 32, 21, -24, -6, 9, 12, 2, 3],\n [-7, -28, -7, -6, 21, 6, -21, -24, 15, 4, -10, -15],\n [-3, 9, -12, -6, -24, -21, -19, -2, 0, 5, -9, -7],\n [-4, -14, 6, 12, -6, -24, -2, 35, 24, 6, -18, 10],\n [18, -32, 2, 22, 9, 15, 0, 24, 31, 18, -1, 4],\n [-21, 12, -10, -4, 12, 4, 5, 6, 18, -17, -20, -8],\n [-17, -16, -3, 5, 2, -10, -9, -18, -1, -20, 6, -2],\n [8, -18, -6, -3, 3, -15, -7, 10, 4, -8, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1521", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[6, -18, 3, 29, -28, 3, -6, -7, 29, 15, 24, -34],\n [0, 26, 16, 2, 22, 3, 0, 27, -4, 21, -9, -26],\n [0, 0, 19, 14, 20, 1, 23, -20, 28, -35, 3, 6],\n [0, 0, 0, -7, -2, -6, 29, 1, -4, 25, -24, 9],\n [0, 0, 0, 0, 18, -26, -14, -31, 28, -12, -22, 33],\n [0, 0, 0, 0, 0, 26, 14, 10, -10, -27, -22, -25],\n [0, 0, 0, 0, 0, 0, -21, 33, 34, -20, 34, 0],\n [0, 0, 0, 0, 0, 0, 0, -16, -20, -28, 23, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 16, 19, 22, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -29, 26, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11372", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[20, -20, 15, -10, 4, 11, 17, -2, -14, 24, -6, -6],\n [-20, -9, 5, 12, 13, -4, 20, 2, -2, 8, 2, -16],\n [15, 5, 27, 7, -7, -1, -3, -25, -4, 25, -24, 4],\n [-10, 12, 7, -18, 28, -8, -18, -10, 20, 30, 6, 4],\n [4, 13, -7, 28, 14, 14, 8, -14, 6, -20, -14, 4],\n [11, -4, -1, -8, 14, 20, -14, -12, 9, -6, -14, -10],\n [17, 20, -3, -18, 8, -14, 25, -27, 11, 25, -15, -12],\n [-2, 2, -25, -10, -14, -12, -27, -30, -26, 0, 0, -23],\n [-14, -2, -4, 20, 6, 9, 11, -26, -3, -17, 8, -8],\n [24, 8, 25, 30, -20, -6, 25, 0, -17, -9, -9, 28],\n [-6, 2, -24, 6, -14, -14, -15, 0, 8, -9, 33, -14],\n [-6, -16, 4, 4, 4, -10, -12, -23, -8, 28, -14, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-6, 27, 18, -25, -4, 22, 8, 12, 23, -21, 10, -34],\n [13, -31, -11, 12, 13, 17, 29, 2, 14, -33, -32, 32],\n [-6, -35, -14, 33, -19, -4, 17, 15, -21, 27, -21, -20],\n [-34, -10, 17, -3, 3, 10, 32, 33, -28, -14, -20, -3],\n [23, 17, -31, 20, -14, -33, 26, 18, -33, 35, -24, 29],\n [33, 28, -13, 16, -28, 10, -23, -12, 7, 17, -33, -8],\n [3, -17, -30, -6, 23, -31, 6, 24, -34, 19, -13, 20],\n [-31, 7, 24, -22, -2, -10, 7, 5, -26, 1, -16, 34],\n [4, -34, -25, -2, 4, -22, -23, 6, -23, -28, -9, 27],\n [24, 4, -6, 33, 24, 12, 19, -20, -35, -19, -17, 23],\n [-16, -25, -4, -23, -14, 16, 11, 15, 20, -7, 0, 33],\n [-11, 32, -23, 31, 10, 4, 32, 3, -8, -35, 6, -29]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-335", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-23, -20, -24, 6, 4, -4, -30, -12, 28, 9, -8, 8],\n [-20, 31, 18, -8, 17, 6, -10, -26, 16, -23, 4, -22],\n [-24, 18, -32, -19, -18, -1, -6, 1, -12, 13, 15, -7],\n [6, -8, -19, -35, -21, 6, -6, -17, -12, -22, -27, -25],\n [4, 17, -18, -21, 34, 14, 26, 12, -26, 8, 9, 2],\n [-4, 6, -1, 6, 14, -5, 15, -23, 22, 20, 26, 32],\n [-30, -10, -6, -6, 26, 15, -3, -2, -10, -10, -10, -4],\n [-12, -26, 1, -17, 12, -23, -2, 4, 10, 4, -1, -5],\n [28, 16, -12, -12, -26, 22, -10, 10, -9, -16, 0, -16],\n [9, -23, 13, -22, 8, 20, -10, 4, -16, -32, -26, -8],\n [-8, 4, 15, -27, 9, 26, -10, -1, 0, -26, 22, 4],\n [8, -22, -7, -25, 2, 32, -4, -5, -16, -8, 4, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3536", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[10, 13, 7, -19, 28, -2, -33, 30, 13, 0, -5, -19],\n [14, -4, 31, 2, 35, 12, 34, 18, 9, -26, -34, -17],\n [23, 34, -13, 21, -7, -20, -19, -1, 13, 1, -17, 33],\n [-33, 35, 15, -11, 15, 7, -27, 16, 8, -24, -22, 3],\n [-34, 26, 17, -8, 15, -12, 15, -22, -17, 2, -13, 10],\n [-20, 35, -19, -6, -28, 2, 24, -25, 17, 3, -7, 13],\n [26, 29, -7, -5, -30, 15, -22, -20, 5, 6, -14, 6],\n [8, 24, 34, 22, 11, -14, -15, 1, -6, -10, -28, 15],\n [14, -17, 27, 11, -10, -32, 1, -4, 25, -7, 28, -33],\n [-32, 29, -26, -10, 4, -15, -6, 20, -9, 14, 31, -20],\n [-15, 7, 31, 10, -9, -13, 33, -34, -9, -26, 30, -16],\n [13, 2, -2, 24, -31, 18, -19, 22, -2, -3, -14, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4618", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-32, 0, 3, 4, 33, -22, -19, 18, 31, 34, -5, -2],\n [-30, -20, -33, 4, 14, 25, -7, -5, 4, 34, 7, -22],\n [-5, -10, -12, 29, -26, 22, 27, -28, 16, -17, 5, 10],\n [-25, 9, 17, -19, -8, -22, -12, 8, 2, -13, 35, 12],\n [19, -4, 33, -28, -15, -8, 31, 0, 12, -11, -4, -11],\n [32, 6, 30, -19, -23, 8, 28, -2, 32, 15, 20, -21],\n [20, -31, 19, -26, 22, -12, -15, -2, 5, -9, 27, 28],\n [32, 17, 23, -7, -26, 26, 15, -7, -8, 29, 21, 21],\n [30, -32, -27, -32, 4, -7, -4, 9, -16, -7, -16, -4],\n [-7, 7, -30, -21, -28, -13, -21, -3, 21, 4, -27, -3],\n [-11, 16, -9, 17, 13, 26, 1, -27, 17, 20, 31, -1],\n [29, 11, 1, -1, -3, 5, 5, 14, 4, -25, 29, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-40", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (9, 7) of the inverse. Round your answer to the nearest integer:\n[[19, 31, 2, 21, 13, -34, 17, -28, 27, -31, 27, -6],\n [0, 29, 34, -16, -26, -3, -32, -20, -5, -26, 23, 29],\n [0, 0, -15, -8, -27, -15, 27, 28, -29, 13, -17, -33],\n [0, 0, 0, -25, 15, -16, -16, 19, -13, -28, -32, -22],\n [0, 0, 0, 0, -9, 6, -20, 14, -30, 22, -22, 1],\n [0, 0, 0, 0, 0, -29, 28, -17, -9, 0, -19, -23],\n [0, 0, 0, 0, 0, 0, -6, -33, -15, 18, -7, 10],\n [0, 0, 0, 0, 0, 0, 0, 8, -15, -13, 34, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, -33, 22, -24, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 18, -11, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-12, -9, 15, 6, -10, 9, 17, 19, -22, 0, 14, 28],\n [-22, -34, -3, 12, 27, -35, 1, 12, -34, -22, -8, 5],\n [-18, 22, -25, -1, 12, -4, 23, 8, 15, -24, -18, 2],\n [34, -23, -29, 35, -1, -34, 31, -9, -25, -29, -34, 22],\n [21, -35, 16, 11, -2, -29, -13, 20, 34, 27, -12, 7],\n [9, -8, -5, 18, -3, 28, -4, -32, 34, -4, -4, 3],\n [-7, 33, 31, -4, -22, -12, -3, -11, -12, 2, 34, 18],\n [1, 25, 18, 4, -22, 3, -16, -29, 19, 16, 28, 26],\n [-15, 30, -9, 28, -6, 2, -15, 2, -3, 20, -8, 22],\n [22, 14, -16, 1, -2, -22, -16, 3, -23, 33, 24, -14],\n [6, 34, -9, -20, 25, 11, 23, -15, 0, -27, -24, 7],\n [-14, 4, 13, -4, 23, -25, 26, -12, 26, 15, -25, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-30, 6, 23, -22, 10, -18, 35, 31, 6, -33, -25, -25],\n [0, -22, 16, 15, 34, -22, 7, 29, -20, -17, 33, -25],\n [0, 0, 3, -25, -25, 19, 26, -31, -12, 27, 31, 14],\n [0, 0, 0, -27, 31, -35, -35, 11, -26, 29, -13, 1],\n [0, 0, 0, 0, -27, 19, -27, 11, -33, -2, 12, 27],\n [0, 0, 0, 0, 0, 21, 11, -15, -14, -5, 1, -2],\n [0, 0, 0, 0, 0, 0, 26, 11, -20, 24, 10, 18],\n [0, 0, 0, 0, 0, 0, 0, -3, -27, -13, 13, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 29, 28, -28, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 32, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-97274", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-2, -14, 22, -6, 13, 12, 4, 8, 23, 20, -8, 1],\n [-14, 17, -28, -2, -6, 27, -8, -14, -16, 8, -13, -10],\n [22, -28, 5, 14, 13, 14, 10, -4, 10, 10, -2, -2],\n [-6, -2, 14, -14, 14, 8, 9, 11, 20, -9, 0, 6],\n [13, -6, 13, 14, 6, 5, -1, 4, -22, -14, -26, -6],\n [12, 27, 14, 8, 5, -7, -12, -19, -14, 8, 16, 22],\n [4, -8, 10, 9, -1, -12, -4, 26, 8, -20, 18, 4],\n [8, -14, -4, 11, 4, -19, 26, 0, 0, -17, 6, -22],\n [23, -16, 10, 20, -22, -14, 8, 0, 34, 4, 0, 12],\n [20, 8, 10, -9, -14, 8, -20, -17, 4, -13, -26, -2],\n [-8, -13, -2, 0, -26, 16, 18, 6, 0, -26, -34, 14],\n [1, -10, -2, 6, -6, 22, 4, -22, 12, -2, 14, 16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "498", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[34, 3, 8, 27, -34, -14, 27, 4, 0, -8, 17, 12],\n [3, -21, -10, 4, 7, -2, -12, 6, -11, -18, -20, 21],\n [8, -10, 4, -20, 32, 22, -10, -24, -2, 8, -10, 0],\n [27, 4, -20, -16, -4, -25, 30, 4, 1, -14, -6, -22],\n [-34, 7, 32, -4, 20, 17, -6, -6, 1, -16, -3, 27],\n [-14, -2, 22, -25, 17, 25, -4, 0, -10, -24, -9, -26],\n [27, -12, -10, 30, -6, -4, -6, 20, -6, -4, -8, 0],\n [4, 6, -24, 4, -6, 0, 20, -7, 24, -3, 0, 10],\n [0, -11, -2, 1, 1, -10, -6, 24, -32, 21, -2, 1],\n [-8, -18, 8, -14, -16, -24, -4, -3, 21, 25, -16, -10],\n [17, -20, -10, -6, -3, -9, -8, 0, -2, -16, 27, 8],\n [12, 21, 0, -22, 27, -26, 0, 10, 1, -10, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (4, 10) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, 8, 33, -21, -26, 6, -24, 32, 2, 19, -16, -27],\n [0, -28, -23, -26, 19, 23, -6, 24, -9, -30, 32, 4],\n [0, 0, -9, 32, -14, -27, -17, -33, 33, 19, -25, -33],\n [0, 0, 0, 11, 17, -30, -34, -6, 18, 32, 32, -31],\n [0, 0, 0, 0, -32, 7, -7, 2, 29, -30, -25, -30],\n [0, 0, 0, 0, 0, 28, -33, 8, 10, -34, -22, 7],\n [0, 0, 0, 0, 0, 0, -9, -25, 11, -34, -31, 6],\n [0, 0, 0, 0, 0, 0, 0, 13, -15, -15, 5, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, -9, 35, -17, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 2, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4983", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 17, 7, 1, -5, -16, 16, 6, 35, 15, 2, 35],\n [0, 14, -28, 18, 4, 11, -32, 12, -12, 22, 34, 15],\n [0, 0, 34, 1, -21, -33, 7, 25, 1, 24, 20, -22],\n [0, 0, 0, -33, 19, -1, -6, 4, -24, -2, -29, 13],\n [0, 0, 0, 0, -25, 15, -28, -28, -31, 10, 11, -27],\n [0, 0, 0, 0, 0, 26, 0, 34, -20, -1, -2, 10],\n [0, 0, 0, 0, 0, 0, -31, -18, 2, 24, -16, -23],\n [0, 0, 0, 0, 0, 0, 0, 7, -25, -5, -15, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, -15, -33, 25, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -31, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-100114", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-3, -1, -31, 21, 12, 1, 5, -4, 34, -20, -32, 9],\n [-27, 15, -9, 8, -26, 28, 9, -18, 34, -18, 30, 15],\n [11, -21, -34, -28, -21, -16, -30, 11, -15, -32, -15, -31],\n [-30, -30, 29, -4, 24, -2, 1, -8, 34, -25, 23, 25],\n [22, -32, -30, -4, 24, 3, 5, 20, -8, 19, -3, -11],\n [-13, -11, -13, -2, -8, 6, 7, -19, -5, -19, -18, 16],\n [28, 20, 12, 10, 3, -22, -2, -24, -27, -32, -28, -35],\n [-26, -18, 33, 20, -5, -14, 0, 12, 31, 26, 32, -26],\n [-31, 21, -7, 34, 11, -19, 25, -3, 20, 12, 0, -25],\n [23, -31, -34, -2, 7, 31, 0, 2, -24, -17, -17, -29],\n [-35, 16, 13, -12, 23, -22, 2, -20, -30, -11, 15, 15],\n [11, 15, 34, -4, 9, 20, 33, 17, 3, -21, 7, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[25, 22, -12, 12, 17, -17, -30, -2, 14, 10, 2, 10],\n [22, 20, -6, -2, 12, -1, 0, 11, 8, -20, 16, -11],\n [-12, -6, 1, -30, -12, -13, -2, -30, 2, 22, 22, -23],\n [12, -2, -30, 31, -6, 5, -18, 8, 7, -2, 4, 28],\n [17, 12, -12, -6, -14, 28, -6, -4, 0, 4, -18, -27],\n [-17, -1, -13, 5, 28, -31, -18, -2, -10, -12, -4, -4],\n [-30, 0, -2, -18, -6, -18, 13, 24, -8, 0, 17, 2],\n [-2, 11, -30, 8, -4, -2, 24, -18, -3, 20, 1, 2],\n [14, 8, 2, 7, 0, -10, -8, -3, -4, -22, 15, -12],\n [10, -20, 22, -2, 4, -12, 0, 20, -22, -29, 2, -14],\n [2, 16, 22, 4, -18, -4, 17, 1, 15, 2, 26, 11],\n [10, -11, -23, 28, -27, -4, 2, 2, -12, -14, 11, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "455", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[19, 10, 35, 4, -17, 3, 31, 13, -16, 5, 11, 33],\n [-32, -32, 25, 2, 22, 33, -13, -25, -10, -27, 25, -15],\n [-27, 1, -10, 22, -5, 2, 18, 28, -9, 7, -35, 28],\n [5, 13, 32, 22, 5, -8, 20, -17, -11, 7, 26, 27],\n [34, -17, 19, -21, -17, -25, -25, 28, 26, 15, -34, 11],\n [23, 29, 16, -7, 5, 13, -3, -22, -3, -21, -13, 24],\n [-30, -9, -24, 7, 19, -11, 9, 29, -28, -26, 13, 28],\n [-23, -27, -15, -23, -24, 28, -20, 1, 0, 4, 27, 32],\n [10, -8, 24, 27, -3, -25, -12, 21, -4, 30, 27, 9],\n [-21, 27, 12, -31, 32, -5, 27, 4, 26, 32, 33, 16],\n [32, 35, -11, 24, 4, 5, 0, 23, 6, -25, -8, -21],\n [-21, 25, -34, -6, -22, -30, -9, 24, 1, -32, -34, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "941", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[10, -28, -12, 16, -6, 24, 0, -28, -20, -28, 28, -16],\n [-28, 23, -18, -14, 9, -10, -18, 31, -12, 16, -12, -8],\n [-12, -18, -4, 18, 22, -12, 25, -10, -10, 28, -22, -11],\n [16, -14, 18, 22, 20, 32, 5, -5, -25, 28, -4, -24],\n [-6, 9, 22, 20, -9, 3, 19, -18, 10, -26, -20, 13],\n [24, -10, -12, 32, 3, 15, -10, 8, 2, -2, 13, -8],\n [0, -18, 25, 5, 19, -10, -25, -8, -12, -20, 7, 5],\n [-28, 31, -10, -5, -18, 8, -8, 13, -12, 20, 32, 24],\n [-20, -12, -10, -25, 10, 2, -12, -12, 17, 6, -3, 16],\n [-28, 16, 28, 28, -26, -2, -20, 20, 6, 24, -26, -16],\n [28, -12, -22, -4, -20, 13, 7, 32, -3, -26, -9, -25],\n [-16, -8, -11, -24, 13, -8, 5, 24, 16, -16, -25, -25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-7, 6, -8, 2, -6, 4, -14, 2, -6, 0, 22, 1],\n [6, -27, -17, -9, -1, -24, -6, 8, -24, 26, 19, 5],\n [-8, -17, 27, -6, 18, 16, -2, 10, 10, 6, 12, -30],\n [2, -9, -6, 11, 4, -14, -14, -3, -2, 14, -18, -14],\n [-6, -1, 18, 4, 20, 18, 2, -4, -20, 28, 16, -5],\n [4, -24, 16, -14, 18, 29, 8, 2, 10, 2, 16, -6],\n [-14, -6, -2, -14, 2, 8, 0, -14, -28, -3, -22, 4],\n [2, 8, 10, -3, -4, 2, -14, -23, 12, 20, -3, 17],\n [-6, -24, 10, -2, -20, 10, -28, 12, 28, -6, -3, -26],\n [0, 26, 6, 14, 28, 2, -3, 20, -6, -32, 16, 4],\n [22, 19, 12, -18, 16, 16, -22, -3, -3, 16, -4, -6],\n [1, 5, -30, -14, -5, -6, 4, 17, -26, 4, -6, 29]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-37", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[9, 2, 8, 6, 10, -3, -14, 6, -12, 2, -6, -2],\n [2, 29, 0, 10, 6, 8, 0, 21, -17, 13, -2, -20],\n [8, 0, 23, 22, -3, 0, 0, 2, -8, 32, -16, -6],\n [6, 10, 22, 31, -9, 4, 1, 1, 8, 17, 8, -10],\n [10, 6, -3, -9, -13, -6, 2, -26, -6, 10, 16, -30],\n [-3, 8, 0, 4, -6, 0, 14, 20, 3, -1, 12, 7],\n [-14, 0, 0, 1, 2, 14, 20, -8, -6, -28, -6, 20],\n [6, 21, 2, 1, -26, 20, -8, 31, -16, 24, -16, -8],\n [-12, -17, -8, 8, -6, 3, -6, -16, -34, 11, 14, -22],\n [2, 13, 32, 17, 10, -1, -28, 24, 11, -5, 12, 10],\n [-6, -2, -16, 8, 16, 12, -6, -16, 14, 12, 0, 2],\n [-2, -20, -6, -10, -30, 7, 20, -8, -22, 10, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2216", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (4, 8) of the inverse. Round your answer to the nearest integer:\n[[-35, -24, -16, -3, -8, 6, -21, 14, -13, 28, -3, -3],\n [0, -33, 4, -15, 30, 14, -18, 21, -4, 12, 3, -7],\n [0, 0, 30, 5, -22, 20, -13, -25, 34, 22, 13, 3],\n [0, 0, 0, -32, -2, -34, -34, -18, -29, 6, -24, -11],\n [0, 0, 0, 0, 11, -27, -16, -3, -15, 27, -26, 7],\n [0, 0, 0, 0, 0, 15, 1, 23, 5, -10, -3, 21],\n [0, 0, 0, 0, 0, 0, 18, -19, -22, -13, 28, 5],\n [0, 0, 0, 0, 0, 0, 0, -1, 25, 32, -33, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, -26, -10, 5, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -27, 3, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-128", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[3, 30, -23, 15, 26, -7, -28, -16, -6, 22, 15, -16],\n [2, -28, 29, -30, 8, -35, 29, 9, -24, -32, 7, -11],\n [-24, 2, 20, -34, -24, 29, 11, 6, 21, 3, 33, 11],\n [33, 30, 3, 20, 7, -5, -31, -34, 20, 12, -29, 16],\n [4, -5, 19, 35, 23, 33, -4, -7, 26, -13, -21, 3],\n [4, -30, 1, -19, 15, -22, -28, 14, -3, 11, -7, -16],\n [12, -20, 19, -20, -33, -11, 1, -34, -33, 34, 27, 23],\n [23, 19, -6, -4, -20, 1, -27, 21, 33, 28, 13, -13],\n [27, 5, 10, 32, 13, -19, -34, 34, 30, -26, -28, 5],\n [2, 32, -3, -13, 22, 28, 4, 9, -35, 22, 8, -1],\n [28, 17, -19, -23, 33, -19, 4, -2, 15, 19, 4, -29],\n [-2, 0, 4, -18, -12, -5, 19, -23, 25, -13, -9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-61", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[7, -6, -14, -2, -19, 6, 10, -16, 2, 0, 0, 16],\n [-6, -21, 18, 7, -10, -11, 2, 20, 4, -12, -2, -2],\n [-14, 18, 15, -18, -22, -9, -8, 13, -5, 0, -4, -13],\n [-2, 7, -18, -16, -4, 4, -6, -11, -2, 11, -3, -7],\n [-19, -10, -22, -4, 34, 14, 9, -24, 13, -28, -16, -10],\n [6, -11, -9, 4, 14, 28, -3, -18, 2, 33, 24, -7],\n [10, 2, -8, -6, 9, -3, 11, -1, 13, 20, 20, 26],\n [-16, 20, 13, -11, -24, -18, -1, 10, -6, 14, -3, 10],\n [2, 4, -5, -2, 13, 2, 13, -6, -4, 2, 14, -16],\n [0, -12, 0, 11, -28, 33, 20, 14, 2, -2, -9, 28],\n [0, -2, -4, -3, -16, 24, 20, -3, 14, -9, 21, 2],\n [16, -2, -13, -7, -10, -7, 26, 10, -16, 28, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-536", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-1, 6, -8, 12, 12, 10, 14, 8, 16, 12, -9, 34],\n [6, 16, 2, 24, -4, 11, 28, 8, 14, -2, 10, 3],\n [-8, 2, 20, -18, -27, 6, -11, -10, 2, 14, -19, -20],\n [12, 24, -18, -14, -7, 1, -34, -10, -9, 2, -12, 0],\n [12, -4, -27, -7, -21, -22, 15, -18, 14, 17, 28, 25],\n [10, 11, 6, 1, -22, 31, 28, 5, -6, -32, 16, 10],\n [14, 28, -11, -34, 15, 28, 9, -22, 18, 1, -6, 8],\n [8, 8, -10, -10, -18, 5, -22, 20, 18, 8, -11, 7],\n [16, 14, 2, -9, 14, -6, 18, 18, -13, -2, -8, 8],\n [12, -2, 14, 2, 17, -32, 1, 8, -2, -6, 16, 16],\n [-9, 10, -19, -12, 28, 16, -6, -11, -8, 16, -14, 11],\n [34, 3, -20, 0, 25, 10, 8, 7, 8, 16, 11, -18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 5) of the inverse of matrix 1/839 * A where A =\n[[20, 6, -10, 6, 22, -8, 14, -12, -10, -4, 0, 10],\n [6, -32, 9, 26, 3, 20, 0, -23, -10, -14, -22, -16],\n [-10, 9, 5, 22, 10, -15, 0, -4, 4, 6, -28, -13],\n [6, 26, 22, 2, 18, -5, 20, 12, -11, 8, 22, 0],\n [22, 3, 10, 18, 8, -10, 14, 8, -18, 23, -10, -2],\n [-8, 20, -15, -5, -10, -26, 5, -14, 18, 26, 22, 7],\n [14, 0, 0, 20, 14, 5, 18, 24, 9, -5, 22, 16],\n [-12, -23, -4, 12, 8, -14, 24, -10, -12, -2, 9, 28],\n [-10, -10, 4, -11, -18, 18, 9, -12, 15, -4, -30, 6],\n [-4, -14, 6, 8, 23, 26, -5, -2, -4, -35, 21, 10],\n [0, -22, -28, 22, -10, 22, 22, 9, -30, 21, 17, -2],\n [10, -16, -13, 0, -2, 7, 16, 28, 6, 10, -2, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-23, 8, 30, -17, 32, 30, -8, 32, 5, -24, 35, -5],\n [0, 8, 15, 0, -19, 23, 18, 14, 32, 22, 21, -20],\n [0, 0, 21, 11, 26, 7, 28, 6, 1, -13, 15, 28],\n [0, 0, 0, 21, 15, -1, 1, -16, 11, 26, -4, -12],\n [0, 0, 0, 0, 13, -21, -21, -11, 23, -3, -23, 29],\n [0, 0, 0, 0, 0, 17, -5, -6, -35, 7, -26, -28],\n [0, 0, 0, 0, 0, 0, 13, -5, -27, -27, 5, 7],\n [0, 0, 0, 0, 0, 0, 0, 30, -27, -23, -14, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, -27, 10, -25, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 35, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21005", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-34, -10, 8, -10, -25, -6, -4, 1, -5, -10, -10, -18],\n [-10, -25, -10, -22, 0, -2, -16, -2, 8, 12, 16, -14],\n [8, -10, 26, -4, 14, 5, -16, 18, -12, -26, 10, 4],\n [-10, -22, -4, 20, -12, 8, -4, 4, 26, 3, -22, 2],\n [-25, 0, 14, -12, 6, -19, 13, -28, -11, -4, 0, -14],\n [-6, -2, 5, 8, -19, -31, -20, 9, 1, -8, -24, -16],\n [-4, -16, -16, -4, 13, -20, 33, -24, 12, -4, 15, -6],\n [1, -2, 18, 4, -28, 9, -24, -22, -24, -2, 6, -22],\n [-5, 8, -12, 26, -11, 1, 12, -24, -23, -20, 22, -10],\n [-10, 12, -26, 3, -4, -8, -4, -2, -20, 21, -17, -2],\n [-10, 16, 10, -22, 0, -24, 15, 6, 22, -17, -23, 15],\n [-18, -14, 4, 2, -14, -16, -6, -22, -10, -2, 15, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1623", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-11, -5, 1, 18, 13, 2, -5, 17, -4, -32, -12, 5],\n [-5, -11, 8, 1, -6, 1, 1, -2, 0, -8, 0, -4],\n [1, 8, -32, -17, -2, -15, -6, -26, 21, -5, -2, -15],\n [18, 1, -17, -9, -14, 4, 16, -19, 16, -15, 20, 8],\n [13, -6, -2, -14, -13, -32, -2, 5, -7, 3, -8, 3],\n [2, 1, -15, 4, -32, -8, -28, 14, 20, 22, -12, -14],\n [-5, 1, -6, 16, -2, -28, -2, 2, -16, 5, -14, 21],\n [17, -2, -26, -19, 5, 14, 2, 25, -8, -14, 16, 19],\n [-4, 0, 21, 16, -7, 20, -16, -8, 22, -10, -10, 20],\n [-32, -8, -5, -15, 3, 22, 5, -14, -10, 27, 8, 2],\n [-12, 0, -2, 20, -8, -12, -14, 16, -10, 8, -16, 13],\n [5, -4, -15, 8, 3, -14, 21, 19, 20, 2, 13, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[29, 30, -26, -23, 35, -21, 13, 20, 20, 8, -17, 9],\n [0, 24, 6, -2, 29, 11, -33, -2, 10, -17, 21, -25],\n [0, 0, 5, 20, -21, -27, -30, -8, -1, 16, 27, -28],\n [0, 0, 0, -17, -31, 23, 21, 3, -33, 5, 35, 2],\n [0, 0, 0, 0, -16, -14, -33, 30, 23, -6, 15, -33],\n [0, 0, 0, 0, 0, -9, 31, 13, -23, 7, 29, 29],\n [0, 0, 0, 0, 0, 0, -26, -16, -25, -2, 21, 16],\n [0, 0, 0, 0, 0, 0, 0, 16, -11, -11, -6, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, -31, 11, -16, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -22, -21, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1044882", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[24, 0, 8, -6, 7, 4, -12, 2, -22, -8, 5, 4],\n [0, -10, 16, 2, 2, 18, 6, 6, -4, 8, 12, -16],\n [8, 16, 20, 0, -4, 4, 7, -13, -8, -2, -11, 32],\n [-6, 2, 0, 16, 21, 6, 0, -6, -12, 26, -15, -10],\n [7, 2, -4, 21, -7, 8, 6, 12, 22, 8, -3, 4],\n [4, 18, 4, 6, 8, -28, 10, -18, -2, 5, -8, 8],\n [-12, 6, 7, 0, 6, 10, 8, 31, -21, 10, -20, -2],\n [2, 6, -13, -6, 12, -18, 31, -19, 20, -14, 16, 10],\n [-22, -4, -8, -12, 22, -2, -21, 20, 12, -5, -12, 23],\n [-8, 8, -2, 26, 8, 5, 10, -14, -5, -12, 0, -2],\n [5, 12, -11, -15, -3, -8, -20, 16, -12, 0, -15, 18],\n [4, -16, 32, -10, 4, 8, -2, 10, 23, -2, 18, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "872", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-24, 14, 2, 10, 2, 20, 16, 0, -9, -17, 0, 8],\n [14, 16, 27, -28, -13, 6, -15, 9, -6, 16, 21, -1],\n [2, 27, 16, 25, -6, 8, -4, -12, 8, -24, 3, -29],\n [10, -28, 25, 3, -8, -16, -4, -28, -21, 0, -14, 3],\n [2, -13, -6, -8, -33, -4, -20, 27, -18, 2, 25, 16],\n [20, 6, 8, -16, -4, 6, 20, 9, 16, -15, -2, -20],\n [16, -15, -4, -4, -20, 20, 5, -12, 1, 10, -11, -12],\n [0, 9, -12, -28, 27, 9, -12, -24, -4, 20, -4, -4],\n [-9, -6, 8, -21, -18, 16, 1, -4, -17, 8, 0, -12],\n [-17, 16, -24, 0, 2, -15, 10, 20, 8, -35, -8, -8],\n [0, 21, 3, -14, 25, -2, -11, -4, 0, -8, -22, -2],\n [8, -1, -29, 3, 16, -20, -12, -4, -12, -8, -2, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-107", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (3, 11) of the inverse. Round your answer to the nearest integer:\n[[-35, 12, 2, -15, -11, -23, 20, -12, 0, 14, 0, -25],\n [0, -26, 2, 0, -16, -2, 24, 0, 8, 23, 11, -16],\n [0, 0, 32, 31, 4, -2, -12, 21, 30, -6, 17, 3],\n [0, 0, 0, -12, 12, 17, 1, 8, 1, 16, -25, 18],\n [0, 0, 0, 0, 14, -11, 24, -17, 35, -20, -9, -3],\n [0, 0, 0, 0, 0, 14, -2, -22, -4, -16, -4, 4],\n [0, 0, 0, 0, 0, 0, 13, 15, -10, -24, 11, 7],\n [0, 0, 0, 0, 0, 0, 0, 24, 18, -9, 12, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 31, -34, -3, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 25, -2, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-156", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, 9, -12, 5, -3, -10, -24, 19, 35, -12, -25, 33],\n [0, -35, -9, -12, 33, 13, 6, 14, -35, 32, -6, -22],\n [0, 0, 32, -30, -23, -24, 33, 15, 17, 3, -35, -8],\n [0, 0, 0, -10, 2, -12, 32, 18, -4, -30, 28, -34],\n [0, 0, 0, 0, 20, -2, 25, 23, 26, 11, 18, -14],\n [0, 0, 0, 0, 0, -10, 35, -24, -29, 26, -23, -20],\n [0, 0, 0, 0, 0, 0, -15, -10, 30, 20, 21, -7],\n [0, 0, 0, 0, 0, 0, 0, -6, 7, 15, -14, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 32, 3, 16, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -19, 17, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-726", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-26, 18, -2, -22, -1, -6, -14, 6, -29, -24, -22, -3],\n [18, 27, -8, -16, 6, -7, -20, 22, 9, 18, -2, -1],\n [-2, -8, 9, -7, -4, -26, -3, -5, 21, -22, 16, 0],\n [-22, -16, -7, -33, 5, -18, -30, -18, 19, 10, 10, 0],\n [-1, 6, -4, 5, 9, 16, -8, -2, -4, 20, 2, -9],\n [-6, -7, -26, -18, 16, -16, 1, 6, 4, 12, 16, -1],\n [-14, -20, -3, -30, -8, 1, 4, 5, -9, -11, -16, 6],\n [6, 22, -5, -18, -2, 6, 5, 17, 14, -2, 8, 4],\n [-29, 9, 21, 19, -4, 4, -9, 14, -26, -8, 24, 10],\n [-24, 18, -22, 10, 20, 12, -11, -2, -8, -28, 10, 12],\n [-22, -2, 16, 10, 2, 16, -16, 8, 24, 10, 17, 2],\n [-3, -1, 0, 0, -9, -1, 6, 4, 10, 12, 2, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-167", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, -16, -24, 22, 22, -14, 6, -6, -16, 3, 0, 14],\n [-16, 20, 3, -10, -14, 4, -10, 16, -6, -8, -9, -2],\n [-24, 3, -16, 7, -12, -15, 11, 17, -28, -16, 24, 10],\n [22, -10, 7, -15, -12, -20, -7, -3, 26, -16, -14, -12],\n [22, -14, -12, -12, 15, -17, -6, 2, 8, -5, -3, -14],\n [-14, 4, -15, -20, -17, 10, 12, 7, 0, -4, -4, 12],\n [6, -10, 11, -7, -6, 12, 15, -2, 4, 2, -26, 20],\n [-6, 16, 17, -3, 2, 7, -2, -20, 26, 20, -24, 14],\n [-16, -6, -28, 26, 8, 0, 4, 26, 15, -11, 6, 8],\n [3, -8, -16, -16, -5, -4, 2, 20, -11, 8, -5, 6],\n [0, -9, 24, -14, -3, -4, -26, -24, 6, -5, 28, -16],\n [14, -2, 10, -12, -14, 12, 20, 14, 8, 6, -16, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[34, 32, 0, 1, -35, -10, 6, 4, 17, 26, 8, 0],\n [0, -15, -19, -20, 5, 19, 21, 30, 2, 20, 1, 14],\n [0, 0, 29, 29, 8, -24, 17, 25, -23, 6, 10, 6],\n [0, 0, 0, -20, -14, -1, 13, 35, 28, -5, -35, -11],\n [0, 0, 0, 0, 19, -10, 29, -8, 10, 18, 18, 13],\n [0, 0, 0, 0, 0, -21, -35, -30, -9, -10, 30, -23],\n [0, 0, 0, 0, 0, 0, 3, 30, 0, 28, -32, -14],\n [0, 0, 0, 0, 0, 0, 0, -27, 29, -13, -1, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, -19, -5, -22, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 14, 5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[0, -4, -13, -2, 4, -4, -2, 20, -3, -6, -21, 27],\n [-4, 34, 8, 26, 28, -1, 4, -1, 6, -30, 0, 20],\n [-13, 8, -35, 2, 0, -8, 1, -21, 0, -4, -8, -16],\n [-2, 26, 2, -34, -12, 14, -24, -10, -24, -16, 2, -15],\n [4, 28, 0, -12, -14, -22, -2, -13, -14, -4, 6, -8],\n [-4, -1, -8, 14, -22, 2, 2, -28, 6, 11, 2, 16],\n [-2, 4, 1, -24, -2, 2, -15, -7, -5, -2, 6, 20],\n [20, -1, -21, -10, -13, -28, -7, -33, -4, -4, 0, 30],\n [-3, 6, 0, -24, -14, 6, -5, -4, 6, 21, -23, -7],\n [-6, -30, -4, -16, -4, 11, -2, -4, 21, 9, -15, 16],\n [-21, 0, -8, 2, 6, 2, 6, 0, -23, -15, -21, 24],\n [27, 20, -16, -15, -8, 16, 20, 30, -7, 16, 24, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1306", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[28, -26, 21, 2, 4, -8, 2, 32, -18, -1, 16, 0],\n [-26, -2, -4, 14, -2, 25, -18, 15, -2, 8, 3, 10],\n [21, -4, -4, 7, -14, 28, 30, -26, -5, 18, -21, -24],\n [2, 14, 7, 10, 25, -10, 9, 10, -1, -8, 4, -16],\n [4, -2, -14, 25, 2, -2, 2, -16, 11, 12, -2, 3],\n [-8, 25, 28, -10, -2, 19, 31, 12, -1, 18, 0, 12],\n [2, -18, 30, 9, 2, 31, -26, -5, -28, -2, 6, 26],\n [32, 15, -26, 10, -16, 12, -5, -18, -3, 6, -11, 4],\n [-18, -2, -5, -1, 11, -1, -28, -3, -10, -4, 15, 16],\n [-1, 8, 18, -8, 12, 18, -2, 6, -4, -14, 11, 20],\n [16, 3, -21, 4, -2, 0, 6, -11, 15, 11, 15, -4],\n [0, 10, -24, -16, 3, 12, 26, 4, 16, 20, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[29, 28, 3, 1, -10, -2, 0, 10, 28, -10, -26, -5],\n [0, -8, -1, 21, -16, 0, 27, 34, 8, -23, -3, 14],\n [0, 0, 14, 16, 11, 7, -26, 12, 32, 19, 6, -5],\n [0, 0, 0, -4, 6, -10, -24, -22, 5, 7, -6, -27],\n [0, 0, 0, 0, 1, -8, 24, 24, -16, 33, -28, -4],\n [0, 0, 0, 0, 0, -7, 26, -2, 11, 6, -27, 0],\n [0, 0, 0, 0, 0, 0, 19, 0, -26, 5, 15, -31],\n [0, 0, 0, 0, 0, 0, 0, -7, 22, -8, -5, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 20, -17, 0, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 19, -27, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32189", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (12, 7) of the inverse. Round your answer to the nearest integer:\n[[35, -28, -26, 34, 12, 18, 14, 11, -7, -27, 30, 33],\n [0, -20, -28, -14, -21, -8, -7, -4, -20, -3, 0, 3],\n [0, 0, -22, 3, 35, -16, 14, 3, -28, -6, -16, -8],\n [0, 0, 0, -13, 3, -2, -14, 21, 11, -18, -28, 25],\n [0, 0, 0, 0, 7, -19, 7, 19, 26, -14, -19, 32],\n [0, 0, 0, 0, 0, -5, -33, -14, 17, 18, -9, -4],\n [0, 0, 0, 0, 0, 0, -3, 24, -6, -23, -16, -28],\n [0, 0, 0, 0, 0, 0, 0, -17, -9, -29, 14, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, -30, -7, 8, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 14, -22, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (10, 11) of the inverse. Round your answer to the nearest integer:\n[[-33, -9, 12, -21, -14, 5, -34, -3, -14, -4, -4, 2],\n [-9, -29, -6, 30, -25, -12, -14, 20, -26, -20, -2, 12],\n [12, -6, 4, -2, 10, -10, -8, -2, -2, -6, -4, -28],\n [-21, 30, -2, 16, -22, 23, 10, -7, -32, 2, 20, -25],\n [-14, -25, 10, -22, -6, 16, 11, 8, 25, -1, -4, 15],\n [5, -12, -10, 23, 16, -28, -28, 12, -29, 9, 3, 10],\n [-34, -14, -8, 10, 11, -28, 12, -12, -26, 7, -9, -10],\n [-3, 20, -2, -7, 8, 12, -12, -19, 23, 15, 7, -22],\n [-14, -26, -2, -32, 25, -29, -26, 23, -6, -15, 19, 18],\n [-4, -20, -6, 2, -1, 9, 7, 15, -15, 19, 18, 4],\n [-4, -2, -4, 20, -4, 3, -9, 7, 19, 18, 19, 8],\n [2, 12, -28, -25, 15, 10, -10, -22, 18, 4, 8, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-34, 20, -20, 9, 11, 5, 8, 35, 22, 19, -11, -24],\n [-18, 29, 18, 28, 27, -21, 33, -30, -7, -10, -35, -7],\n [-21, 10, 28, 1, 19, 20, -19, 21, -14, -29, -33, 18],\n [20, 28, -27, 14, 35, 21, -28, 17, -1, 13, -12, -29],\n [4, 15, 0, -2, 17, 31, -3, 30, 18, 29, 33, 4],\n [28, -26, -22, 15, -35, -11, -14, 0, -9, -15, -5, -30],\n [16, -28, 26, -26, 35, 4, -1, -10, 28, -32, 35, -32],\n [-20, -23, 14, 31, -4, -33, 2, 31, 3, 21, 19, -9],\n [-20, -32, 14, 10, 6, 13, 8, -4, 10, 35, 1, -34],\n [31, 33, 27, -25, -18, 13, -22, -14, -14, -11, -20, 3],\n [-6, -15, 7, 25, -17, -16, 11, -12, 28, -16, 29, 35],\n [-11, 21, -3, 25, 8, 25, 11, -4, -32, 29, -6, -34]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "932", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (1, 10) rounded to the nearest integer?\n[[12, -30, 31, 34, -2, -33, 1, 18, -14, -34, -30, 2],\n [32, 21, -30, -2, 16, -30, 28, 23, 4, -20, 30, -26],\n [-6, -3, 32, 3, -32, 28, -11, -21, -30, 33, 7, 15],\n [-21, 19, -33, -26, -12, 6, 30, -26, 5, -15, 17, 33],\n [21, -16, -14, 14, -28, -24, -7, 2, -10, -26, 21, 15],\n [-11, 13, -21, 6, -15, -9, 27, 15, -4, -24, -12, 7],\n [6, 34, -9, 26, -22, 20, -34, 33, -18, 29, -32, 11],\n [9, 34, 29, 34, 23, -4, 7, 2, -7, 33, 10, -35],\n [-30, 0, 28, -9, -35, -7, 34, -4, -34, -12, -20, 16],\n [-10, -35, -12, -8, -3, 6, 14, -25, 26, 11, -30, -26],\n [13, -28, -7, 9, -24, 2, 19, 16, -18, 30, 28, -35],\n [33, 27, -24, -27, -20, 5, -14, -22, 13, 20, 22, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-40", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-33, -8, 1, 0, -6, 8, 0, 10, -20, 2, -12, -2],\n [-8, -25, -6, 8, -4, -28, -1, 4, -12, -25, -12, -16],\n [1, -6, -6, -16, -17, 8, 13, 3, -18, 2, 1, -12],\n [0, 8, -16, 27, 0, -4, -19, 0, 2, 0, -10, 7],\n [-6, -4, -17, 0, 33, -9, 8, -2, -1, 2, 4, 15],\n [8, -28, 8, -4, -9, 7, -3, 8, 32, 6, -6, -11],\n [0, -1, 13, -19, 8, -3, -18, -2, -26, 18, -10, -6],\n [10, 4, 3, 0, -2, 8, -2, -20, 12, 10, -5, 0],\n [-20, -12, -18, 2, -1, 32, -26, 12, 13, 2, 2, 8],\n [2, -25, 2, 0, 2, 6, 18, 10, 2, -18, 12, -2],\n [-12, -12, 1, -10, 4, -6, -10, -5, 2, 12, -25, 2],\n [-2, -16, -12, 7, 15, -11, -6, 0, 8, -2, 2, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-145", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[31, 22, -10, 14, -29, -17, 32, 22, -9, 1, -28, -35],\n [35, 33, -32, 29, -4, -13, -18, -30, 23, 26, -24, 10],\n [-12, -23, 3, -34, -25, 35, 19, -12, 34, -28, 14, 33],\n [-11, -32, 31, -29, 8, -14, 22, -19, -28, 21, -4, 6],\n [6, 4, -15, 32, -1, 9, -31, -27, -26, -6, 10, 26],\n [-34, 17, 13, -35, -18, 7, -3, 16, -31, -34, -1, -27],\n [35, -20, -6, -28, 11, -21, -23, -21, -1, 7, -33, -3],\n [-8, -21, -28, 23, -29, -6, -17, -22, -6, 18, -12, -17],\n [-17, -16, 20, -24, 10, 21, 14, 3, -17, -23, 0, -12],\n [-13, 25, 3, 1, -16, -10, 33, 19, 22, -24, 3, 31],\n [-1, 20, 27, -21, 11, 30, -11, 14, -31, 25, -10, 15],\n [-33, -18, -28, 22, 8, 14, 30, 13, -17, 30, 4, 32]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-83", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (12, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, -24, -9, -31, 11, -27, -13, 27, -29, 17, 19, -6],\n [15, -27, -5, -31, 25, 16, -3, 22, 5, -19, 16, -25],\n [12, -5, 25, 9, -5, 28, -29, 16, 26, -16, 24, -33],\n [7, 17, 22, -27, -10, 31, 23, -15, 9, -1, -2, 31],\n [34, 0, -2, -30, 7, 11, -33, -33, 0, 16, -3, -35],\n [8, -2, 1, -25, 15, -25, -13, 0, 16, 25, -4, 16],\n [-25, 0, 17, -32, -2, 7, 17, 22, 30, 17, 26, 28],\n [17, -26, 21, 29, 26, -22, -33, -31, 6, 14, 27, -34],\n [35, -32, 24, 2, -28, 21, 16, 32, 26, -19, 24, -17],\n [15, -9, -21, -32, -17, 28, -7, -32, -31, -8, -31, -4],\n [2, -23, -9, 19, -18, -3, 6, 13, 26, 26, -18, -4],\n [2, 24, -8, -9, -25, -4, -7, -30, -33, 8, -29, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-33, 6, -8, 15, -24, -3, 17, 10, 27, 16, 16, 10],\n [6, -26, 6, 18, 30, -16, 3, 19, 24, -20, 28, 4],\n [-8, 6, 32, 29, -16, -2, 32, 0, -4, -12, 18, 16],\n [15, 18, 29, -35, -20, -27, -16, 8, -22, -16, -18, 3],\n [-24, 30, -16, -20, -21, 9, -4, 4, 6, -12, 9, -5],\n [-3, -16, -2, -27, 9, -15, 18, 10, -3, -8, -6, -10],\n [17, 3, 32, -16, -4, 18, -8, -16, 8, -26, -14, -11],\n [10, 19, 0, 8, 4, 10, -16, 9, -16, 18, 6, 3],\n [27, 24, -4, -22, 6, -3, 8, -16, 21, -21, 9, 14],\n [16, -20, -12, -16, -12, -8, -26, 18, -21, 9, 0, -16],\n [16, 28, 18, -18, 9, -6, -14, 6, 9, 0, -25, -6],\n [10, 4, 16, 3, -5, -10, -11, 3, 14, -16, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-539", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (12, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[32, 14, -2, -2, -3, 18, 12, -13, -6, 2, 10, -14],\n [14, -26, -9, 4, 8, -3, 30, -9, -6, 24, 10, 6],\n [-2, -9, 2, 11, 32, 2, 32, 10, 14, -12, -16, 14],\n [-2, 4, 11, 20, 11, 26, -12, 22, -15, 27, 17, -4],\n [-3, 8, 32, 11, -28, 8, 4, -3, -16, 19, -16, -14],\n [18, -3, 2, 26, 8, -1, -4, -10, -24, -6, 28, 30],\n [12, 30, 32, -12, 4, -4, -15, -19, -2, 12, -1, 3],\n [-13, -9, 10, 22, -3, -10, -19, -7, -22, -3, -14, 2],\n [-6, -6, 14, -15, -16, -24, -2, -22, -29, 7, -24, -21],\n [2, 24, -12, 27, 19, -6, 12, -3, 7, 3, 20, -18],\n [10, 10, -16, 17, -16, 28, -1, -14, -24, 20, 28, 9],\n [-14, 6, 14, -4, -14, 30, 3, 2, -21, -18, 9, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[8, 14, -2, 16, -12, 6, 7, -21, -10, -19, -34, 10],\n [14, -33, 22, 0, 23, 10, -6, 15, 10, -24, 14, -14],\n [-2, 22, 30, 10, -9, -32, -28, 4, -14, -4, -2, 5],\n [16, 0, 10, 32, 22, 16, 2, -17, 9, 6, -3, 4],\n [-12, 23, -9, 22, -7, 6, -8, -22, 19, -8, 0, -24],\n [6, 10, -32, 16, 6, -8, -10, 6, -21, -20, -4, -2],\n [7, -6, -28, 2, -8, -10, -15, -5, 11, -7, 6, 28],\n [-21, 15, 4, -17, -22, 6, -5, -35, -17, 9, 4, 23],\n [-10, 10, -14, 9, 19, -21, 11, -17, 13, -4, 15, -2],\n [-19, -24, -4, 6, -8, -20, -7, 9, -4, 22, -23, -3],\n [-34, 14, -2, -3, 0, -4, 6, 4, 15, -23, -32, -2],\n [10, -14, 5, 4, -24, -2, 28, 23, -2, -3, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-43", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[29, -12, 24, 24, -22, -6, -28, 24, -10, 16, 28, 18],\n [1, 32, -4, -25, -28, 33, -6, 21, -11, -8, 29, 4],\n [-10, -17, -15, 27, 7, 29, 5, -16, -17, -15, -1, -2],\n [6, 10, -7, -10, -5, 33, 5, 32, 2, 23, 2, -2],\n [-11, 20, 11, -9, 18, 22, -14, 33, 0, -19, -8, 8],\n [-7, -33, -25, -33, 1, 20, -5, 11, 24, 13, -12, -8],\n [20, -5, -7, 30, -31, -27, 13, 1, 28, -15, 3, -2],\n [-33, -13, 0, 34, 11, 21, -1, -29, 10, 23, -34, -8],\n [-6, -29, 2, -4, -1, -17, -24, 7, 30, 6, 31, -27],\n [20, 29, 14, -21, 28, 24, 24, 11, -18, 17, 29, 9],\n [-4, -5, 23, 25, -9, 33, -23, 3, 33, 2, -16, -11],\n [9, -17, 0, -13, -14, -3, -7, -9, 32, -8, -25, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-33, -15, -14, -25, 33, -22, 32, 8, -6, 19, -11, -26],\n [27, -14, 17, -11, 17, -12, 1, 9, -22, 3, 32, -31],\n [-12, 4, 7, -21, -15, 24, -31, -26, 14, 30, 24, 32],\n [25, -24, -13, -4, -10, 22, -8, -16, 19, -31, 14, -26],\n [-27, -35, -3, 23, -20, 30, -26, -9, 19, 0, 19, 18],\n [-5, 6, -10, -16, -24, 11, -7, 15, -20, -10, -18, 17],\n [-5, 17, 21, -21, -12, 23, 29, -15, -22, 22, -7, 31],\n [29, -11, -29, -23, -16, -27, -31, -8, -10, 34, -30, -7],\n [24, -26, 25, -22, -15, 19, 18, 1, 10, 11, -22, 28],\n [3, 21, -23, -6, -28, -23, 0, 25, 20, -10, -27, 5],\n [-21, -35, -35, 26, -30, -35, -17, 30, -34, -20, 2, 30],\n [-34, -19, 16, 33, 11, -3, 15, -14, 28, 22, -10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-281", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-34, 5, 14, -12, -6, 1, -5, -8, 4, 3, 0, 14],\n [5, 22, 0, -20, 8, 9, 2, 10, -16, -6, -14, -12],\n [14, 0, -34, 13, 26, -4, 11, -4, -20, -8, 4, 2],\n [-12, -20, 13, 13, 30, -16, -18, 26, 17, 34, -25, 2],\n [-6, 8, 26, 30, 12, 14, 12, -15, -15, 28, 9, 0],\n [1, 9, -4, -16, 14, 31, -6, -2, 0, -18, -30, 7],\n [-5, 2, 11, -18, 12, -6, 23, 3, -32, -17, -19, 8],\n [-8, 10, -4, 26, -15, -2, 3, 20, -8, 12, -8, 8],\n [4, -16, -20, 17, -15, 0, -32, -8, -24, 12, 26, -11],\n [3, -6, -8, 34, 28, -18, -17, 12, 12, 13, 16, 0],\n [0, -14, 4, -25, 9, -30, -19, -8, 26, 16, -23, 24],\n [14, -12, 2, 2, 0, 7, 8, 8, -11, 0, 24, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[28, -10, -7, -12, -1, 0, 0, 6, -5, -11, 0, 21],\n [-10, -16, 1, -4, 8, -4, -6, -2, 3, -12, 15, 20],\n [-7, 1, -9, -6, 2, -18, 10, -18, 8, -6, -15, -13],\n [-12, -4, -6, -3, 10, -18, 2, -17, -16, 2, 20, 24],\n [-1, 8, 2, 10, 23, 20, 12, 16, -6, -3, -23, 20],\n [0, -4, -18, -18, 20, -19, 22, -7, 0, -14, 4, -16],\n [0, -6, 10, 2, 12, 22, -3, -14, -5, -2, 4, 6],\n [6, -2, -18, -17, 16, -7, -14, -24, 2, -14, 5, -18],\n [-5, 3, 8, -16, -6, 0, -5, 2, 14, 19, 22, -8],\n [-11, -12, -6, 2, -3, -14, -2, -14, 19, 26, -5, 27],\n [0, 15, -15, 20, -23, 4, 4, 5, 22, -5, 1, 7],\n [21, 20, -13, 24, 20, -16, 6, -18, -8, 27, 7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1450", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-10, -7, 14, 22, 14, -3, 3, -15, -2, 0, -3, 16],\n [-7, 1, 28, 3, -28, -23, 20, 19, 0, 14, 0, 8],\n [14, 28, 35, -24, -22, -2, 6, -20, -12, 16, -19, -20],\n [22, 3, -24, 4, -5, 1, 26, 18, -2, 29, 0, 23],\n [14, -28, -22, -5, -14, 22, -20, 12, 20, 12, 12, 26],\n [-3, -23, -2, 1, 22, 21, 6, 2, 28, -13, 6, 28],\n [3, 20, 6, 26, -20, 6, -15, -10, 2, -18, 17, 4],\n [-15, 19, -20, 18, 12, 2, -10, -34, 16, 6, 4, 12],\n [-2, 0, -12, -2, 20, 28, 2, 16, 8, 6, 2, -4],\n [0, 14, 16, 29, 12, -13, -18, 6, 6, 9, 8, -10],\n [-3, 0, -19, 0, 12, 6, 17, 4, 2, 8, 1, -6],\n [16, 8, -20, 23, 26, 28, 4, 12, -4, -10, -6, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-111", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[35, -20, 9, -1, 20, 22, -28, 12, -6, 26, 22, 7],\n [-20, 31, 13, -8, 18, 14, 30, 6, -6, 22, 6, -4],\n [9, 13, 0, -16, -33, 22, -2, 0, -1, 0, -10, 28],\n [-1, -8, -16, 3, -7, 2, 2, 13, -16, 8, -2, -13],\n [20, 18, -33, -7, 27, -6, -5, 32, 24, 6, 0, -5],\n [22, 14, 22, 2, -6, -12, -8, 8, -6, 3, 8, -12],\n [-28, 30, -2, 2, -5, -8, -15, -15, -7, -8, 8, 12],\n [12, 6, 0, 13, 32, 8, -15, -21, 12, 1, 16, -18],\n [-6, -6, -1, -16, 24, -6, -7, 12, -4, -14, -8, -2],\n [26, 22, 0, 8, 6, 3, -8, 1, -14, 35, 14, 13],\n [22, 6, -10, -2, 0, 8, 8, 16, -8, 14, 32, -6],\n [7, -4, 28, -13, -5, -12, 12, -18, -2, 13, -6, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[7, -8, -5, 19, -23, -27, 7, 12, 13, 3, -32, -23],\n [8, -35, 8, 17, -20, -26, 30, -33, 11, -27, 10, -9],\n [15, 27, 23, 2, 14, 24, 34, 8, -2, 35, 16, -26],\n [11, 24, -20, -2, -8, -29, 21, -10, 14, 4, -7, -22],\n [-22, 25, 2, -28, -7, 3, 0, 16, 13, 24, -18, -5],\n [24, -22, 9, 4, 26, 33, 35, -35, -4, 31, 19, -21],\n [25, 20, 3, -14, -17, 25, 14, -18, 25, 9, -25, -23],\n [3, 30, 9, -1, -3, -5, -18, 29, 13, -21, 28, -29],\n [21, 13, -15, 4, -24, -14, -27, -5, -33, 7, 12, -13],\n [25, -21, 10, 20, -22, 12, 9, -12, 17, -17, -29, 26],\n [11, 14, 27, 14, -11, 3, -24, 19, -13, 23, -4, -19],\n [-8, 7, 13, 8, 21, -22, -9, -29, 20, 11, -24, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-281", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[20, -20, -11, -33, 9, 14, -31, -3, 29, -4, -7, -13],\n [0, 24, 11, -25, 2, 32, -15, -30, 35, 0, -21, -27],\n [0, 0, -19, -2, 10, -6, -24, -29, 30, -15, 14, -35],\n [0, 0, 0, -11, -7, 16, 28, -8, 3, 32, 25, -26],\n [0, 0, 0, 0, 3, -23, 6, -10, 23, 22, -5, -9],\n [0, 0, 0, 0, 0, -35, -20, 9, -2, -14, -33, 2],\n [0, 0, 0, 0, 0, 0, 13, 25, 6, -9, -16, -15],\n [0, 0, 0, 0, 0, 0, 0, -24, 18, 5, 15, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, -14, 19, -33, -2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -12, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3936", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-22, -7, 2, 6, 10, 14, -19, -12, -6, -15, -7, -20],\n [-7, -7, -20, 14, 26, -32, -2, -26, -26, 20, 16, 9],\n [2, -20, -18, 12, -7, 8, 0, -4, 24, 3, -20, -4],\n [6, 14, 12, 26, -8, -26, 2, 16, 9, -24, -9, 15],\n [10, 26, -7, -8, 26, -10, -16, -9, 8, -8, 19, 7],\n [14, -32, 8, -26, -10, 29, 0, 12, -2, 2, -16, 4],\n [-19, -2, 0, 2, -16, 0, 18, -24, -13, -1, -9, -1],\n [-12, -26, -4, 16, -9, 12, -24, 7, 0, 4, 2, -20],\n [-6, -26, 24, 9, 8, -2, -13, 0, -21, -24, 2, -10],\n [-15, 20, 3, -24, -8, 2, -1, 4, -24, -8, 2, 13],\n [-7, 16, -20, -9, 19, -16, -9, 2, 2, 2, -29, 10],\n [-20, 9, -4, 15, 7, 4, -1, -20, -10, 13, 10, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-268", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -23, -19, 28, 15, -11, -16, 23, 33, -15, -3, 27],\n [0, -30, -24, 21, 21, 32, 14, -9, 25, -31, 31, -32],\n [0, 0, 35, -21, -17, -5, -21, 12, 18, 19, 22, 20],\n [0, 0, 0, -5, -17, 22, 17, 32, -27, -26, 12, -13],\n [0, 0, 0, 0, -9, 0, -4, -9, -22, 10, 13, -2],\n [0, 0, 0, 0, 0, -22, 25, -15, -7, -27, 26, 21],\n [0, 0, 0, 0, 0, 0, -17, -13, 32, -8, -2, -18],\n [0, 0, 0, 0, 0, 0, 0, 3, 27, -3, -21, -11],\n [0, 0, 0, 0, 0, 0, 0, 0, 4, 6, -35, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -15, 35, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1077752", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[5, 5, 23, -23, -24, -10, 18, 10, -2, 20, 21, -1],\n [0, -3, 19, -18, -2, -30, 26, 32, 25, 27, -14, -16],\n [0, 0, 20, 29, -21, -8, -20, 24, 21, -21, 14, -15],\n [0, 0, 0, 23, 2, 1, -22, 26, 34, 11, 34, 3],\n [0, 0, 0, 0, -2, 11, 1, -33, 32, -26, -15, 19],\n [0, 0, 0, 0, 0, 29, 29, 24, -19, 22, -5, -30],\n [0, 0, 0, 0, 0, 0, 14, 22, -2, -29, -34, -1],\n [0, 0, 0, 0, 0, 0, 0, -35, -4, -8, 16, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 13, -23, 0, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 23, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86445", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-10, 32, -23, -25, 15, 18, -12, -14, -17, -4, -1, 13],\n [0, 7, 18, 24, -2, -18, 2, 25, 15, 32, -10, 30],\n [0, 0, -24, 33, 29, -20, -30, 20, 2, 8, 9, 3],\n [0, 0, 0, 30, 8, 9, -28, -31, 13, 16, -4, -23],\n [0, 0, 0, 0, -14, -23, -18, -10, 32, -8, 35, -23],\n [0, 0, 0, 0, 0, 14, 32, 34, -2, -11, 9, -35],\n [0, 0, 0, 0, 0, 0, -16, -2, -33, 20, -2, -13],\n [0, 0, 0, 0, 0, 0, 0, -19, -1, -34, -18, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, -12, -17, -16, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -33, -18, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, -1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25826", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 30, -9, -23, 6, -16, -33, 18, -19, -20, 2, -17],\n [28, 31, 0, -28, 3, 31, -3, 12, 10, -3, -20, 1],\n [32, 14, -31, 29, 8, -17, 10, -30, 12, 29, 23, -4],\n [-25, -18, -22, -27, 25, -34, -7, -19, 23, -11, -6, -28],\n [17, -2, -25, 24, 12, -8, 19, 3, 26, 27, 21, 18],\n [-14, 13, 31, -4, 6, 33, -26, 4, 18, -28, -11, 4],\n [-30, 5, -5, -14, 16, 20, -14, -17, -15, -33, 33, -30],\n [19, -7, -35, 30, -28, 7, 32, 26, -7, 5, 0, -21],\n [24, -29, 21, -5, -16, -19, -24, -34, 14, 8, -18, 20],\n [18, -28, -1, -22, -2, -18, -34, -14, 1, 26, -33, 22],\n [31, 25, 28, 18, -14, -8, -19, -8, -4, 32, 25, 14],\n [-6, 5, -30, 17, 22, -35, -5, -16, 2, 20, 10, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, -22, -11, 24, 24, -18, -17, -11, 18, -13, -3, 15],\n [-5, -30, -9, -23, -30, 15, 11, 4, 30, 27, 30, 1],\n [23, 2, -13, 35, 33, 25, -11, -33, -2, -3, -15, 18],\n [28, -16, -5, 7, 14, -23, 5, 28, -3, 4, 1, 17],\n [0, 16, -28, -13, -7, -24, 31, -35, -20, 31, 32, 17],\n [-1, 29, 34, 34, 14, -11, -9, -31, 30, 26, 4, 17],\n [3, -32, -27, 35, 6, -31, -5, 26, 5, -7, -8, 2],\n [-8, -27, -5, -23, -14, 6, 1, 0, -25, -20, -15, 18],\n [-27, 4, 15, 34, -14, -7, -12, -5, 6, 19, -34, 14],\n [34, -7, -13, 4, 0, -8, -12, 19, 13, -32, 12, -23],\n [8, 23, -14, -29, -7, 2, -19, -12, -22, -29, 29, 16],\n [-31, -25, 11, -15, -8, -23, -2, -15, 22, -29, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-71", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (4, 8) rounded to the nearest integer?\n[[-10, 16, 23, 9, -3, 32, -1, 11, -9, 3, -8, -16],\n [-14, -10, 20, -12, -34, 31, -20, 4, -9, -4, -17, -18],\n [-33, 25, -8, -15, -32, 29, -18, 1, -6, 33, 16, 28],\n [2, -19, -24, -5, -25, -12, -10, 18, -21, -25, -8, 5],\n [26, -1, 7, 5, 20, -3, 18, -20, 15, -15, -18, -22],\n [-17, -24, 33, 28, 15, 2, -2, 33, -12, 17, -20, 4],\n [30, 29, 4, 16, 13, 9, -16, 35, -5, 3, -27, -23],\n [33, -17, 6, -21, 16, -8, 14, -21, -17, -1, 0, -3],\n [3, 1, 13, 17, -12, 3, -11, -2, -26, 24, 28, 20],\n [-19, 6, 6, 11, 5, -5, 29, 35, -5, -9, -32, -11],\n [-6, 30, 11, 3, 20, 23, 5, -5, -1, 15, -3, 22],\n [33, -15, 32, -28, 16, -6, -3, 9, 18, -4, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 11, 10, 0, -17, -6, -14, 8, -17, 8, 4, 21],\n [11, -24, 6, -16, 15, -12, -18, 32, 16, -24, 6, 10],\n [10, 6, 32, 0, -14, -22, -20, 6, 12, -3, 28, 12],\n [0, -16, 0, -30, 0, 14, -16, 12, 8, 6, 16, 0],\n [-17, 15, -14, 0, 15, -8, 6, -34, 11, -18, -15, -2],\n [-6, -12, -22, 14, -8, 17, 0, -2, -6, 4, 0, 15],\n [-14, -18, -20, -16, 6, 0, -32, 0, 2, -28, 10, -3],\n [8, 32, 6, 12, -34, -2, 0, 8, -2, 26, 12, 20],\n [-17, 16, 12, 8, 11, -6, 2, -2, 13, -10, 1, 8],\n [8, -24, -3, 6, -18, 4, -28, 26, -10, 5, 8, 14],\n [4, 6, 28, 16, -15, 0, 10, 12, 1, 8, 25, -1],\n [21, 10, 12, 0, -2, 15, -3, 20, 8, 14, -1, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-363", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[28, -23, -18, -31, -10, -1, -9, -29, -29, -27, -16, -25],\n [-25, 24, 16, -19, 31, 9, 16, 31, 17, 11, -24, -16],\n [-10, -6, 24, 8, -22, -26, 16, -27, 21, -29, 28, -28],\n [35, -7, 19, -24, 13, 10, 24, -17, 16, 11, -10, 11],\n [-29, -13, 35, -31, -30, -11, 19, -4, 29, 24, 35, -29],\n [-30, -1, -22, 12, -21, 24, 28, 1, -32, -23, 4, -2],\n [12, 24, 20, 7, 12, 9, 16, -4, 27, 29, 6, 12],\n [20, -25, 7, 26, -34, -9, 34, -35, 3, 24, 15, -17],\n [-35, 20, 10, -35, 26, -19, -27, 7, 3, -27, -25, -25],\n [-10, -27, -27, -28, 18, 33, 33, -21, -2, -35, -18, 31],\n [-22, -9, -29, 16, -20, 6, -4, 33, -34, 31, 35, -34],\n [-30, 33, -25, -17, 11, 33, 14, -22, -33, -32, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "477", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -10, -24, 16, 7, -9, -35, -16, -18, -30, 35, 20],\n [0, -31, 12, 31, 33, 22, -28, 29, -1, -32, 33, -27],\n [0, 0, -25, -6, 13, -16, -17, -28, 1, 19, -27, -11],\n [0, 0, 0, -11, -21, 3, -15, -13, 12, 2, -24, -31],\n [0, 0, 0, 0, -30, 10, -13, -13, -32, -34, 5, -10],\n [0, 0, 0, 0, 0, -1, -24, 16, 27, -12, 35, -24],\n [0, 0, 0, 0, 0, 0, 16, 29, -10, 35, 33, -23],\n [0, 0, 0, 0, 0, 0, 0, 20, 21, -18, -1, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, -34, 11, -16, -16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -7, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35246", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[25, 28, 3, 22, -13, 0, 6, -8, 24, 2, 10, -2],\n [28, 22, -2, -9, -2, 8, -13, 20, 2, -14, 5, -10],\n [3, -2, 23, 4, 5, 19, -10, -7, 18, -12, -20, 22],\n [22, -9, 4, -34, 1, 26, 23, -6, 2, 2, -10, 12],\n [-13, -2, 5, 1, 20, 26, -28, -20, -16, 20, 0, 15],\n [0, 8, 19, 26, 26, 15, 4, -21, 16, 32, 27, -3],\n [6, -13, -10, 23, -28, 4, -18, 2, -2, -6, 4, -4],\n [-8, 20, -7, -6, -20, -21, 2, -9, 21, 8, -29, -3],\n [24, 2, 18, 2, -16, 16, -2, 21, -3, -8, -24, 6],\n [2, -14, -12, 2, 20, 32, -6, 8, -8, -13, -4, -18],\n [10, 5, -20, -10, 0, 27, 4, -29, -24, -4, -1, -10],\n [-2, -10, 22, 12, 15, -3, -4, -3, 6, -18, -10, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[1, -12, -6, 2, 32, 16, -6, 12, 6, -3, -16, 5],\n [-12, 1, 8, -2, 24, 8, -6, -6, 5, -29, 10, 15],\n [-6, 8, -4, 10, -16, 11, 11, 26, 20, 14, -6, 4],\n [2, -2, 10, 14, -8, 6, 11, -6, 12, -23, -20, 18],\n [32, 24, -16, -8, -24, 4, -24, -24, 10, -26, -15, -6],\n [16, 8, 11, 6, 4, 32, 14, 20, 2, -2, -24, 6],\n [-6, -6, 11, 11, -24, 14, 13, 4, 12, -5, -7, 12],\n [12, -6, 26, -6, -24, 20, 4, -14, -3, -11, -3, 1],\n [6, 5, 20, 12, 10, 2, 12, -3, -25, -2, -28, 24],\n [-3, -29, 14, -23, -26, -2, -5, -11, -2, 12, -4, -10],\n [-16, 10, -6, -20, -15, -24, -7, -3, -28, -4, -12, -13],\n [5, 15, 4, 18, -6, 6, 12, 1, 24, -10, -13, -21]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-47", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[27, -2, 19, 0, -30, -24, -22, 21, -14, 27, 7, -20],\n [0, -24, -22, 1, 16, 14, 21, -10, 1, -18, -1, -26],\n [0, 0, 9, -33, 9, -2, 34, -14, 30, -25, -19, 1],\n [0, 0, 0, -25, -6, -34, -1, -7, 15, -31, 33, -14],\n [0, 0, 0, 0, -3, -13, 2, 17, 27, -32, 1, -35],\n [0, 0, 0, 0, 0, 25, -35, 21, -23, -12, -8, 16],\n [0, 0, 0, 0, 0, 0, 8, -12, 32, -23, 0, 12],\n [0, 0, 0, 0, 0, 0, 0, 29, -3, -4, -32, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, -5, 12, -6, -20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 34, 6, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26287", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-33, 35, -35, 13, -1, -1, 13, 26, -20, 29, -34, -34],\n [0, 23, 6, -4, -20, 13, 17, 30, 1, 17, 15, 30],\n [0, 0, -7, 30, -21, 9, 35, -7, -3, 15, -31, 1],\n [0, 0, 0, -29, 32, -17, -2, -26, -34, 35, -1, -4],\n [0, 0, 0, 0, -9, 19, -4, -26, -1, -32, 3, 7],\n [0, 0, 0, 0, 0, -9, 17, -27, 15, -24, -24, -6],\n [0, 0, 0, 0, 0, 0, 7, -15, -24, 10, 2, 15],\n [0, 0, 0, 0, 0, 0, 0, 33, -31, 8, 14, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 8, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -31, -15, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2536", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-10, -26, -16, 19, 11, 13, 26, -28, -21, -23, -11, 9],\n [0, 6, -8, 25, 3, 2, -26, 16, 23, -23, -11, 19],\n [0, 0, -15, -15, -8, 27, -16, -31, -13, -27, -27, 16],\n [0, 0, 0, -19, 14, -32, 31, 10, -17, -35, 30, 16],\n [0, 0, 0, 0, 18, 16, 22, 33, 34, 22, -5, 0],\n [0, 0, 0, 0, 0, 7, -6, 11, -33, -26, -19, 24],\n [0, 0, 0, 0, 0, 0, 10, 23, 34, 12, -31, 27],\n [0, 0, 0, 0, 0, 0, 0, -31, -7, -17, -10, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 18, 11, 9, 17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -25, -25, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24284", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, 10, -3, -10, 0, 2, -6, -10, -22, -18, 20, -4],\n [10, -30, 8, 12, 2, -14, 6, -7, -6, 16, 12, -6],\n [-3, 8, 33, 5, 14, -6, -1, 22, 8, -12, -4, -1],\n [-10, 12, 5, -21, 14, 6, 3, 14, 4, -12, 28, -20],\n [0, 2, 14, 14, -8, 10, 8, 24, 14, -26, 8, -18],\n [2, -14, -6, 6, 10, -6, 3, -13, 6, -25, -4, 22],\n [-6, 6, -1, 3, 8, 3, -2, 9, -14, -22, 7, -3],\n [-10, -7, 22, 14, 24, -13, 9, 29, -2, 7, -19, -18],\n [-22, -6, 8, 4, 14, 6, -14, -2, 0, -12, -24, 2],\n [-18, 16, -12, -12, -26, -25, -22, 7, -12, -27, 4, -20],\n [20, 12, -4, 28, 8, -4, 7, -19, -24, 4, -23, 9],\n [-4, -6, -1, -20, -18, 22, -3, -18, 2, -20, 9, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-56", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-27, 19, 19, 16, 11, -4, 31, -28, 6, -19, 5, -3],\n [0, 9, -27, -17, 2, 7, 2, 24, -35, -15, 26, -32],\n [0, 0, 12, 0, -34, 12, -18, -6, -28, 35, -11, 2],\n [0, 0, 0, 2, 34, 24, -28, 13, 18, -15, 19, -23],\n [0, 0, 0, 0, -22, 4, 4, 8, 20, -19, -19, -20],\n [0, 0, 0, 0, 0, 22, -15, 0, -16, 34, -35, -19],\n [0, 0, 0, 0, 0, 0, 12, 11, 8, 24, 23, -21],\n [0, 0, 0, 0, 0, 0, 0, -10, 4, 24, -10, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 5, 3, 33, 28],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 34, -25, 3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 20],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-19, 15, 19, -7, 3, -20, 0, -28, 25, 35, -23, -15],\n [0, -31, 5, -8, 23, 7, -32, 20, 1, 4, -27, 4],\n [0, 0, 14, 24, 2, 6, -19, 18, -25, -18, -17, 16],\n [0, 0, 0, 25, 4, -10, 26, 4, 31, 35, -33, -18],\n [0, 0, 0, 0, 33, 17, 33, -29, -3, 24, 12, 35],\n [0, 0, 0, 0, 0, 14, -12, -27, 27, 33, 8, 15],\n [0, 0, 0, 0, 0, 0, 15, 35, 2, 25, -34, 22],\n [0, 0, 0, 0, 0, 0, 0, 6, -35, -6, -6, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, -8, -22, 31, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 22, -7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1294222", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[22, -28, -29, -20, -33, -34, -6, -7, 21, 28, 24, 8],\n [-27, -1, -12, 24, 30, -34, -17, -25, -20, -4, 22, 17],\n [15, 22, 35, -18, -28, 8, -4, -32, 14, -30, -5, 8],\n [22, -2, 29, -17, -34, 19, 33, 0, 25, -24, 24, -6],\n [13, 11, 22, -29, -14, -10, -1, -18, 28, -10, 15, 10],\n [-27, 14, -20, 16, 28, 25, -35, 16, 5, 7, 32, -26],\n [-7, -34, 23, -3, 13, -32, 16, 19, 33, 12, 9, -8],\n [25, 10, 10, 32, 4, -18, -20, 17, -18, 0, 21, -2],\n [27, 12, 17, -11, 27, -27, -13, 34, 1, -14, -28, -27],\n [-10, 11, 13, -6, 8, -1, 26, 2, -28, 20, 34, 2],\n [-18, -35, -28, -24, 29, 24, -19, 34, -14, 11, -15, -31],\n [-5, -6, 9, 5, -7, 5, 18, -26, 11, -17, 28, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1646", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[27, -20, 8, 12, 11, 3, 34, -5, -4, 15, 9, -33],\n [-25, -32, 17, -32, 31, -13, 20, -19, -24, 3, 6, 13],\n [-31, -21, 27, -10, -12, 7, 0, -10, 28, -25, -16, 16],\n [-3, -30, -34, -17, -6, -11, -22, -20, -28, -21, 29, -19],\n [2, -22, 12, 6, -21, -15, -18, 35, 21, -35, 35, 28],\n [-16, 24, -4, -31, 8, -14, -4, 6, 35, 35, 15, -15],\n [8, 8, 18, 23, 8, 23, -21, 13, -10, -34, -12, -33],\n [9, -15, 16, -25, 29, 8, -30, 35, 32, -28, -13, 17],\n [26, 15, -22, 19, -3, -31, -30, 9, -21, 25, 17, 17],\n [21, 31, -22, -15, 30, 13, -16, -18, 16, -19, -23, -9],\n [-30, -1, -18, -2, 0, -14, 32, 27, 5, 20, -4, -20],\n [29, -20, 9, 12, 7, -16, -4, 35, 34, -17, -28, 13]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1713", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-17, -27, -2, -2, 30, -19, -26, 32, 28, -13, -28, 10],\n [0, -18, 32, -19, 2, 34, -28, 20, 24, 15, -24, -21],\n [0, 0, -19, -9, 11, -1, -7, -23, -12, -18, 26, -22],\n [0, 0, 0, -27, -7, -23, -20, -9, -30, -26, -1, -10],\n [0, 0, 0, 0, -26, 12, -13, 7, 3, -27, -10, -14],\n [0, 0, 0, 0, 0, -1, -11, 33, 26, 31, 9, -19],\n [0, 0, 0, 0, 0, 0, 33, -4, 21, -24, -9, 12],\n [0, 0, 0, 0, 0, 0, 0, -10, 32, 15, -33, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, -15, 31, 11, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -26, -22, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2516594", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (3, 10) rounded to the nearest integer?\n[[12, 27, -28, -1, -4, -2, 9, -14, -28, 3, -2, 20],\n [27, -32, 28, -4, 0, 1, -4, -25, -29, -2, -2, 0],\n [-28, 28, 4, 0, -12, -16, -2, -3, -2, 11, 16, 23],\n [-1, -4, 0, -28, -18, 2, -1, 7, -4, -6, 4, -10],\n [-4, 0, -12, -18, -21, 18, 22, 16, 17, -3, 4, -4],\n [-2, 1, -16, 2, 18, 34, 14, 6, -25, -6, -8, 14],\n [9, -4, -2, -1, 22, 14, -10, 4, -8, -20, -3, 11],\n [-14, -25, -3, 7, 16, 6, 4, 22, -4, -1, 12, 20],\n [-28, -29, -2, -4, 17, -25, -8, -4, -21, 0, -4, 8],\n [3, -2, 11, -6, -3, -6, -20, -1, 0, 27, 8, 11],\n [-2, -2, 16, 4, 4, -8, -3, 12, -4, 8, 25, 24],\n [20, 0, 23, -10, -4, 14, 11, 20, 8, 11, 24, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[9, 12, 0, -10, 28, -26, -8, -5, 0, 20, 0, 8],\n [12, 9, -6, -6, 6, -18, 21, 29, -20, 16, 0, 24],\n [0, -6, -31, 8, 11, 4, 0, -24, 10, -29, 10, 0],\n [-10, -6, 8, -19, 6, 16, 10, 6, 2, 16, 2, 5],\n [28, 6, 11, 6, -30, -2, 27, -20, -13, 14, -3, 0],\n [-26, -18, 4, 16, -2, -13, 21, -26, 19, 11, -12, -18],\n [-8, 21, 0, 10, 27, 21, 35, -13, -2, 14, -7, -2],\n [-5, 29, -24, 6, -20, -26, -13, 16, -18, 12, 8, 12],\n [0, -20, 10, 2, -13, 19, -2, -18, -24, 0, -16, -16],\n [20, 16, -29, 16, 14, 11, 14, 12, 0, -12, -12, 10],\n [0, 0, 10, 2, -3, -12, -7, 8, -16, -12, -2, 4],\n [8, 24, 0, 5, 0, -18, -2, 12, -16, 10, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2376", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (12, 11) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -35, -9, 9, 1, -10, 14, 2, -25, 33, -31, -22],\n [0, 16, -12, -31, 6, 10, -5, 15, -1, -19, 25, 0],\n [0, 0, -22, 20, -5, 15, 27, -10, -22, 5, -23, -28],\n [0, 0, 0, 8, 21, -5, -7, 23, -24, -31, 35, -10],\n [0, 0, 0, 0, -14, -11, -34, 12, -22, 30, 16, -18],\n [0, 0, 0, 0, 0, 21, -18, -18, -7, 6, -33, -14],\n [0, 0, 0, 0, 0, 0, -22, 35, -26, -23, 27, 32],\n [0, 0, 0, 0, 0, 0, 0, 18, 5, 27, -11, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, -8, 18, -35, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-31, 34, 3, 10, -15, -4, -33, -24, 12, 12, -12, 13],\n [0, -6, 13, 13, -35, -29, -19, 6, -5, -23, -25, -8],\n [0, 0, 32, 18, -29, 28, 26, -12, 31, 24, 7, 35],\n [0, 0, 0, 23, 24, 3, -35, -3, 5, -31, 23, 1],\n [0, 0, 0, 0, -8, -27, -4, 6, -2, 32, -18, 4],\n [0, 0, 0, 0, 0, -33, 28, 9, 20, 30, -29, 10],\n [0, 0, 0, 0, 0, 0, -5, 25, 12, -25, -25, -28],\n [0, 0, 0, 0, 0, 0, 0, 28, -17, 32, 29, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, -1, -7, 31, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 24, -5, 1],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "712129", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, 9, 2, 4, 0, -2, -16, 1, 6, 20, -7, 22],\n [9, -11, 0, 12, 6, 16, -10, 0, -21, -13, -2, 28],\n [2, 0, -29, -16, 18, 3, 32, -16, -3, 13, -2, 0],\n [4, 12, -16, -18, 1, 3, -16, -8, -6, 0, -17, 30],\n [0, 6, 18, 1, 11, -4, 12, 10, 2, 31, 2, -6],\n [-2, 16, 3, 3, -4, -29, -2, -10, 16, 4, 2, -18],\n [-16, -10, 32, -16, 12, -2, -23, 10, 24, -8, -4, 2],\n [1, 0, -16, -8, 10, -10, 10, 31, -2, -6, 14, 11],\n [6, -21, -3, -6, 2, 16, 24, -2, -14, -21, 18, -13],\n [20, -13, 13, 0, 31, 4, -8, -6, -21, -27, 18, -6],\n [-7, -2, -2, -17, 2, 2, -4, 14, 18, 18, -23, 4],\n [22, 28, 0, 30, -6, -18, 2, 11, -13, -6, 4, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2103", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-29, 14, -20, -8, 24, 14, -5, 2, -32, -8, 16, -20],\n [14, 1, -2, -22, -6, 19, -13, 10, 1, 8, -6, -8],\n [-20, -2, 12, -18, 2, 18, 15, 2, -17, 23, 22, -28],\n [-8, -22, -18, 4, 24, -7, 10, 12, 7, -15, -13, -3],\n [24, -6, 2, 24, -1, 10, 14, -6, 22, -10, 10, 0],\n [14, 19, 18, -7, 10, -30, -34, 18, 12, -24, 6, 22],\n [-5, -13, 15, 10, 14, -34, -25, 29, -20, -10, 9, 10],\n [2, 10, 2, 12, -6, 18, 29, -14, 4, -17, 16, 0],\n [-32, 1, -17, 7, 22, 12, -20, 4, -28, -7, 21, 2],\n [-8, 8, 23, -15, -10, -24, -10, -17, -7, 31, -12, -32],\n [16, -6, 22, -13, 10, 6, 9, 16, 21, -12, -35, 11],\n [-20, -8, -28, -3, 0, 22, 10, 0, 2, -32, 11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-175", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[6, -12, -14, 3, 28, 6, -1, 8, 4, 0, -5, -28],\n [-12, 7, -2, -4, -9, 10, 13, 16, 17, 11, 18, -17],\n [-14, -2, -33, 20, -9, 16, -10, -18, 0, 14, 4, -14],\n [3, -4, 20, 14, 12, 8, -18, 0, -2, -6, 1, 8],\n [28, -9, -9, 12, -12, 13, 24, 24, -2, -8, -20, 9],\n [6, 10, 16, 8, 13, -4, 6, -17, -16, -16, -6, -10],\n [-1, 13, -10, -18, 24, 6, -6, -8, 29, 4, -11, -16],\n [8, 16, -18, 0, 24, -17, -8, -15, 1, 10, 5, -13],\n [4, 17, 0, -2, -2, -16, 29, 1, -4, 14, 0, 14],\n [0, 11, 14, -6, -8, -16, 4, 10, 14, -9, -2, -1],\n [-5, 18, 4, 1, -20, -6, -11, 5, 0, -2, -28, -24],\n [-28, -17, -14, 8, 9, -10, -16, -13, 14, -1, -24, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "193", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-13, -25, 32, -5, 5, -2, 30, 30, -35, -7, 21, 27],\n [12, 0, -33, 13, 22, 0, 9, -2, -14, 29, 26, 16],\n [-10, 33, -30, 22, 0, 10, -15, 19, 7, -1, -22, -11],\n [3, 31, 34, 17, -24, 21, 24, 0, 29, 27, 2, -5],\n [-19, -2, 11, 16, 7, -7, -14, 2, 26, -1, 19, 8],\n [-30, -17, -24, -9, -3, 1, 22, -5, 11, 30, -16, -7],\n [-11, -24, -28, 27, 31, 25, -8, -21, 20, -31, 26, -32],\n [-9, -32, 28, -22, -35, -5, -24, -28, 26, -13, 29, 29],\n [22, 10, 26, 0, -33, -16, 28, 1, 26, -22, 5, 30],\n [-32, -26, 35, -17, 35, -9, -2, 33, 4, 4, -10, 15],\n [-1, -30, 25, 25, -17, -1, -10, -1, 15, 24, 31, -31],\n [9, 24, 24, -7, 8, -16, 18, 20, 20, 4, -14, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1481", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (11, 8) rounded to the nearest integer?\n[[24, 0, -2, -2, -9, 29, -7, -4, 21, -23, 0, -23],\n [0, -31, 17, -19, -34, -11, -29, -2, -10, 22, 25, -16],\n [0, 0, -19, 27, 30, -20, 19, 20, 7, -26, 17, 24],\n [0, 0, 0, -14, 0, -14, -17, -25, 29, 30, -21, -7],\n [0, 0, 0, 0, 21, -14, -6, -11, 31, -27, -2, 28],\n [0, 0, 0, 0, 0, 3, 29, 31, 17, 7, -18, -2],\n [0, 0, 0, 0, 0, 0, 25, 26, -15, 29, -16, 15],\n [0, 0, 0, 0, 0, 0, 0, -29, 35, 12, -21, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 13, -5, 4, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -22, -12, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[13, -28, 19, -17, -3, -12, 13, 31, -33, 17, -35, -9],\n [0, -5, -8, -20, -27, -4, 29, 29, -12, 30, 21, -18],\n [0, 0, 30, -34, -25, 24, 25, 29, -8, -9, -24, 3],\n [0, 0, 0, 10, -22, -4, -29, 7, 29, -15, -6, -10],\n [0, 0, 0, 0, -6, 2, -13, 0, 14, -24, -6, 18],\n [0, 0, 0, 0, 0, -10, 27, -7, 19, 29, 26, -1],\n [0, 0, 0, 0, 0, 0, -17, 33, -23, 33, 4, 33],\n [0, 0, 0, 0, 0, 0, 0, 24, -20, 28, 24, 23],\n [0, 0, 0, 0, 0, 0, 0, 0, 32, 0, -5, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -10, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18839", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[12, -9, 28, 11, -28, 28, 20, 29, -34, 4, -24, 8],\n [0, -24, -24, 35, 2, -19, 11, 9, 30, 3, 4, -13],\n [0, 0, 5, 2, 14, 27, 27, -7, -18, 9, 17, 2],\n [0, 0, 0, -3, 21, -6, 6, 22, 29, -17, -17, 4],\n [0, 0, 0, 0, -5, 16, 28, -5, -20, 4, 33, -11],\n [0, 0, 0, 0, 0, 18, 30, -4, 3, -23, 30, 1],\n [0, 0, 0, 0, 0, 0, 34, 16, 9, 4, -24, 17],\n [0, 0, 0, 0, 0, 0, 0, -14, 27, 15, -5, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 24, 25, 33, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 2, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, -14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8842", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[24, 29, -34, -34, -11, -20, -30, -8, 34, -35, 9, -22],\n [-9, 3, -27, -14, -31, -1, -8, 18, -27, 11, 32, -2],\n [28, -25, 1, 24, 24, 23, 4, 8, 26, 0, 25, -21],\n [-30, 6, 27, -5, -1, -9, -2, -11, 33, -30, 11, 20],\n [2, -10, -8, 35, -35, 5, 12, -35, -19, -9, 8, 5],\n [-32, -3, -35, -25, -28, 28, 22, 24, -6, 16, 4, -33],\n [-5, 28, 32, 32, 0, -34, -33, 11, 23, -26, -10, -34],\n [-22, -34, 26, 23, -18, -27, 24, 17, -25, 26, -15, -18],\n [-12, -24, 26, -30, -29, -18, 27, 1, 35, 15, -16, 25],\n [0, -7, 7, -15, 30, -7, -17, -2, -28, -18, -32, -18],\n [12, -28, -17, -12, 13, -20, 18, 29, 9, -21, -27, 6],\n [-32, 6, 18, 22, 33, -29, 14, 30, 31, -35, -18, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "113", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[20, -30, -2, 7, 33, -15, -35, 7, 23, -1, 25, -17],\n [18, 22, 27, 6, -30, 18, 8, 23, -22, -20, 24, -7],\n [25, -22, -5, 19, -18, -32, 0, 17, -26, 22, 24, -32],\n [-26, 4, -8, 30, -30, -13, 29, 31, 10, -8, 23, 12],\n [-10, 22, 31, 21, -8, -7, -23, 17, -16, -14, -23, 21],\n [33, 33, 13, -25, -29, -20, -18, 34, 29, 14, -28, 33],\n [19, 7, -15, 11, 27, 7, 1, 26, 23, 23, -23, 10],\n [-4, 31, -13, -10, 35, -26, 26, -31, 14, -11, 3, 2],\n [-21, -4, 25, 28, 16, -12, 4, 21, 5, 5, -13, -17],\n [10, -25, 15, 11, -18, 4, -4, 26, 7, 1, 31, 4],\n [15, -20, 33, 11, -31, 20, -25, 4, -26, -28, -7, -3],\n [10, 35, -13, 14, -31, 6, -25, -35, 26, 8, 33, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[28, -8, -8, -14, -13, -16, -8, -22, -16, 10, 0, 16],\n [-8, 23, 13, -33, 18, 12, -14, 34, 27, -10, 0, -14],\n [-8, 13, 19, 19, -17, -24, 3, -2, 8, 4, -1, -5],\n [-14, -33, 19, 9, -4, 14, 25, -23, -8, -10, 12, -18],\n [-13, 18, -17, -4, 17, 0, -14, -18, 20, -22, 0, 2],\n [-16, 12, -24, 14, 0, -29, 10, -18, 12, 6, 26, 20],\n [-8, -14, 3, 25, -14, 10, -18, -8, 0, 9, 14, -14],\n [-22, 34, -2, -23, -18, -18, -8, -3, 0, -11, 17, 12],\n [-16, 27, 8, -8, 20, 12, 0, 0, -1, 4, -8, -22],\n [10, -10, 4, -10, -22, 6, 9, -11, 4, -30, -8, -28],\n [0, 0, -1, 12, 0, 26, 14, 17, -8, -8, 9, 8],\n [16, -14, -5, -18, 2, 20, -14, 12, -22, -28, 8, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1149", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[17, -31, -12, 3, 8, 29, -24, 17, 0, -33, 16, 4],\n [33, -4, -19, 31, -17, 19, 20, 12, 5, -20, -33, -12],\n [-10, -9, 1, 21, 24, 34, 3, 31, 0, 20, -3, -3],\n [-31, -31, -33, -5, 11, -8, -31, -6, -19, 17, 19, 25],\n [-4, 19, -21, -6, 28, 1, -3, -11, -33, -18, 7, 18],\n [-29, 10, -10, -15, 24, 25, -26, 11, 3, -16, -22, -8],\n [-32, -2, -10, -25, -6, -18, -6, -18, 22, 30, -17, -15],\n [-19, -2, 3, 1, -32, -19, -11, -28, 21, -9, 20, -5],\n [-11, 24, 6, 8, -35, 18, 19, -22, 21, 6, 12, 32],\n [-10, -22, 28, 22, 4, 9, 0, 11, -33, 22, 34, -15],\n [-25, 19, -22, 11, 34, 8, 5, 28, 32, 14, 18, 13],\n [28, 19, -3, 4, -32, -24, 10, -10, -16, 6, 33, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-102", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (2, 10) of the inverse. Round your answer to the nearest integer:\n[[6, 7, 15, -23, -12, 34, -4, 19, 30, -31, -31, -30],\n [0, -19, -33, 19, -3, 34, -27, -28, -11, -27, 23, 32],\n [0, 0, 2, -33, -17, 25, -15, 18, 18, -35, -18, -4],\n [0, 0, 0, 24, -29, -14, 2, 32, -15, 1, 9, 22],\n [0, 0, 0, 0, 24, -32, 33, 17, 31, 19, 34, -28],\n [0, 0, 0, 0, 0, -12, 11, -12, 11, -5, 22, 13],\n [0, 0, 0, 0, 0, 0, 23, 32, -6, -28, 26, -21],\n [0, 0, 0, 0, 0, 0, 0, 19, -24, -34, -1, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, -10, 30, 35, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 26, -23],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117288", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (6, 9) of the inverse. Round your answer to the nearest integer:\n[[-31, 28, -13, -6, 24, -1, 20, 8, 9, -17, 18, -10],\n [28, -19, -16, 15, 4, 6, -10, 0, -22, 8, 8, 19],\n [-13, -16, 20, 14, 2, 8, 9, -4, -2, -18, 12, -4],\n [-6, 15, 14, -8, -6, -12, 16, 4, 9, -8, 13, 6],\n [24, 4, 2, -6, -28, -6, -6, -4, 2, 10, 18, -20],\n [-1, 6, 8, -12, -6, -25, -4, -17, 31, 7, -19, -18],\n [20, -10, 9, 16, -6, -4, -22, 2, -12, 5, 2, -25],\n [8, 0, -4, 4, -4, -17, 2, -10, 10, 12, 22, -18],\n [9, -22, -2, 9, 2, 31, -12, 10, 18, -13, 7, 0],\n [-17, 8, -18, -8, 10, 7, 5, 12, -13, 28, 9, 18],\n [18, 8, 12, 13, 18, -19, 2, 22, 7, 9, -27, -15],\n [-10, 19, -4, 6, -20, -18, -25, -18, 0, 18, -15, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[17, -19, 33, -22, -22, 3, -32, -26, 15, -12, -6, -5],\n [0, -12, 26, -4, -28, 33, -16, -21, 23, -27, -8, 14],\n [0, 0, -13, -12, -20, 20, -14, -13, -17, -3, 23, 5],\n [0, 0, 0, 21, -19, 23, -25, -31, 5, 28, 5, 21],\n [0, 0, 0, 0, -2, 6, -12, -24, -7, 24, 20, 10],\n [0, 0, 0, 0, 0, -6, -14, 1, -31, -17, 10, -13],\n [0, 0, 0, 0, 0, 0, 11, 3, -19, 21, 34, 30],\n [0, 0, 0, 0, 0, 0, 0, -31, -25, -2, -2, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, -16, -34, -20, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 32, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, -8],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16836", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-29, -34, 0, -30, 10, 16, 20, -30, 12, 20, -10, -8],\n [-34, 32, 20, 24, -14, 0, 6, 16, -28, 0, 8, -20],\n [0, 20, 29, -14, 22, 34, 14, 0, 0, 16, -15, 4],\n [-30, 24, -14, 22, 23, 16, -18, -20, 20, -28, 9, 3],\n [10, -14, 22, 23, 25, 10, 8, -30, 12, 11, 0, -26],\n [16, 0, 34, 16, 10, 16, 6, 26, -10, -30, 3, -32],\n [20, 6, 14, -18, 8, 6, 32, -14, 6, 8, 7, 2],\n [-30, 16, 0, -20, -30, 26, -14, 14, -22, 12, 9, 8],\n [12, -28, 0, 20, 12, -10, 6, -22, -21, -12, -14, 2],\n [20, 0, 16, -28, 11, -30, 8, 12, -12, -4, -1, 0],\n [-10, 8, -15, 9, 0, 3, 7, 9, -14, -1, -28, -6],\n [-8, -20, 4, 3, -26, -32, 2, 8, 2, 0, -6, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-331", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-34, -24, -2, 6, 14, 8, -28, -12, 17, 0, -8, -22],\n [-24, -26, -27, -16, -23, -18, 34, 11, 29, 8, 2, 10],\n [-2, -27, -8, 4, -20, 10, -19, 0, 12, 0, 0, 16],\n [6, -16, 4, -18, 2, 22, -20, -5, 0, -30, 14, 0],\n [14, -23, -20, 2, -15, -6, -32, 2, -18, 24, 14, 17],\n [8, -18, 10, 22, -6, 12, -6, -1, 24, 34, -22, 10],\n [-28, 34, -19, -20, -32, -6, 2, -28, 2, 24, 8, -10],\n [-12, 11, 0, -5, 2, -1, -28, -13, 13, 7, -2, -4],\n [17, 29, 12, 0, -18, 24, 2, 13, -15, -4, -20, -6],\n [0, 8, 0, -30, 24, 34, 24, 7, -4, 5, 26, 4],\n [-8, 2, 0, 14, 14, -22, 8, -2, -20, 26, 0, -22],\n [-22, 10, 16, 0, 17, 10, -10, -4, -6, 4, -22, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-26, 2, -5, 15, -3, 5, -8, 0, 24, 17, -14, 28],\n [2, -31, -32, -5, 4, -8, -10, 12, 14, -18, 12, -10],\n [-5, -32, 25, -3, 2, 16, -16, -26, 15, -2, 10, -22],\n [15, -5, -3, -14, -10, -6, -11, -4, 2, -10, -7, 4],\n [-3, 4, 2, -10, 21, 14, 22, -7, 0, -16, 26, -8],\n [5, -8, 16, -6, 14, 6, -4, -2, 10, -2, 10, -10],\n [-8, -10, -16, -11, 22, -4, 16, -10, -16, -10, 15, -26],\n [0, 12, -26, -4, -7, -2, -10, -5, 5, 4, -16, -20],\n [24, 14, 15, 2, 0, 10, -16, 5, 29, -26, 12, 2],\n [17, -18, -2, -10, -16, -2, -10, 4, -26, -9, -19, -8],\n [-14, 12, 10, -7, 26, 10, 15, -16, 12, -19, -18, -2],\n [28, -10, -22, 4, -8, -10, -26, -20, 2, -8, -2, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-281", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-28, -7, 26, 8, 14, -22, 12, 18, -8, -2, 23, 8],\n [-7, -8, 20, -13, 9, -11, 13, 4, 5, 16, -4, -14],\n [26, 20, 0, -12, -12, 5, 4, 3, 21, 12, 12, -8],\n [8, -13, -12, -3, 24, 19, -1, -34, 9, -22, 4, -24],\n [14, 9, -12, 24, -6, 19, -24, -3, 26, 5, -11, -15],\n [-22, -11, 5, 19, 19, -3, 8, -12, -18, -14, 6, 20],\n [12, 13, 4, -1, -24, 8, 0, -10, 5, 30, -2, 3],\n [18, 4, 3, -34, -3, -12, -10, -29, 14, 10, -12, 2],\n [-8, 5, 21, 9, 26, -18, 5, 14, -29, 6, -10, -28],\n [-2, 16, 12, -22, 5, -14, 30, 10, 6, -7, 0, -2],\n [23, -4, 12, 4, -11, 6, -2, -12, -10, 0, 7, 29],\n [8, -14, -8, -24, -15, 20, 3, 2, -28, -2, 29, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "777", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (12, 6) rounded to the nearest integer?\n[[17, -25, 13, 12, 34, -24, -33, 23, 16, -32, -13, 20],\n [29, 32, -27, -18, -19, -17, -15, 35, 23, 18, -15, 7],\n [3, 35, -33, 11, 35, -6, 12, 5, 30, -15, 28, -6],\n [-26, -11, 6, -17, 1, -11, 33, -32, -18, -19, -21, -19],\n [-19, 12, -7, -3, 28, -1, -24, 13, 17, 7, -31, 22],\n [9, 14, -2, 30, -10, -35, -31, -4, -34, -10, -26, 9],\n [23, 22, 25, -31, 15, 7, 5, 28, -21, 5, 29, -1],\n [-21, 0, 2, -16, -1, -15, -20, -33, -12, -20, 0, 29],\n [-12, 13, -2, 27, 22, 6, -25, -33, 8, 14, 8, -7],\n [-13, -15, -15, -12, -24, 12, 3, -17, 13, -1, -31, 34],\n [16, 6, -35, -2, 20, 17, 23, 19, 34, -6, -15, -7],\n [28, -13, -11, -27, -28, 28, -3, 14, -19, 22, -20, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (3, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[33, -22, -18, -2, -2, 4, -12, -18, 30, -19, -35, -12],\n [-9, -34, -25, -31, 2, -29, -11, -22, 21, -6, 3, 21],\n [-14, 25, -3, 17, -6, 8, 24, -28, -35, 15, 12, 27],\n [33, 20, -4, 4, 15, 25, 7, 16, -30, -20, 6, -10],\n [24, 7, 17, -20, 17, 31, -17, -11, -16, 16, -26, -15],\n [-29, 25, -3, -35, 18, 18, 7, -12, 33, 33, -10, -20],\n [6, 34, -35, 20, -18, -18, -17, -22, 22, 3, 35, -19],\n [-32, 32, 18, 3, -23, 15, 2, 28, 18, -9, 18, 18],\n [35, -8, -5, 25, 20, -27, 1, 20, 33, 10, -17, 15],\n [29, -30, 8, -13, 24, -17, 27, -22, 35, -22, 15, 4],\n [-19, 22, 3, -34, 9, 26, -23, 5, 20, -15, -9, -6],\n [-5, -12, 15, -2, -17, -19, 17, -2, -22, -8, -25, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 9) of the inverse of matrix 1/839 * A where A =\n[[13, 18, -29, -18, -3, 26, -25, 13, 22, 19, -18, 14],\n [23, -21, -32, 2, 28, 10, 7, 27, 2, -30, -6, 33],\n [-25, -23, 24, -19, 19, -28, -34, -17, 15, 23, -14, -25],\n [-20, -1, -28, -31, -23, -20, 35, 21, 3, -3, 2, 26],\n [0, 4, 25, 27, 31, 10, 12, -24, -33, -20, -4, -16],\n [-6, 24, 4, -3, -10, 11, 12, 26, -20, -7, -5, 26],\n [26, -10, -18, 9, -31, -31, -29, -27, 27, 21, 23, 0],\n [27, -23, -17, -26, -6, 0, -32, -6, 25, -4, 9, -5],\n [20, 6, -23, 17, 18, 7, -12, -13, -17, 3, -15, 11],\n [-26, 23, 5, 27, -1, -20, -2, -2, 8, -30, -15, 35],\n [20, -11, 16, 15, 22, 26, 12, -7, 16, 32, 8, 7],\n [5, -8, -15, -34, 18, -20, 2, 8, -30, -19, 16, -30]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "221", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 6) of the inverse of matrix 1/839 * A where A =\n[[33, 33, 5, 22, 18, 10, 17, -2, -1, -8, -16, 33],\n [0, 20, 33, -1, -28, -3, -6, -3, 26, 24, -13, 20],\n [0, 0, -16, 35, 34, 25, -3, -28, 25, -14, 20, 12],\n [0, 0, 0, 18, 23, -30, -11, -4, 25, -1, 26, -11],\n [0, 0, 0, 0, -2, -7, 7, 24, 10, 10, 30, 19],\n [0, 0, 0, 0, 0, 24, 32, 8, 5, 10, 13, -27],\n [0, 0, 0, 0, 0, 0, -13, -31, -8, 15, -26, -25],\n [0, 0, 0, 0, 0, 0, 0, 14, 10, -34, 6, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 7, -21, 22, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 14, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "264", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (5, 9) of the inverse. Round your answer to the nearest integer:\n[[-33, 20, 17, -15, 2, -16, -8, 4, 6, -29, 2, -19],\n [20, 25, 8, -21, -2, -22, -2, 0, -2, 4, 0, -24],\n [17, 8, -12, 8, 22, 18, -12, -15, 0, -13, 18, -8],\n [-15, -21, 8, -13, -16, 30, -28, 21, 12, -16, -26, 7],\n [2, -2, 22, -16, 23, -11, 19, 2, 32, 5, 21, -16],\n [-16, -22, 18, 30, -11, 33, 10, -10, -6, 2, 8, -6],\n [-8, -2, -12, -28, 19, 10, 16, -7, -9, 17, -3, 0],\n [4, 0, -15, 21, 2, -10, -7, -23, 1, 11, -14, -8],\n [6, -2, 0, 12, 32, -6, -9, 1, 20, -20, 12, -2],\n [-29, 4, -13, -16, 5, 2, 17, 11, -20, -35, 15, -14],\n [2, 0, 18, -26, 21, 8, -3, -14, 12, 15, -34, 5],\n [-19, -24, -8, 7, -16, -6, 0, -8, -2, -14, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[18, 18, 0, -18, -31, 10, -4, 33, -8, -19, 18, -22],\n [4, -22, -34, -29, -14, -18, -28, 7, 2, 19, 14, 13],\n [0, -6, -20, 34, 35, -12, 31, 17, 20, 12, -15, -27],\n [20, 5, 7, -24, -12, 8, -16, -1, -1, 13, -31, 12],\n [11, 19, 34, 35, -35, -14, 0, 27, -31, 11, 14, 20],\n [0, -21, 13, 3, 34, -20, 18, -6, 22, 31, 5, -18],\n [27, -7, 24, -33, -26, 21, 35, -17, -22, 14, -3, 28],\n [4, 29, -4, -4, -16, 0, -2, -3, -14, -6, 27, 11],\n [-28, -8, 9, 20, 19, 29, -31, 19, -24, -26, 9, 30],\n [2, -3, 25, 35, 11, -29, -25, -24, 30, 34, 12, -11],\n [3, -12, -15, -16, 8, 12, -30, -5, 35, 0, 1, -2],\n [-30, 24, -5, -6, -17, -14, -7, -17, 12, 17, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-32, -2, 8, -2, 18, -26, -20, 13, -3, 14, -16, -22],\n [-2, 15, 22, -11, -1, -23, -20, 12, -16, -8, 0, 4],\n [8, 22, 31, 14, 0, -14, -7, 10, 2, 2, -8, 6],\n [-2, -11, 14, 16, -13, -16, 18, 4, 30, 6, 25, 16],\n [18, -1, 0, -13, 12, -8, 27, 27, -13, 4, -5, 4],\n [-26, -23, -14, -16, -8, -3, -8, -4, -20, 17, 20, 24],\n [-20, -20, -7, 18, 27, -8, 16, 24, 20, 4, -10, -24],\n [13, 12, 10, 4, 27, -4, 24, -11, 11, -12, -8, -4],\n [-3, -16, 2, 30, -13, -20, 20, 11, 20, 6, -12, -10],\n [14, -8, 2, 6, 4, 17, 4, -12, 6, 1, -15, 1],\n [-16, 0, -8, 25, -5, 20, -10, -8, -12, -15, 29, 14],\n [-22, 4, 6, 16, 4, 24, -24, -4, -10, 1, 14, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19876", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[18, -8, -34, -7, 24, 22, -31, -23, 34, 23, -28, -34],\n [-26, -32, -1, 13, -17, -29, -6, 26, -13, 34, 33, -9],\n [-14, -23, -15, -4, 11, -30, 26, 28, -24, 2, -29, 27],\n [-25, -8, -7, 4, -9, -4, -16, 8, 21, 19, -34, 28],\n [8, 15, 23, -2, -17, -33, 21, 12, 20, -17, 20, 29],\n [19, -3, -7, 28, -15, 34, -17, -22, 13, -18, 23, 22],\n [-34, -34, 14, -33, 3, -15, -6, 21, -27, -33, -16, 8],\n [-13, 14, 1, 24, -31, 2, 12, 20, 26, 21, -12, 1],\n [24, -19, 7, -24, -32, -31, -29, 19, 14, 2, -35, 16],\n [-15, -32, 13, -8, -27, 17, 12, 9, -12, 20, 16, 28],\n [-32, -3, -31, 26, -33, 17, 12, -15, 17, -35, -10, -9],\n [11, -3, 8, 21, -20, 1, -27, -7, -16, -28, 11, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2115", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[6, -29, 24, 5, -19, 1, 26, 8, 0, 28, 6, -6],\n [-30, -12, -7, -20, 19, 34, -19, 20, -25, -8, -29, -7],\n [-7, 25, 30, -6, -17, 8, 20, 26, 29, 14, 14, 20],\n [-20, 33, 29, -20, 34, 26, 27, -27, 3, 16, -27, 30],\n [10, 33, -28, -6, -33, -6, -16, 3, 13, 17, -23, 7],\n [5, 5, 6, -32, 9, 14, -20, 20, 11, 25, 10, -8],\n [-31, 2, 14, -17, 28, -10, -21, 25, -3, 27, -26, 33],\n [5, -27, -6, 2, 31, 21, -4, 33, 12, 29, 20, 12],\n [-8, -30, 11, 29, 18, -21, 13, 25, -27, 24, 2, 1],\n [35, -8, -33, -2, 33, 17, 35, -21, 35, 33, 1, 0],\n [26, -16, -16, -29, -6, -25, -2, 29, -3, 12, -16, -25],\n [30, 32, -14, 21, 8, -4, -14, -31, 33, -8, -22, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (11, 5) rounded to the nearest integer?\n[[11, -31, 11, -33, 23, -17, -29, -24, -25, -14, -5, -33],\n [33, -3, -16, -5, 15, 33, -23, -23, -25, -31, -17, 33],\n [26, -35, -1, -31, 27, -30, -35, 10, -23, 19, -17, -7],\n [-33, -29, -30, 6, 26, -26, -5, -28, 34, -29, 34, -17],\n [-9, 30, 13, 10, 3, 0, 16, 22, -7, -27, 5, -10],\n [27, -8, 17, -5, 7, -20, 12, -3, -18, -5, -5, -25],\n [35, -6, -17, -10, -16, -33, -14, -2, 18, 20, 27, -32],\n [-33, -34, 12, -17, 17, -30, -4, 2, -31, 16, -1, 18],\n [16, -20, -22, -28, 7, -1, 34, 30, 29, -7, -28, 19],\n [-2, 20, -10, 12, 26, -18, -28, 15, -27, 3, 6, 0],\n [24, -12, 10, -28, -10, -1, 8, 13, -12, 21, -20, 5],\n [8, -30, 4, -23, 16, -14, -29, -18, -28, 14, -4, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-22, 10, -28, -11, -4, -18, -4, -18, -10, -21, 22, 6],\n [10, 13, 25, -23, -14, -20, 4, -14, -4, 1, -6, 12],\n [-28, 25, 18, -3, 3, -12, 6, -9, -14, 5, 0, -24],\n [-11, -23, -3, 29, -6, -24, 20, 14, 14, 10, 23, 0],\n [-4, -14, 3, -6, -4, -12, 2, -2, 0, 2, 31, 6],\n [-18, -20, -12, -24, -12, 17, 0, -1, -12, 2, -22, -20],\n [-4, 4, 6, 20, 2, 0, -21, 31, -11, 16, -2, 10],\n [-18, -14, -9, 14, -2, -1, 31, 9, -13, 17, -24, 21],\n [-10, -4, -14, 14, 0, -12, -11, -13, -9, -16, 6, -8],\n [-21, 1, 5, 10, 2, 2, 16, 17, -16, 35, 12, 6],\n [22, -6, 0, 23, 31, -22, -2, -24, 6, 12, -14, -2],\n [6, 12, -24, 0, 6, -20, 10, 21, -8, 6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-48", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-14, -26, 2, 28, 7, 19, -25, -20, -11, 19, 31, 30],\n [0, 10, -25, 34, -8, 31, 8, 34, 19, -19, 4, 34],\n [0, 0, 17, 29, -35, 3, -6, 7, -13, -5, 33, 16],\n [0, 0, 0, -19, 11, 20, 11, 1, -8, 5, 20, 30],\n [0, 0, 0, 0, 29, -5, 17, 15, -25, -1, -11, 16],\n [0, 0, 0, 0, 0, -32, -28, 11, 24, 20, -27, 32],\n [0, 0, 0, 0, 0, 0, -30, -21, -31, 10, 33, 3],\n [0, 0, 0, 0, 0, 0, 0, 4, 27, -16, 16, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 28, -7, -18, -27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -14, -25, -17],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13485", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[13, -21, 26, -17, 3, -35, -19, -12, -7, 5, 26, -25],\n [0, 10, -17, 19, 9, 24, -29, 13, 5, 0, 21, -9],\n [0, 0, 4, -12, 23, 1, -23, 35, -16, -10, 20, 4],\n [0, 0, 0, 22, 28, -3, 20, 6, -5, 11, -16, 7],\n [0, 0, 0, 0, 29, 26, 35, 23, -33, -2, -21, 29],\n [0, 0, 0, 0, 0, -17, 20, -14, -30, 31, -34, -1],\n [0, 0, 0, 0, 0, 0, 29, 9, 7, 35, -20, 17],\n [0, 0, 0, 0, 0, 0, 0, 7, 34, -35, 11, -21],\n [0, 0, 0, 0, 0, 0, 0, 0, 2, -35, -35, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -33, -28, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15, 30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "900", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-18, -12, 14, -5, -12, 6, -24, 25, 3, -10, -22, -6],\n [-12, 18, 1, -4, 20, -10, 0, -21, -9, 10, -12, 14],\n [14, 1, 11, 2, -20, -1, -15, 18, -6, -13, 15, -10],\n [-5, -4, 2, 5, -21, 0, -16, -5, 12, 20, 18, -10],\n [-12, 20, -20, -21, 11, -2, 10, -7, 10, 10, -13, 19],\n [6, -10, -1, 0, -2, 21, 0, 4, 6, 12, 10, 0],\n [-24, 0, -15, -16, 10, 0, -32, 4, -22, 9, 2, 10],\n [25, -21, 18, -5, -7, 4, 4, 0, 15, -2, -8, -7],\n [3, -9, -6, 12, 10, 6, -22, 15, -15, -10, -1, 6],\n [-10, 10, -13, 20, 10, 12, 9, -2, -10, -18, 6, -18],\n [-22, -12, 15, 18, -13, 10, 2, -8, -1, 6, -25, 18],\n [-6, 14, -10, -10, 19, 0, 10, -7, 6, -18, 18, -29]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-41", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, 35, 4, -30, -4, -27, 8, 13, -10, 16, -1, -16],\n [0, 17, 18, -17, 31, 12, -25, -9, 32, 9, 25, -1],\n [0, 0, -16, 23, 33, -18, 33, 2, -17, -27, -18, 18],\n [0, 0, 0, 31, -33, -23, -31, 15, -17, 26, -9, -11],\n [0, 0, 0, 0, -9, 18, -10, -3, -8, -19, -17, 4],\n [0, 0, 0, 0, 0, -17, 21, 23, -11, -5, 35, 35],\n [0, 0, 0, 0, 0, 0, 2, 35, -5, 1, 23, -4],\n [0, 0, 0, 0, 0, 0, 0, -31, 21, 19, 4, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 9, 12, 24, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -31, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10745550", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-33, 31, -11, -12, 4, -5, -33, -26, 28, -14, -19, 5],\n [0, -32, 16, -18, 15, -31, 19, 6, -2, 5, 33, -33],\n [0, 0, 24, 29, -34, 9, -28, 22, 15, 20, 31, -12],\n [0, 0, 0, -23, -27, -13, -11, 11, 23, 16, 5, -19],\n [0, 0, 0, 0, -14, -35, -9, -21, 8, -5, 33, 24],\n [0, 0, 0, 0, 0, -22, -29, -33, 17, -11, -4, 19],\n [0, 0, 0, 0, 0, 0, 32, 6, 14, -2, 27, -32],\n [0, 0, 0, 0, 0, 0, 0, 30, 30, -8, -13, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 17, 2, -1, 9],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -15, 1, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1409", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (7, 4) rounded to the nearest integer?\n[[-16, 4, -2, -29, 11, 12, -7, 11, -34, -32, 19, -15],\n [31, 5, 14, -10, -15, -16, 16, 11, 35, -13, -19, -5],\n [5, -28, -13, -8, 35, 15, 17, 5, -9, 11, -21, -32],\n [0, -30, -14, 32, 24, -10, -25, 14, -28, 32, 9, 35],\n [9, 29, -20, 10, -33, 24, 7, -3, 35, -21, -11, -35],\n [28, -20, 20, -24, -28, 30, 5, 24, -16, 22, 16, 14],\n [-8, 30, 31, 1, 28, -7, 20, -29, 8, 23, 6, -18],\n [9, 22, -10, -23, 0, 30, -3, -8, 10, -13, -13, 8],\n [3, 17, -13, 17, -13, 13, 5, 15, -8, -21, -15, -30],\n [-28, -3, -15, 32, -27, -8, 2, -11, -15, -16, -20, -34],\n [11, 0, 1, -25, -29, 5, -29, 17, 27, 24, 5, -3],\n [-28, -35, 25, -4, -33, 33, 8, -22, 14, -12, 17, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-58", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-27, 8, 4, -21, -6, 6, -23, 24, -15, -35, 22, -20],\n [-7, -1, 21, -9, 24, 22, -29, 12, 4, -26, -14, -3],\n [27, -15, 2, 13, -4, 34, -3, -6, -9, -10, 20, 27],\n [23, -8, -32, -15, -24, -35, 17, 20, -24, 34, 18, -8],\n [20, 6, 25, -12, -10, 11, -14, 12, 4, -24, 28, -27],\n [1, -18, 4, -1, -16, 25, -24, 25, 23, 8, 1, 3],\n [19, -6, 31, 17, 6, -8, 19, 29, -21, -24, 25, -17],\n [9, 2, 31, 31, 9, -24, 14, -22, -13, -2, 7, -1],\n [17, -22, 31, 30, 19, 6, -10, -9, 2, -17, 22, -30],\n [8, -35, -6, 15, 27, -7, -20, 10, -12, 7, 0, -21],\n [10, 2, -15, -35, -11, 15, -18, -32, 9, -13, -11, -6],\n [10, -8, 2, -2, 22, 8, 0, -3, 31, 21, -27, -34]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-176", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-22, -10, 0, -9, -20, 0, -8, 2, -8, 2, 25, 13],\n [-10, -30, 29, 2, 13, -5, 18, -10, -2, -22, -14, 26],\n [0, 29, -18, -29, 26, -8, -5, -6, 12, -12, -5, 16],\n [-9, 2, -29, -2, -5, 1, 0, 10, 10, -7, 20, -8],\n [-20, 13, 26, -5, 29, -6, 0, 0, 6, -16, 3, -1],\n [0, -5, -8, 1, -6, 4, 16, -9, -4, -18, 18, 0],\n [-8, 18, -5, 0, 0, 16, 10, -12, 1, 18, -28, -1],\n [2, -10, -6, 10, 0, -9, -12, 33, 6, 8, -20, 18],\n [-8, -2, 12, 10, 6, -4, 1, 6, 34, 22, -20, -1],\n [2, -22, -12, -7, -16, -18, 18, 8, 22, 5, -7, 3],\n [25, -14, -5, 20, 3, 18, -28, -20, -20, -7, -5, 15],\n [13, 26, 16, -8, -1, 0, -1, 18, -1, 3, 15, -16]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-469", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the value at position (3, 10) rounded to the nearest integer?\n[[-24, 28, -2, 4, 10, -6, 11, 10, -14, -29, 0, -27],\n [0, -32, 2, -8, 33, -34, -25, -6, 8, -21, 4, 18],\n [0, 0, -8, -14, 24, -11, -27, -28, 7, 17, -14, 21],\n [0, 0, 0, 19, -17, 15, 6, -12, -26, 9, -18, -11],\n [0, 0, 0, 0, 28, -27, -1, -8, -23, -15, 20, -27],\n [0, 0, 0, 0, 0, -7, 29, -27, 31, -27, -12, -10],\n [0, 0, 0, 0, 0, 0, 13, -13, -20, 22, -22, 25],\n [0, 0, 0, 0, 0, 0, 0, 27, 16, -30, 2, -22],\n [0, 0, 0, 0, 0, 0, 0, 0, 11, 4, 25, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 21, 12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3224", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-15, -16, 20, -31, 0, 10, 0, -22, -14, 20, -2, 10],\n [-16, 28, -28, -10, -10, -18, 12, -11, -10, 25, -4, 4],\n [20, -28, 24, 10, -6, 14, -18, 0, -8, -7, -20, 1],\n [-31, -10, 10, 4, -2, -4, -2, -6, -34, 32, 26, 0],\n [0, -10, -6, -2, 14, 10, 0, -10, 10, 7, -2, -3],\n [10, -18, 14, -4, 10, -20, 9, 8, 7, -12, 4, -5],\n [0, 12, -18, -2, 0, 9, 26, -10, 24, -14, 16, -15],\n [-22, -11, 0, -6, -10, 8, -10, -35, 6, 9, 0, 0],\n [-14, -10, -8, -34, 10, 7, 24, 6, -27, -4, -1, -4],\n [20, 25, -7, 32, 7, -12, -14, 9, -4, -3, 12, 30],\n [-2, -4, -20, 26, -2, 4, 16, 0, -1, 12, 19, -13],\n [10, 4, 1, 0, -3, -5, -15, 0, -4, 30, -13, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-97", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-30, -29, 31, 25, 6, -31, 15, -1, 21, 22, 23, 13],\n [2, -15, 0, -16, 9, 10, -22, -17, 34, 15, -33, -33],\n [15, 18, -2, 22, -33, -15, -33, 1, -19, -14, -26, 8],\n [15, -28, 6, -22, -19, -19, 8, -23, -30, -10, -6, 14],\n [-13, 33, -25, -19, -16, -6, -5, 35, 32, -24, -20, 24],\n [-27, 14, -27, 16, 10, 29, -1, -12, -9, 1, -9, 28],\n [-2, -15, 28, -1, -19, -5, 8, -24, -12, -24, -14, 32],\n [20, -21, -6, -3, 12, 3, 5, 10, -20, 21, 15, -29],\n [11, 1, 11, -8, 8, 6, 11, 8, -32, -19, -26, -6],\n [15, 34, -16, -13, 23, 32, -25, 30, -16, -3, -34, 3],\n [-23, -23, -31, -2, 2, 16, 24, -33, -13, 5, 13, 19],\n [22, 4, -18, 20, -1, -26, -29, 4, 20, -35, -19, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6191", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-13, 8, 31, -15, 19, 14, -18, -9, -1, -3, -11, 19],\n [24, -16, -15, 2, 20, 31, 18, -2, -26, 14, -19, 24],\n [33, 33, -2, 11, -3, -21, 22, -34, 20, 0, -30, -9],\n [-7, 27, 5, 6, 34, 27, 26, -2, -11, 2, 10, -23],\n [-23, 3, 22, 31, 18, 17, 15, -7, 35, 26, -31, 15],\n [25, 2, -26, 29, -28, 22, -6, -18, 34, -24, 30, 34],\n [20, 8, -32, 18, -21, 1, -3, -6, 23, -18, 4, -22],\n [7, 1, -8, -19, -18, -10, 4, 31, 26, 9, -21, 33],\n [13, 4, 22, 10, 9, 7, -10, -10, 8, 27, -32, -30],\n [-17, 12, -31, 19, -7, -17, -29, -23, 22, 6, -17, -31],\n [-31, -23, 4, 22, 16, 2, 27, 2, 25, -24, 6, 14],\n [-35, 28, -32, -35, 6, -12, -15, 1, -18, 8, -33, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3085", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-34, -2, 11, -2, -1, 10, -2, -2, 1, 5, 14, -11],\n [-2, 26, -28, -26, 18, 8, 1, -23, 2, -14, -1, 15],\n [11, -28, -27, -18, -24, 2, -4, -18, 28, 4, 10, -5],\n [-2, -26, -18, 24, -14, 10, -32, 6, 14, -6, 12, -18],\n [-1, 18, -24, -14, 3, 2, -6, 10, 6, -10, 13, -1],\n [10, 8, 2, 10, 2, 17, -4, -8, 21, 14, -23, -22],\n [-2, 1, -4, -32, -6, -4, -24, 2, -14, -8, -21, 2],\n [-2, -23, -18, 6, 10, -8, 2, 11, 12, -14, 18, 0],\n [1, 2, 28, 14, 6, 21, -14, 12, 9, 5, 28, 15],\n [5, -14, 4, -6, -10, 14, -8, -14, 5, -13, 0, 21],\n [14, -1, 10, 12, 13, -23, -21, 18, 28, 0, 30, -8],\n [-11, 15, -5, -18, -1, -22, 2, 0, 15, 21, -8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-20, 28, -9, 3, -3, -32, -25, -14, 3, -34, -25, 20],\n [33, 15, 31, 20, 10, 35, -8, 2, -12, -12, 3, -33],\n [-10, -21, 32, 33, -18, 32, -33, -19, 18, -32, 20, -7],\n [14, 27, -24, 10, -20, -6, 9, 7, -15, -11, 34, 9],\n [21, -7, -29, -7, 23, -27, 14, -15, -15, 10, -19, -17],\n [-7, 17, 12, -29, -2, -7, 5, -27, 13, 14, -31, 1],\n [-3, -21, -14, 29, 16, 13, -2, 1, 32, -19, 16, 31],\n [24, 21, 14, 19, -35, 17, 33, 10, 21, 18, -25, -12],\n [-27, -26, -13, 26, 31, -34, -10, 17, 33, 19, 4, 18],\n [8, 35, -21, -18, 35, 31, -18, -7, 3, 18, 21, -23],\n [33, -13, -30, -11, -22, -21, 28, -15, -21, -18, 17, 23],\n [-7, 18, 26, 17, 21, 0, -30, 21, 14, 32, -35, -20]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2069", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-31, -20, -30, -7, 31, 6, -16, 17, -31, 5, 18, -33],\n [-11, -19, -1, -11, 30, -8, 16, 32, 32, -17, -24, -9],\n [-20, -2, -17, -26, -18, 20, -28, 17, 12, 0, 21, 11],\n [32, -10, -22, -28, 11, -3, -27, -12, -4, 2, 12, -30],\n [-18, 27, 26, 2, -11, -25, -7, -9, -31, 27, -27, -13],\n [-23, 4, 8, -27, 26, 23, -34, 29, -4, -15, 19, -14],\n [30, 22, 7, -26, 29, 9, 7, 8, 19, -26, -28, -32],\n [-2, 20, -10, -7, 23, 18, -17, -28, -24, -23, 30, -17],\n [-22, -12, -2, -22, -35, -19, 31, -12, -19, 2, -25, -10],\n [-23, 7, 21, -20, 17, -17, -17, 1, 35, -23, -31, 18],\n [-1, 28, -29, -14, -31, -28, -7, 5, 6, -12, -12, -34],\n [4, -16, 33, 15, -16, 31, -17, 20, -13, -25, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-295", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[25, 23, 10, -5, 26, -35, -2, 17, -10, 33, 9, 15],\n [0, 12, -29, -26, -24, 31, -26, 29, -15, -35, -20, -19],\n [0, 0, -11, 21, -6, -30, -19, 8, 33, 20, -1, 6],\n [0, 0, 0, -13, -13, 9, -20, -26, -18, 12, -12, -14],\n [0, 0, 0, 0, -32, -18, -18, -17, -27, -2, -26, 1],\n [0, 0, 0, 0, 0, -17, -26, -35, 33, 0, 29, 21],\n [0, 0, 0, 0, 0, 0, -6, 5, -18, 8, -33, -22],\n [0, 0, 0, 0, 0, 0, 0, -35, 16, 15, -4, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 28, 24, 12, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 35, -24, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29, 31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-220", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -21, -4, -19, 11, 22, 35, -11, -23, -24, 9, -1],\n [-29, 34, 9, 26, 13, 34, -31, 11, -15, -9, -31, -13],\n [10, 5, 29, 19, 12, 34, 3, -19, -22, -21, 6, 32],\n [6, 34, -17, 14, 2, -13, -26, 10, 25, -22, -27, -14],\n [32, -19, 14, -2, 4, 33, -22, -27, -11, 29, 34, -32],\n [-18, -20, 33, -32, 26, -13, 15, 32, -15, -9, -24, -16],\n [9, 9, 1, 4, -17, -18, -30, -21, 14, 28, -3, -9],\n [23, -19, 31, 4, -20, -15, 7, 3, 18, 34, 10, 10],\n [-26, 18, -2, -4, 21, -8, -31, 31, 35, -8, -11, -2],\n [-9, 25, 21, -28, 7, -22, -34, 4, -12, 31, -35, -8],\n [-10, -9, -26, 23, 23, 4, -4, -25, -35, 30, -21, -23],\n [-10, -2, -35, -31, 5, 5, 17, -17, 21, -34, -26, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[25, 1, 7, 25, -30, 26, 28, 0, 24, 25, -25, -21],\n [-14, -33, 17, 2, 11, 15, 15, -27, 17, -21, -14, 0],\n [19, 12, -29, 33, -34, -14, 34, 13, 22, 31, 21, -32],\n [10, 26, -23, -17, -2, 9, 13, 8, -28, -26, -15, -17],\n [27, -27, 23, 8, 2, 25, -35, -7, -5, -16, 34, 24],\n [-19, 18, -12, 34, 22, 19, -17, 5, 10, 15, -33, 27],\n [2, -19, 32, 27, -27, -6, 32, -12, 20, 19, -16, 14],\n [-4, -29, 0, -31, 30, -27, -10, -6, -31, 7, -16, 34],\n [-28, 24, -16, 4, -20, -15, 22, -15, 8, -31, -25, 34],\n [-27, -7, 3, -30, -30, -9, -21, 31, -27, -17, 6, -2],\n [-7, 23, -13, 2, -21, 14, 18, -23, 2, 33, 9, -8],\n [27, -25, -11, 1, -18, 15, 19, -24, -34, -35, -19, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[1, 0, -7, 8, 15, 10, 24, 12, -14, -11, -19, -12],\n [0, -21, 9, -34, -26, -23, 27, -23, -9, 32, -35, 7],\n [0, 0, -18, -20, 23, 7, -2, 8, -35, 25, 15, 23],\n [0, 0, 0, -17, 19, -17, -21, -5, 24, 6, 15, -5],\n [0, 0, 0, 0, 35, -21, -4, -18, 12, 25, 15, 11],\n [0, 0, 0, 0, 0, -10, -7, -16, 1, -24, -18, 34],\n [0, 0, 0, 0, 0, 0, 30, -28, 13, 13, -30, 23],\n [0, 0, 0, 0, 0, 0, 0, -13, 11, -5, 31, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, -15, 2, -31, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 28, -24, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27983", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[7, 31, 28, -26, -33, -22, -3, -3, 16, -20, 35, 8],\n [0, 24, -10, 3, 16, 23, 3, -8, 5, 4, -32, -21],\n [0, 0, 24, 33, 31, 35, 30, -25, -2, 9, -15, -33],\n [0, 0, 0, -24, 22, -3, -32, 34, -4, -35, 7, 22],\n [0, 0, 0, 0, -6, -35, 15, 26, 18, 14, 22, -21],\n [0, 0, 0, 0, 0, -1, 11, -28, 31, 31, 31, -17],\n [0, 0, 0, 0, 0, 0, -29, -24, 28, -33, -23, -27],\n [0, 0, 0, 0, 0, 0, 0, -20, 22, -22, -30, 29],\n [0, 0, 0, 0, 0, 0, 0, 0, -15, 32, 30, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -31, 3, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-473571", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[27, 9, 33, -9, 3, 10, 30, 25, 7, -31, -25, 30],\n [-35, -3, -18, -2, -13, 22, -25, 5, -2, 32, 19, 24],\n [-21, -17, -8, -8, 35, -21, -26, -8, -24, 28, 9, -20],\n [-6, -1, 31, -18, -25, 0, 6, 31, -28, 30, 29, -21],\n [-33, 20, 28, 32, -17, -21, -6, -1, 11, 14, 21, -12],\n [7, 28, -11, 23, -18, 32, -6, 24, -8, -15, 16, 25],\n [-10, 15, 24, 5, -18, 13, -6, -27, 11, 27, 28, 22],\n [1, 19, -2, 29, -3, 1, -8, -22, -3, -16, -24, 4],\n [-31, 3, 28, -27, -6, -30, 24, -33, -23, 26, -27, -30],\n [-4, -5, 15, -1, -15, 13, 20, 30, -6, -20, 19, 25],\n [7, -17, 31, -24, 10, -17, -9, -13, 30, -4, 29, 12],\n [-7, 33, 35, -35, -34, 14, 35, -19, -24, 6, 18, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6844", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-17, 21, 9, -26, 16, -5, 35, 34, 13, 3, 20, -28],\n [16, 24, 6, -21, -33, -9, -3, 5, -13, 15, 0, -1],\n [3, 10, -12, -20, 30, -3, -16, 21, 6, 34, 31, -14],\n [20, -10, 33, -10, -21, -29, -6, -16, -29, 1, 30, 22],\n [-31, -27, 5, 15, -12, 23, -32, 2, -30, -14, 29, 21],\n [23, -12, -2, -9, -32, 17, -10, 0, -31, 20, 13, 2],\n [-12, -6, 19, 32, -2, 7, 27, 10, -35, 10, 35, 7],\n [35, 22, -2, 19, 13, 11, 21, 32, 22, -19, -17, 4],\n [-8, 0, 11, -13, -16, -34, -21, -24, 11, 0, -8, -26],\n [20, -27, -20, -20, -7, 33, -13, 17, 32, -8, 33, 27],\n [12, -19, -33, 30, 18, -15, 18, 32, -6, 2, -32, -33],\n [5, 32, -19, -33, -19, 11, -32, 34, -7, 0, 25, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1454", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-4, 11, -31, 29, -14, 24, -12, 22, 9, 25, 17, 31],\n [0, -25, -1, 24, 28, 25, -27, -4, 3, -25, -23, 27],\n [0, 0, -27, 8, -30, -12, -1, 1, 10, 6, -6, -13],\n [0, 0, 0, -12, -29, 33, 14, 28, -31, 3, 22, 16],\n [0, 0, 0, 0, -35, 5, -6, -26, 9, -33, 21, -21],\n [0, 0, 0, 0, 0, -33, -8, -7, -5, -5, 10, -33],\n [0, 0, 0, 0, 0, 0, 5, 8, -18, 27, 29, 26],\n [0, 0, 0, 0, 0, 0, 0, -13, 3, -35, 13, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, -24, -6, -25, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 31, 11],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-172141", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-16, 14, -19, -23, -35, -28, -18, -35, -16, 3, -31, -10],\n [25, 18, 25, -30, 21, 12, -29, -10, 5, 8, -18, -12],\n [-35, -31, -3, 20, 13, -3, -13, -30, 31, 22, -17, -6],\n [4, 10, 6, -19, 2, -11, 10, 8, 29, -20, -33, 32],\n [-4, -33, 9, 14, -18, 2, 27, 33, 33, 20, -27, -14],\n [26, -16, 28, -31, -33, -16, -31, 15, 29, 23, 7, 35],\n [-15, -1, 6, 14, 18, -16, 3, 10, -17, -33, 12, 20],\n [-33, 22, 1, 31, 17, 2, -19, 25, -18, -11, -3, -5],\n [-28, 18, 12, -16, 8, 7, 23, -10, -7, -12, 24, -25],\n [35, -30, 13, -12, 19, -26, -7, 33, 15, -25, 32, -20],\n [3, 24, -3, 16, -22, -21, 21, 7, -14, 15, -34, -27],\n [-8, 10, 7, 4, -2, 29, 7, -9, 17, -19, 31, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[24, -10, -4, 17, 12, 10, 0, 26, 0, -10, 11, 16],\n [-10, 17, -31, 16, 10, 6, 30, -26, 2, 3, 26, -22],\n [-4, -31, 7, -19, 3, 8, -14, -4, 4, 0, 20, -3],\n [17, 16, -19, -29, 6, 23, 2, -11, -3, 28, 17, -12],\n [12, 10, 3, 6, -25, 24, -4, 27, 18, -10, 2, 3],\n [10, 6, 8, 23, 24, 8, -29, 12, -24, 5, 16, 10],\n [0, 30, -14, 2, -4, -29, -8, -12, -1, -20, -6, -1],\n [26, -26, -4, -11, 27, 12, -12, -32, 5, -2, 1, -8],\n [0, 2, 4, -3, 18, -24, -1, 5, -24, 2, -10, -18],\n [-10, 3, 0, 28, -10, 5, -20, -2, 2, 23, 6, 21],\n [11, 26, 20, 17, 2, 16, -6, 1, -10, 6, -1, -4],\n [16, -22, -3, -12, 3, 10, -1, -8, -18, 21, -4, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1618", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-29, -32, 10, -19, -7, -8, -8, -32, -32, -25, 29, 13],\n [0, 22, -22, 27, -33, -5, 14, 19, 27, 23, -9, -11],\n [-30, -26, -10, -30, -15, -14, 11, 4, 11, 2, -8, 16],\n [-24, -12, -12, 33, -27, -1, -17, 21, -35, 13, 22, 4],\n [26, -15, -29, -35, -15, -29, -20, 18, 27, 16, -22, -34],\n [-16, 32, 6, -8, -15, -24, 19, -33, -17, -35, -35, -32],\n [-32, -32, -20, 5, -2, -35, 28, -16, -13, -22, 3, 11],\n [4, 10, 0, 5, 23, -20, -1, -7, 24, -5, -19, -10],\n [-19, 24, 31, -18, 17, 24, 10, 18, 27, -10, -1, 20],\n [-1, -31, 15, -4, 2, -11, -11, 4, 34, 35, -6, 15],\n [-12, -28, -28, 24, -5, 9, 27, 32, -34, -14, -1, 3],\n [21, 33, 29, -5, 11, -19, 31, 33, 23, -7, 7, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5856", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-26, 22, -16, 18, -17, 0, 17, 22, 1, -6, -7, 24],\n [0, 18, -3, 32, 14, -11, 3, -27, -34, 4, -11, 2],\n [-11, 13, 27, 21, 30, -33, -9, -6, -18, 22, -9, 25],\n [27, 22, -19, -32, -15, 22, -25, -18, -19, -22, 26, -22],\n [-2, 24, 30, -20, 0, -8, -24, -7, 16, -32, 16, -12],\n [-30, -1, -23, 5, -6, -14, -8, -30, 4, 28, 6, -22],\n [23, 18, -6, -35, -13, 1, 9, -12, -35, -32, -19, 7],\n [-16, -3, 21, 21, -11, 16, 22, 21, 30, 34, -1, 30],\n [-28, 10, 26, 28, -6, -7, 10, 15, 1, -17, -32, 18],\n [16, 2, -35, -2, -5, -1, -25, -18, 34, 8, 7, -1],\n [-22, 13, 31, -26, 24, -4, 21, -7, 31, -12, -9, -21],\n [-8, 34, -35, -35, -16, 35, -8, -34, 13, 33, 26, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-386", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-28, -14, 15, -12, -14, 12, 10, 9, 4, -2, 4, -17],\n [-14, 17, -2, -6, -24, -14, -8, 32, 14, 5, 8, 12],\n [15, -2, -29, 20, 33, -9, -5, -2, 15, 15, 12, 5],\n [-12, -6, 20, 35, -2, 30, -10, 14, 0, -2, 34, 18],\n [-14, -24, 33, -2, 30, -30, 22, -9, 18, 8, -15, -4],\n [12, -14, -9, 30, -30, -31, -18, 16, 18, -2, 25, 9],\n [10, -8, -5, -10, 22, -18, -8, -16, 17, -8, -14, 14],\n [9, 32, -2, 14, -9, 16, -16, 25, -20, 0, -4, 0],\n [4, 14, 15, 0, 18, 18, 17, -20, -18, 10, 22, -15],\n [-2, 5, 15, -2, 8, -2, -8, 0, 10, 21, 30, 6],\n [4, 8, 12, 34, -15, 25, -14, -4, 22, 30, 16, 31],\n [-17, 12, 5, 18, -4, 9, 14, 0, -15, 6, 31, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-98", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-18, 16, -7, -5, -35, -30, -19, -27, 29, -21, -19, 20],\n [14, 29, -9, 15, 34, -16, 33, 25, -5, -18, -18, 34],\n [-1, 2, -33, -7, 3, 16, 3, 22, 20, 22, -32, 21],\n [24, 29, -21, -16, -26, -16, 4, 15, -23, -26, -8, -7],\n [29, 0, -11, 23, 15, -33, 27, -11, -8, 9, 0, 0],\n [-19, 32, -9, -16, 27, -20, -19, -2, -18, 31, 13, -24],\n [1, -19, 8, 22, -33, -35, 11, 34, 8, 21, -23, -32],\n [-26, 30, -27, 26, -29, -20, 26, -34, 2, -10, -25, -3],\n [15, 34, 17, -17, -12, -12, -1, -29, -35, 16, 34, -24],\n [-8, 2, -10, -18, 21, 21, 14, -26, 11, -20, 24, 7],\n [35, 18, 23, 8, 12, 28, 17, -1, 33, -7, 16, 1],\n [-2, -19, 13, -23, 19, 28, -31, 12, -15, -12, 2, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-30, -2, 10, -13, 13, -18, 2, -4, 27, -14, -1, 26],\n [0, -16, -8, 24, 11, 3, 25, 35, 22, -33, -12, -29],\n [0, 0, -15, -19, 20, 34, -32, 27, -10, -35, 32, -1],\n [0, 0, 0, 25, -28, -4, 10, -26, -17, 17, -18, 26],\n [0, 0, 0, 0, 26, 25, 18, -27, -15, 5, -20, -26],\n [0, 0, 0, 0, 0, -10, -1, 22, 26, -34, -18, -6],\n [0, 0, 0, 0, 0, 0, -5, 12, -35, -33, -33, 17],\n [0, 0, 0, 0, 0, 0, 0, 33, -10, 6, 7, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, -16, 8, -20, 33],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -33, 28, -13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11849", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (1, 10) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-20, 14, 24, -18, -17, 28, -8, 33, 22, -27, 11, 20],\n [0, -24, 10, -6, 23, 8, -27, 4, -14, 10, -9, -26],\n [0, 0, 11, -24, -8, 23, 26, 0, -21, -27, -12, -2],\n [0, 0, 0, 12, -8, -15, 13, -13, -7, -25, 27, 2],\n [0, 0, 0, 0, 10, -30, -10, 0, 27, 32, -34, 19],\n [0, 0, 0, 0, 0, 27, -11, -28, -4, 9, -10, -3],\n [0, 0, 0, 0, 0, 0, -3, -17, -16, 15, 15, -10],\n [0, 0, 0, 0, 0, 0, 0, 16, -19, -34, 23, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 32, -21, -19, -12],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, -6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7491", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[35, 0, 6, -10, 22, -4, -3, 26, 2, 12, 6, 13],\n [0, -12, 16, 4, 0, -18, 7, -27, 2, -15, 35, -12],\n [6, 16, -32, -4, 22, -8, -22, 30, -12, 5, -11, -5],\n [-10, 4, -4, -32, 4, 16, 1, 2, -4, -21, 8, -20],\n [22, 0, 22, 4, 21, 16, -11, 6, -4, -4, -10, -16],\n [-4, -18, -8, 16, 16, 16, 6, 12, -14, 21, -16, -4],\n [-3, 7, -22, 1, -11, 6, -22, 16, 22, -16, -24, -14],\n [26, -27, 30, 2, 6, 12, 16, 16, 16, -14, 0, 12],\n [2, 2, -12, -4, -4, -14, 22, 16, 1, 10, -33, -12],\n [12, -15, 5, -21, -4, 21, -16, -14, 10, 5, 2, -23],\n [6, 35, -11, 8, -10, -16, -24, 0, -33, 2, 19, 19],\n [13, -12, -5, -20, -16, -4, -14, 12, -12, -23, 19, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1021", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[31, -2, -8, -22, 31, -20, -25, -29, -34, 8, -1, -27],\n [0, 12, -23, -33, 11, -18, -35, 19, -35, -2, 7, 10],\n [0, 0, -5, 4, 17, 28, -28, -19, -12, -4, 35, -13],\n [0, 0, 0, -32, -21, -9, 4, 12, -11, 6, 25, -35],\n [0, 0, 0, 0, -9, -11, -7, 10, 7, 34, 20, -35],\n [0, 0, 0, 0, 0, 17, 26, 8, 33, 26, 3, 1],\n [0, 0, 0, 0, 0, 0, -25, 31, 27, -15, 7, -7],\n [0, 0, 0, 0, 0, 0, 0, -26, -13, 4, -14, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 31, -17, -30, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 27, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33952", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[27, 24, 28, 20, -5, 22, 34, 32, 18, -12, 10, -14],\n [0, 29, 14, -26, 30, -13, 13, -30, -15, -29, -10, 1],\n [0, 0, -13, -30, 35, 24, 4, 20, 32, -32, 1, 18],\n [0, 0, 0, 18, 18, -25, -23, -7, -21, 10, -9, 3],\n [0, 0, 0, 0, -31, 30, -13, 2, -10, -28, 4, -11],\n [0, 0, 0, 0, 0, 22, 5, 4, 26, 9, -22, -18],\n [0, 0, 0, 0, 0, 0, 12, 25, 1, 20, -12, -7],\n [0, 0, 0, 0, 0, 0, 0, 16, -22, 28, -10, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, 22, 22, 13, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27, -27, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16657", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[22, 28, 34, -21, 29, -8, 6, -18, -24, -1, -24, 29],\n [19, 27, -11, -9, -23, -15, -29, -31, -27, 35, -34, -19],\n [5, -33, -10, 2, -18, 33, 2, -16, -8, 14, -11, -13],\n [-3, 15, -12, 4, -32, 21, 10, 12, -30, 18, -21, -21],\n [-9, 3, 6, 20, -19, -13, -31, 9, 22, 19, 14, -19],\n [-7, -3, -11, -20, 31, 25, -6, 9, -8, 1, 18, 29],\n [-21, 31, 11, -33, 27, 18, -5, 13, -27, -9, 12, -5],\n [28, 29, 10, 6, 34, 24, -3, -9, 33, 32, 14, 0],\n [30, 15, -17, 13, 23, 29, 27, -23, 30, 10, -32, -35],\n [9, -17, 21, 35, 21, 27, -27, 19, 32, 1, -22, -14],\n [12, -26, -8, -26, 23, 25, 4, -29, 33, -15, -29, 24],\n [-35, 28, -3, -11, 8, -12, -28, -6, -27, -35, -16, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (12, 7) of the inverse of matrix 1/839 * A where A =\n[[-6, 24, 20, 34, -33, 7, 4, 20, 34, -9, -18, 20],\n [34, -3, 13, 32, -7, 25, 35, 4, 22, -16, 18, -3],\n [-26, -25, -1, 24, -1, -9, -22, 31, 21, -15, 20, 5],\n [-9, -34, 6, 17, -16, 13, 8, -12, -22, 15, -9, 8],\n [-14, 9, 11, -24, -32, -15, 8, 1, 6, 2, -20, -26],\n [-2, 6, 1, -1, -31, 2, -25, 4, 22, 17, 34, -5],\n [1, -25, 13, 5, -20, -29, -3, 9, 3, -1, 10, 6],\n [31, -4, -5, 5, 32, 6, -16, -6, 9, 27, -3, -27],\n [-27, -21, 28, -27, 14, -14, 16, -35, 4, 35, -1, 3],\n [-27, 14, -1, 0, 34, 5, -14, -14, -28, -10, 17, 22],\n [-4, -22, 10, 27, -27, 1, 35, 15, -17, -19, 9, 17],\n [5, 12, 21, 14, -34, 17, 34, -8, 23, -30, 20, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-28, -15, 26, 7, -10, 4, 4, 1, 8, 12, 24, 3],\n [-15, 11, 0, 25, -6, 3, 26, -23, -14, 2, -32, 10],\n [26, 0, -30, 22, -7, -12, 17, -2, -19, -8, -8, -11],\n [7, 25, 22, 35, -30, -4, -14, -12, 2, 1, -10, 29],\n [-10, -6, -7, -30, 27, 6, -13, -4, -12, 14, 13, 10],\n [4, 3, -12, -4, 6, 34, 8, 18, -16, 12, 4, -24],\n [4, 26, 17, -14, -13, 8, 35, -2, 4, 22, 4, -11],\n [1, -23, -2, -12, -4, 18, -2, 33, -12, -9, -7, -24],\n [8, -14, -19, 2, -12, -16, 4, -12, -24, 25, -20, 19],\n [12, 2, -8, 1, 14, 12, 22, -9, 25, -34, 8, 10],\n [24, -32, -8, -10, 13, 4, 4, -7, -20, 8, 24, -6],\n [3, 10, -11, 29, 10, -24, -11, -24, 19, 10, -6, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-18, -34, -4, 22, -4, 29, 24, 9, -20, -4, 29, 21],\n [-1, -19, -14, 29, 12, 3, 31, -32, -16, -8, -35, 35],\n [26, 2, 15, 14, 35, -16, -20, -15, 17, 22, 29, 26],\n [-19, 0, 13, 30, -31, 23, 5, 22, 23, -2, -15, 32],\n [23, -10, 24, 25, -10, 5, 23, -9, 12, 15, 21, 1],\n [-19, 4, 14, -26, -4, -21, -7, -29, 27, -10, 30, 26],\n [13, -8, 28, 19, -2, 20, 35, -14, -12, -32, -20, -10],\n [26, -4, -24, 23, -22, -17, 12, -18, -2, -4, 21, 26],\n [20, -11, 10, -3, 32, 10, 27, 18, -25, 13, -15, -15],\n [15, 22, -22, -23, -2, -19, 8, -19, 33, -15, -18, 22],\n [32, 5, -25, 25, -3, -25, 29, -13, -34, -8, 27, -14],\n [16, -31, 34, 3, -1, 16, -22, 23, -22, -9, -18, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-209", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (10, 10) of the inverse of matrix 1/839 * A where A =\n[[-33, 15, -22, 24, -29, -12, 29, -32, -8, 14, 24, -3],\n [-14, 32, 28, 29, -7, -29, -23, 24, -25, -21, 7, 10],\n [33, -18, 29, -34, -33, 3, 28, -2, -7, -16, 35, -20],\n [-2, -13, 7, 0, -25, -34, 34, 11, -23, 6, 23, 10],\n [-34, -21, 30, -14, -23, 1, -11, 5, 28, -21, -12, 22],\n [-11, -35, 2, -30, -26, 19, 10, -34, -10, 3, 14, 7],\n [-34, -10, 6, -17, -30, 7, 5, 7, 0, 0, -22, 19],\n [33, 34, 28, -4, 14, 5, 22, 23, -28, 1, 4, 23],\n [19, -5, -9, -24, -15, 14, -28, 2, -17, -1, -4, 6],\n [25, 28, 32, 29, 3, -8, 9, -21, 9, 16, 11, 0],\n [-17, -9, -24, 19, -25, 3, -35, 15, -26, 9, 14, 0],\n [32, -6, 2, -10, -15, -9, 35, 5, -19, 22, -3, -25]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[-14, -13, 1, 14, 23, 12, -35, 7, -27, 11, -6, -4],\n [0, 20, -4, -22, -29, 25, -26, -10, 5, 19, -12, -27],\n [0, 0, -28, 14, 3, -9, 8, 6, -33, 5, 17, -10],\n [0, 0, 0, 17, -11, 6, 15, 12, 11, 12, 31, 13],\n [0, 0, 0, 0, 16, 29, -28, 28, -23, 14, -8, -28],\n [0, 0, 0, 0, 0, -3, -20, 4, -31, -5, 28, 10],\n [0, 0, 0, 0, 0, 0, -32, -12, -20, 6, 31, -12],\n [0, 0, 0, 0, 0, 0, 0, 24, -7, 14, 24, -33],\n [0, 0, 0, 0, 0, 0, 0, 0, 24, 29, -34, -4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -31, -17, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29, -19],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-58660", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (10, 9) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-27, 0, 27, 7, 0, -8, 25, -30, 7, -26, 25, 15],\n [-17, 30, 21, 7, 22, 8, -15, -5, 14, -21, -22, -16],\n [10, 13, 7, 29, 14, -14, 30, 16, -27, 22, -14, -18],\n [4, 18, -19, -31, -34, -22, -22, -34, 18, -11, -26, 33],\n [35, -1, 30, 19, -23, -9, 33, 33, -20, 15, -30, -11],\n [17, 23, 31, 4, 0, 30, -30, 22, 20, 2, 19, 14],\n [-35, -16, 12, 21, 0, 6, -2, 16, 32, 10, 24, -22],\n [10, -11, 13, 10, 34, 25, -21, 33, 27, 21, -34, 9],\n [17, 11, -15, -31, -2, 4, 23, 5, -27, 24, -1, -25],\n [-3, -21, 33, 28, 12, 13, 4, -25, 25, -17, -5, -6],\n [-17, 22, -15, 8, -31, 18, -5, 12, -10, 35, 1, -13],\n [16, 16, -8, 30, 0, 18, -27, -11, 0, -22, -26, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-33, -33, -26, 16, -11, -13, -25, -14, 17, -9, 31, 11],\n [0, -6, 10, -6, 23, -35, 0, -24, -16, -34, 25, -4],\n [0, 0, 20, -12, 6, -33, 32, 32, 35, -25, -15, 3],\n [0, 0, 0, -18, 32, 34, -20, -4, 17, 13, 15, -24],\n [0, 0, 0, 0, -8, -27, -14, 21, 10, -33, -18, 33],\n [0, 0, 0, 0, 0, 4, 15, 30, 13, 12, -15, 20],\n [0, 0, 0, 0, 0, 0, 25, -11, -14, 3, 29, -13],\n [0, 0, 0, 0, 0, 0, 0, 17, 14, 3, 6, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 18, 7, 14, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -9, 10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-193975", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[34, -15, -5, -29, -8, 32, 29, -27, -29, 19, 34, 32],\n [0, -6, 10, -4, -13, -23, 6, -35, -22, -20, 27, 13],\n [0, 0, 3, -24, -9, -7, 11, 25, 22, 33, -11, 33],\n [0, 0, 0, -5, 22, -27, -6, 25, 12, 1, 29, 35],\n [0, 0, 0, 0, 11, -25, 20, 12, 34, -22, 28, -7],\n [0, 0, 0, 0, 0, 16, 21, -25, -5, -16, -27, 35],\n [0, 0, 0, 0, 0, 0, 3, -9, 24, 7, 8, -30],\n [0, 0, 0, 0, 0, 0, 0, 28, 14, 16, -5, 18],\n [0, 0, 0, 0, 0, 0, 0, 0, 12, 30, -17, -10],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 15, -35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29, -24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1595175", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-10, -14, 15, 4, -11, -4, -2, -4, -10, 0, 12, 12],\n [-14, -32, 11, 24, -2, -28, 9, 0, 5, -8, 20, 2],\n [15, 11, -11, -27, 26, 12, 13, -5, 11, -23, -8, 22],\n [4, 24, -27, 0, 12, 28, -20, -22, -2, 10, -12, -2],\n [-11, -2, 26, 12, 8, 0, 28, 1, 33, -16, -31, 0],\n [-4, -28, 12, 28, 0, 21, -2, -17, 3, -2, -24, -19],\n [-2, 9, 13, -20, 28, -2, 14, 2, -5, -16, 14, 1],\n [-4, 0, -5, -22, 1, -17, 2, 4, 18, -2, -4, 23],\n [-10, 5, 11, -2, 33, 3, -5, 18, 24, 7, 18, 2],\n [0, -8, -23, 10, -16, -2, -16, -2, 7, -5, -19, -2],\n [12, 20, -8, -12, -31, -24, 14, -4, 18, -19, 14, 18],\n [12, 2, 22, -2, 0, -19, 1, 23, 2, -2, 18, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-36", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-32, -24, -25, -32, 16, 32, 21, 12, -19, -1, 2, 31],\n [-24, 23, 2, -25, 10, 30, 11, -2, 23, 33, -17, -16],\n [-34, 24, -5, 14, 2, -19, -11, 29, -20, -33, 11, 16],\n [-14, -8, -5, -29, -2, -6, -11, 31, 30, 31, 18, 21],\n [33, -19, -9, 21, 31, -8, -16, -5, 11, -1, -8, 34],\n [19, 11, 17, -8, 0, 13, 12, 17, -12, 7, -11, 16],\n [-2, -31, 9, -14, -35, -20, 1, 3, -17, -11, 12, 12],\n [-7, -30, -20, -5, -25, 13, 30, 17, -34, 18, -24, -30],\n [30, 32, -18, -16, 27, -27, 5, -7, 20, -3, -30, 5],\n [16, -24, -4, 27, 7, -19, -18, 4, -11, 33, 35, 22],\n [7, 2, -30, 18, -2, -6, -7, -11, -7, 19, -2, 13],\n [-9, -34, -10, -25, 20, 10, 31, -4, 7, -16, 6, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[15, -13, -14, -15, 1, -33, -14, 6, -16, 22, 30, -32],\n [0, -8, 11, 21, 27, -30, 24, -5, 32, -13, -33, -32],\n [0, 0, 26, 5, 14, -5, -23, -30, -16, 6, -20, -33],\n [0, 0, 0, -10, -7, 2, -29, -23, 3, -35, -4, -19],\n [0, 0, 0, 0, 32, -32, 2, -33, 21, -15, -21, -9],\n [0, 0, 0, 0, 0, 2, -32, -3, -17, 18, 1, 32],\n [0, 0, 0, 0, 0, 0, 35, 15, -27, -7, 19, 33],\n [0, 0, 0, 0, 0, 0, 0, -33, -26, 26, 25, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 23, 8, -28, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -33, -33, 16],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 21],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4674", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-33, -8, -32, 2, 13, 12, 0, 16, 10, 18, -8, 24],\n [-8, -25, 9, 2, 15, 2, -14, 16, -26, 8, -26, 18],\n [-32, 9, -26, 0, -28, -7, 2, -20, -15, 2, -19, -27],\n [2, 2, 0, -20, 18, 22, -24, 11, -24, -9, -2, 2],\n [13, 15, -28, 18, -18, 14, 8, 10, 19, -6, 8, 24],\n [12, 2, -7, 22, 14, -33, -12, -9, -24, -20, -6, 5],\n [0, -14, 2, -24, 8, -12, 28, 8, -20, -4, 7, 5],\n [16, 16, -20, 11, 10, -9, 8, -23, 30, 4, 27, 6],\n [10, -26, -15, -24, 19, -24, -20, 30, 7, 30, 18, -2],\n [18, 8, 2, -9, -6, -20, -4, 4, 30, 9, -10, 24],\n [-8, -26, -19, -2, 8, -6, 7, 27, 18, -10, -10, 0],\n [24, 18, -27, 2, 24, 5, 5, 6, -2, 24, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1088", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-11, 6, 12, 17, -12, 11, 21, -15, -7, 2, -35, -32],\n [0, 12, 22, -27, 16, -14, 3, 29, -2, -10, -31, -26],\n [0, 0, -26, -30, 20, -34, -22, -18, -9, -31, 18, 17],\n [0, 0, 0, -17, 8, -3, 27, -6, -7, -28, 8, -1],\n [0, 0, 0, 0, 19, -4, -26, 18, -28, -13, 22, 34],\n [0, 0, 0, 0, 0, 34, -31, 17, -35, 13, 26, 12],\n [0, 0, 0, 0, 0, 0, -35, -26, -28, 16, -11, -2],\n [0, 0, 0, 0, 0, 0, 0, -33, 11, 18, 12, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, -30, -14, -21, -29],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -10, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 13],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "981", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[8, -27, -3, -28, -27, 14, -32, -9, 10, 24, 28, 10],\n [0, 33, 18, -24, -18, -26, -16, -2, -32, 4, 11, 29],\n [0, 0, 35, 23, -24, 24, -8, -21, 13, -33, -17, -11],\n [0, 0, 0, 34, 27, 0, 4, 32, 20, -7, -11, -16],\n [0, 0, 0, 0, -12, -28, 19, 23, -14, -16, -16, -6],\n [0, 0, 0, 0, 0, 18, 20, 25, 0, 23, 14, -24],\n [0, 0, 0, 0, 0, 0, -14, 27, -24, 35, 22, -8],\n [0, 0, 0, 0, 0, 0, 0, 14, -7, -10, 29, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 28, 30, 20, 35],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 27, -34, 27],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 15],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19733", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-25, 1, -10, 18, -9, -16, -31, -9, -10, -21, -11, -18],\n [-13, 10, -5, 19, 29, -9, -21, 29, -22, 28, 10, -34],\n [0, 5, -16, -17, 12, -25, 26, 26, 29, -21, -34, 30],\n [34, 23, -4, -27, -18, 33, -28, 11, 23, 31, -11, 13],\n [11, -31, -7, -13, -23, 12, -3, 9, 33, -31, 25, -29],\n [13, -35, -10, -22, 5, 4, 33, 11, 1, -15, -2, 20],\n [-30, -3, -23, 7, -2, -15, 23, 32, 20, 17, -29, 32],\n [19, 17, 35, 27, -4, -10, 16, 9, -34, -2, -2, -12],\n [-11, 3, -3, -9, -9, 23, 5, -26, 19, 28, 13, 1],\n [33, 22, 1, -4, -8, -2, 26, 32, -17, 12, 14, 14],\n [-14, -13, 24, 25, 31, -31, -6, -27, 29, -25, 27, -21],\n [22, -2, -9, -1, -16, -28, 10, 4, -28, 20, -14, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "991", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-29, 16, -22, 17, -18, -21, -9, 15, 29, 23, 22, -14],\n [-10, 25, 9, 25, 9, -10, -20, -25, 12, -24, 20, 19],\n [-25, -33, 12, -4, -19, 6, -24, -1, -6, -34, -27, 5],\n [-1, -6, -8, -32, 9, 13, 18, 28, -17, 0, -17, -14],\n [1, 10, -4, 11, -13, 17, -6, -22, -13, 29, -1, 11],\n [-4, 0, -23, 16, 13, -7, -20, -16, 4, 4, 1, -9],\n [-16, -29, -29, -20, -9, -33, 34, -15, 22, -3, -6, -16],\n [-17, 19, -34, 35, 10, 29, -29, -3, -27, 26, -15, 20],\n [-6, -17, -1, -7, -2, -7, 34, 22, -20, -30, 4, 17],\n [-35, 27, 20, -30, 18, -1, -19, -16, 23, -17, -23, -22],\n [-6, -30, 7, -32, -18, -18, -30, -15, 30, -15, -24, 4],\n [-18, 29, -11, -16, -33, 7, 27, 22, 13, 35, 7, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-316", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-23, -20, 26, 14, 22, 25, -28, -20, 25, -20, 1, 17],\n [34, 22, -11, -35, -4, 9, 14, -23, -12, -6, 7, 26],\n [19, -15, 8, -13, -22, 20, -3, 23, -33, 33, -28, 14],\n [35, 23, -1, -26, -18, -30, 22, 20, 19, 3, -5, 13],\n [2, 10, 18, -3, 15, -29, 35, 24, 24, -21, -10, 22],\n [-17, 17, 2, 18, -18, -35, 34, -16, -5, -18, -19, -4],\n [27, 20, 6, 33, 27, 23, 35, -20, -29, 21, -16, 22],\n [-28, 13, 11, 23, -21, -25, -12, 33, -8, -13, -34, -22],\n [-12, -28, 17, 23, -35, 32, -13, -16, -19, 3, -7, 15],\n [34, 23, -18, 27, 24, 11, -35, 33, -32, 10, 1, 27],\n [-34, -1, -17, -11, 6, 6, 29, -29, -1, 30, 4, -27],\n [-33, 15, -7, -22, 5, 20, 28, -12, -10, -25, -31, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[20, 3, -28, 9, -21, 0, -11, 28, 5, 1, 6, 22],\n [0, -18, 18, 35, 4, -18, -34, -29, 1, 2, -26, 29],\n [0, 0, 29, 0, 5, -2, 35, -13, -18, 29, -25, -16],\n [0, 0, 0, -9, 32, 28, -13, 27, -31, 34, -4, 23],\n [0, 0, 0, 0, 28, 29, -15, -14, -26, 7, -29, -27],\n [0, 0, 0, 0, 0, 34, 11, -10, -31, 17, -1, -3],\n [0, 0, 0, 0, 0, 0, -7, -18, 2, -8, 29, 32],\n [0, 0, 0, 0, 0, 0, 0, -1, -7, 4, 25, 8],\n [0, 0, 0, 0, 0, 0, 0, 0, -27, 19, -34, 34],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 17, -8, -25],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 7],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1110", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[3, -28, 19, 12, -12, 2, 2, 0, -4, 2, 0, 18],\n [-28, -35, 12, 10, 19, 12, -16, 0, -10, -2, -18, -6],\n [19, 12, 0, 4, 12, -4, -12, 16, -27, 17, 12, 14],\n [12, 10, 4, 18, -4, 16, -1, -12, 4, -19, -1, 14],\n [-12, 19, 12, -4, 17, -2, -16, -22, -20, 1, 18, -10],\n [2, 12, -4, 16, -2, 17, 2, 12, 14, -4, 12, 6],\n [2, -16, -12, -1, -16, 2, 29, 18, 12, 0, -2, -11],\n [0, 0, 16, -12, -22, 12, 18, -4, 6, 3, -4, -2],\n [-4, -10, -27, 4, -20, 14, 12, 6, -2, 13, 4, -20],\n [2, -2, 17, -19, 1, -4, 0, 3, 13, -21, 17, -12],\n [0, -18, 12, -1, 18, 12, -2, -4, 4, 17, -11, 4],\n [18, -6, 14, 14, -10, 6, -11, -2, -20, -12, 4, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (9, 10) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[28, -18, -21, 17, 7, 12, -28, 29, -24, -20, -2, -20],\n [0, -15, 28, 2, 21, -20, 13, -1, -11, 8, -12, -32],\n [0, 0, 31, -2, -34, -29, -1, -13, -11, 32, -29, -18],\n [0, 0, 0, -20, -25, -34, 9, 16, 4, 34, 4, -8],\n [0, 0, 0, 0, 17, 35, -25, -25, 24, -11, -28, -10],\n [0, 0, 0, 0, 0, -33, 1, 33, 30, -15, 34, 14],\n [0, 0, 0, 0, 0, 0, -10, 34, -18, -1, 9, 3],\n [0, 0, 0, 0, 0, 0, 0, 2, -20, 23, 6, -31],\n [0, 0, 0, 0, 0, 0, 0, 0, -1, -23, -17, 4],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 11, 24],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19, -32],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19320", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the inverse of matrix 1/839 * A where A =\n[[31, -34, -2, 22, 10, -23, -26, 23, 17, 3, 9, -14],\n [-34, 9, 9, 0, 0, 20, 23, 9, -13, 0, -18, 0],\n [-2, 9, 14, -18, 18, 17, -2, -2, -24, -5, 13, 24],\n [22, 0, -18, -21, -7, -30, -13, 6, 6, 14, 12, -16],\n [10, 0, 18, -7, 13, 12, 17, -10, 10, 12, 9, 1],\n [-23, 20, 17, -30, 12, 31, -10, -3, -14, 4, -28, -4],\n [-26, 23, -2, -13, 17, -10, 4, -2, -20, 20, 2, -16],\n [23, 9, -2, 6, -10, -3, -2, -34, 20, 10, -10, -8],\n [17, -13, -24, 6, 10, -14, -20, 20, 18, -2, 25, -6],\n [3, 0, -5, 14, 12, 4, 20, 10, -2, 31, 6, -5],\n [9, -18, 13, 12, 9, -28, 2, -10, 25, 6, 32, 13],\n [-14, 0, 24, -16, 1, -4, -16, -8, -6, -5, 13, -22]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3125", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 3) of the inverse of matrix 1/839 * A where A =\n[[-18, -20, -7, -33, 10, 16, -16, 2, -24, -1, -18, -16],\n [-30, 17, 11, 35, -32, -8, 28, -13, 32, -4, 13, -26],\n [3, -3, -19, -14, -1, 8, 22, -18, 13, 8, 21, 1],\n [32, -27, -35, -24, -32, 32, -22, 22, -18, 22, -10, -17],\n [-13, 20, 26, 35, 29, 7, 5, -5, -32, -6, 3, 10],\n [12, -1, 25, -31, -18, -1, 16, 11, -23, -15, -3, -7],\n [19, 20, 3, 2, 14, 2, 17, 35, -2, 9, 14, 15],\n [-33, -30, 0, 12, 6, -4, 19, 20, 35, -18, 24, -3],\n [19, -31, -2, 4, 10, -13, -34, -4, 19, 35, -21, -22],\n [12, -14, -13, -14, -17, 29, -1, 9, -1, 3, 19, -3],\n [-9, 33, 34, -9, 2, 18, -14, 4, -15, -18, -22, 6],\n [18, -21, -33, -30, -34, -31, -6, 4, 11, -21, -2, -17]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (11, 11) of the inverse. Round your answer to the nearest integer:\n[[13, -25, 6, -10, -30, -10, 16, -9, 26, -20, 17, -4],\n [-25, -16, -28, 14, 32, -1, -13, 16, -17, -30, -18, -10],\n [6, -28, -35, -8, -15, 24, -6, 6, -16, 9, 22, -6],\n [-10, 14, -8, 28, 4, 20, 6, -8, -7, -10, -6, -10],\n [-30, 32, -15, 4, 6, 8, -2, -6, -13, -4, -7, -4],\n [-10, -1, 24, 20, 8, 9, 8, -4, 4, 0, 0, 18],\n [16, -13, -6, 6, -2, 8, -13, 0, 22, -14, 19, 20],\n [-9, 16, 6, -8, -6, -4, 0, 35, -26, 5, -2, -8],\n [26, -17, -16, -7, -13, 4, 22, -26, 24, -8, 22, 24],\n [-20, -30, 9, -10, -4, 0, -14, 5, -8, -33, -2, -26],\n [17, -18, 22, -6, -7, 0, 19, -2, 22, -2, 31, 8],\n [-4, -10, -6, -10, -4, 18, 20, -8, 24, -26, 8, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[33, 9, 6, 6, 2, 3, -9, -3, 1, 14, -20, -26],\n [9, 21, -6, -22, -4, -16, 13, 20, 0, -20, -28, 6],\n [6, -6, 14, -12, 27, -10, 3, 8, -2, 2, -19, -4],\n [6, -22, -12, 10, -2, -10, -12, 24, -6, 10, 24, 2],\n [2, -4, 27, -2, 35, 10, -1, 7, 29, -21, -14, -17],\n [3, -16, -10, -10, 10, 2, 24, 4, -4, -21, -8, -10],\n [-9, 13, 3, -12, -1, 24, 3, -4, 10, 6, 5, -4],\n [-3, 20, 8, 24, 7, 4, -4, -17, -30, 3, 14, 6],\n [1, 0, -2, -6, 29, -4, 10, -30, -14, -14, 11, 12],\n [14, -20, 2, 10, -21, -21, 6, 3, -14, -13, -16, -11],\n [-20, -28, -19, 24, -14, -8, 5, 14, 11, -16, -15, -16],\n [-26, 6, -4, 2, -17, -10, -4, 6, 12, -11, -16, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-167", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-10, 14, -6, -22, -21, 29, -19, 15, -22, 17, 13, 13],\n [16, 10, 34, 19, 15, -15, -23, 3, -34, -9, -19, 8],\n [-11, -2, 3, -23, -35, -26, 28, -3, -18, 14, 2, -5],\n [6, 3, -28, 26, 9, 32, 23, 10, 15, -22, 1, -5],\n [-4, -2, -1, 19, -27, 24, 34, -16, -12, 13, 15, -14],\n [-13, -15, 19, -12, -2, -26, -22, 8, 3, 6, 10, -3],\n [33, -24, -20, 19, 24, 29, 6, 34, -31, 5, -27, 29],\n [12, 31, -6, 5, 26, -19, 32, 21, 9, -8, -12, 21],\n [7, 28, -3, -8, 30, -5, -22, -17, -2, 16, 1, -27],\n [23, 18, -4, 2, 2, 10, -31, -28, -18, 34, -31, 30],\n [-35, -2, -2, 8, -26, 5, 4, -34, 31, -5, -5, 19],\n [-14, -18, 27, 34, 23, 10, 24, -4, -34, -35, -3, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7998", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, -8, 13, -6, -8, 3, 2, 6, 20, 1, 5, -11],\n [-8, -7, -3, 16, -6, -4, -14, -2, -10, 9, 12, 2],\n [13, -3, -2, 14, 4, -4, -2, 8, -33, 20, -4, 16],\n [-6, 16, 14, 2, -2, 2, -14, 24, -16, 27, -13, 14],\n [-8, -6, 4, -2, -11, -29, -12, -12, -4, -16, 10, 2],\n [3, -4, -4, 2, -29, -12, -12, 3, -18, -29, 2, -12],\n [2, -14, -2, -14, -12, -12, -12, -9, 12, -21, -6, -6],\n [6, -2, 8, 24, -12, 3, -9, 24, 3, -12, -25, 2],\n [20, -10, -33, -16, -4, -18, 12, 3, -25, -24, 14, 6],\n [1, 9, 20, 27, -16, -29, -21, -12, -24, -2, 12, -29],\n [5, 12, -4, -13, 10, 2, -6, -25, 14, 12, 31, 20],\n [-11, 2, 16, 14, 2, -12, -6, 2, 6, -29, 20, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value at position (1, 5) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[35, -7, 29, -9, -9, -34, 12, -19, 3, 3, -28, 10],\n [0, 29, -7, -5, 35, 15, 22, -15, -10, 27, 25, 24],\n [0, 0, 33, -30, -8, 26, -17, 12, 25, -8, -22, 34],\n [0, 0, 0, -26, 22, 0, 29, -4, -9, -2, -23, -25],\n [0, 0, 0, 0, 33, -15, 15, 17, -34, 17, -8, -31],\n [0, 0, 0, 0, 0, 35, 1, 0, 18, 30, -34, 0],\n [0, 0, 0, 0, 0, 0, 26, -35, -27, 27, 15, -23],\n [0, 0, 0, 0, 0, 0, 0, -29, 33, 26, 7, 6],\n [0, 0, 0, 0, 0, 0, 0, 0, -6, 17, -20, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -24, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-27, -30, -8, -29, 13, -9, -20, -18, -35, 8, -18, -20],\n [-16, -4, -2, -2, -35, -35, -23, 24, -8, -28, 31, -33],\n [-34, -3, 23, 23, 9, 11, 35, -2, -29, 24, 13, 11],\n [11, -8, 21, -12, -18, -15, -31, -20, -3, 17, 10, 33],\n [14, 18, -8, -27, 25, -9, 13, -18, 30, -26, -20, -16],\n [4, -28, 19, -19, 14, -7, -10, -3, 15, -33, 35, -24],\n [-16, 26, 7, 12, -8, 11, 15, -19, 2, 20, 17, -17],\n [-16, -20, 4, -14, -21, 20, 32, 21, 9, -22, -11, 6],\n [2, 1, 23, -8, -7, -6, 2, -5, 10, 33, 20, 23],\n [-29, 27, -30, 22, 24, 10, -24, 15, -28, 1, -26, 25],\n [18, 2, -22, -1, 21, -28, 19, 30, -30, -20, -13, -26],\n [18, 2, 8, -14, -21, 24, -5, -33, 30, 9, -11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "181", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, -33, 26, 32, -17, -25, 31, 21, -13, -32, -4, -31],\n [0, 10, 31, 25, -11, 22, -20, 31, 0, -5, -29, -31],\n [0, 0, 34, 2, -35, -4, -22, -17, 5, 26, -16, -3],\n [0, 0, 0, 23, -15, 18, 35, -34, 17, 22, -15, 5],\n [0, 0, 0, 0, 14, 30, -17, 28, -34, 32, -22, 22],\n [0, 0, 0, 0, 0, -2, 25, -5, 13, -24, -3, -18],\n [0, 0, 0, 0, 0, 0, 2, -18, 30, -12, -22, 11],\n [0, 0, 0, 0, 0, 0, 0, 35, 27, 22, -17, -9],\n [0, 0, 0, 0, 0, 0, 0, 0, 33, 27, 32, -3],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 4, -30],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 2],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1003771", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[19, -2, 16, 14, -9, 14, -6, 18, 0, -6, 20, 4],\n [-2, 27, 16, -10, 1, 4, -10, 19, -6, 6, -6, -26],\n [16, 16, 8, 6, -4, 6, -18, -4, 1, 12, 6, 5],\n [14, -10, 6, -12, -3, -20, 26, -2, -4, 12, 4, 10],\n [-9, 1, -4, -3, -34, -26, -6, 11, -20, -3, 14, -17],\n [14, 4, 6, -20, -26, 25, -8, 24, 16, -4, -6, 6],\n [-6, -10, -18, 26, -6, -8, 20, 18, 29, 12, -34, -4],\n [18, 19, -4, -2, 11, 24, 18, 33, 29, 19, -16, 15],\n [0, -6, 1, -4, -20, 16, 29, 29, 13, 3, 2, -4],\n [-6, 6, 12, 12, -3, -4, 12, 19, 3, 34, 14, 0],\n [20, -6, 6, 4, 14, -6, -34, -16, 2, 14, -33, -26],\n [4, -26, 5, 10, -17, 6, -4, 15, -4, 0, -26, 32]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[21, 10, 19, -4, -17, -28, 1, 22, 1, -6, -24, 22],\n [-14, -13, 30, 0, 16, 23, 24, 28, -4, 13, 30, -32],\n [-28, 29, -27, -9, -8, -35, 6, -30, -1, -21, -26, 10],\n [29, -16, -6, 6, -26, 16, -13, -16, -2, 2, -35, -17],\n [28, 6, 9, 9, -19, 29, 24, 17, -3, -6, -22, 4],\n [18, 35, -15, 14, 17, -28, 6, -20, 12, -9, 20, 8],\n [-17, -3, -4, -9, -11, 23, -2, 21, 25, 35, 24, 22],\n [-18, -34, -24, -35, 32, 35, -12, 25, 4, -6, 16, -14],\n [24, -14, -16, 17, -8, -31, 8, 10, -13, -26, -29, -2],\n [10, 15, -17, -21, 30, 9, -11, -1, -28, -17, 33, 2],\n [-29, 5, -24, 15, 9, -3, -34, -31, 14, 8, -25, 6],\n [32, -3, 29, -5, -23, -1, -2, 14, 26, -26, -27, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-34", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[7, -31, -22, -29, 17, -33, -23, -33, 22, -1, 21, 32],\n [0, -34, -24, -34, 3, 19, 15, 28, 0, -13, 35, 26],\n [0, 0, -1, 31, 17, 0, -1, -23, -12, 33, -24, -7],\n [0, 0, 0, 22, 5, -29, -33, -29, -20, -15, -21, 1],\n [0, 0, 0, 0, 35, 11, 34, 31, 23, -20, -8, 33],\n [0, 0, 0, 0, 0, -34, -14, 1, 24, 17, 14, -31],\n [0, 0, 0, 0, 0, 0, -8, -29, -30, 16, -30, -14],\n [0, 0, 0, 0, 0, 0, 0, -23, 4, 16, -12, 14],\n [0, 0, 0, 0, 0, 0, 0, 0, 3, 24, -24, -18],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 29, -5],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, -26],\n [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-234", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-5, -31, 32, 19, 30, 28, 13, 26, 29, -15, -28, -30],\n [7, 18, -18, 1, -29, 4, -2, 3, 32, 24, 11, -20],\n [15, -29, -30, -9, -26, 25, -15, 28, -17, -6, 34, 21],\n [-6, 8, 31, -23, -18, -28, -4, -32, 7, 12, 17, 20],\n [-23, 29, 15, 11, -18, 17, 15, 2, -18, 23, 29, 32],\n [-3, -9, -34, 33, 7, 27, 17, 15, 7, -21, -14, -17],\n [-32, -16, -13, 9, 22, 34, 12, 13, 2, -15, -11, -7],\n [5, -12, -21, -30, -29, 18, 18, -7, 21, 8, 30, -22],\n [-14, -21, 14, 12, 28, 7, -23, 7, -35, 3, -23, -28],\n [-25, 34, 32, 12, -12, 28, 34, -19, -21, -23, -28, 2],\n [-27, 31, 4, 23, -23, 7, -6, -24, 10, -16, 20, -30],\n [24, -15, -4, -32, 4, 22, -4, 11, 16, 5, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (2, 5) of the inverse. Round your answer to the nearest integer:\n[[11, -30, 4, 22, -16, 10, -5, -32, 11, -16, -30, 20],\n [-30, -18, 0, 24, -26, -2, 8, -2, -4, 5, -32, 2],\n [4, 0, 17, 14, 29, -30, 15, -14, -3, -6, -12, -13],\n [22, 24, 14, 6, -22, -22, 10, 5, -22, 22, 24, 4],\n [-16, -26, 29, -22, 18, 14, -4, 2, -10, -14, 18, 24],\n [10, -2, -30, -22, 14, 13, -2, 8, -9, -2, -15, 25],\n [-5, 8, 15, 10, -4, -2, -24, 4, -2, 14, 24, -14],\n [-32, -2, -14, 5, 2, 8, 4, -11, -2, -26, -10, -11],\n [11, -4, -3, -22, -10, -9, -2, -2, 3, -10, 18, -2],\n [-16, 5, -6, 22, -14, -2, 14, -26, -10, -8, 14, -14],\n [-30, -32, -12, 24, 18, -15, 24, -10, 18, 14, -16, -8],\n [20, 2, -13, 4, 24, 25, -14, -11, -2, -14, -8, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/839 * A where A =\n[[-10, -24, 19, -27, 6, 8, -16, 10, 24, -5, -20, 8],\n [-24, 5, 7, 24, 24, -2, 4, 7, -2, 22, 21, -14],\n [19, 7, 12, -7, -14, 14, -7, 6, 4, -8, 0, -12],\n [-27, 24, -7, 31, -32, -14, -11, -4, 24, -10, -4, 6],\n [6, 24, -14, -32, -2, 4, 2, -30, -6, -15, 10, -10],\n [8, -2, 14, -14, 4, 20, 24, -6, 12, -6, 4, 2],\n [-16, 4, -7, -11, 2, 24, -22, -14, -10, 2, 16, 22],\n [10, 7, 6, -4, -30, -6, -14, -15, 3, -18, 20, -18],\n [24, -2, 4, 24, -6, 12, -10, 3, 25, 0, 14, -19],\n [-5, 22, -8, -10, -15, -6, 2, -18, 0, 14, -15, 17],\n [-20, 21, 0, -4, 10, 4, 16, 20, 14, -15, -20, 15],\n [8, -14, -12, 6, -10, 2, 22, -18, -19, 17, 15, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 32, 22, -30, -3, -17, -21, 3, 8, 24, 10, 35],\n [0, -2, 31, 22, -24, 5, -16, -11, -17, 13, -34, -15],\n [27, -23, 12, 5, -5, -13, 9, 2, -24, -20, -21, 34],\n [-26, 10, -30, -25, -33, -24, -3, -5, 4, 19, -10, -29],\n [-26, 4, -18, 6, -8, -29, -10, -22, 31, -3, -28, 3],\n [7, -7, -28, 1, -12, -22, 34, 9, 35, 31, 2, 16],\n [22, 0, -5, -7, -22, 5, -22, 15, 21, -31, -34, -19],\n [26, 21, 4, -30, -17, 12, -10, 32, 11, -30, -17, -20],\n [4, -26, -15, -9, -17, -22, 19, 32, -2, -12, 12, 35],\n [0, 24, -27, -18, -11, 23, 25, 35, -28, -29, -20, 14],\n [1, -1, -11, 8, 14, 32, -23, -33, -12, 23, 19, -14],\n [-8, 9, -9, 7, 6, -21, -10, 7, 20, 2, 29, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-156", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/839 * A where A =\n[[-14, 6, 22, 23, -14, -18, 0, -10, -24, 8, -6, -6],\n [6, 9, -32, -12, 14, -4, 6, 12, 6, -8, -32, 20],\n [22, -32, -35, 5, -4, -28, -16, 14, 8, 24, 4, -17],\n [23, -12, 5, -8, 5, 26, -4, 2, -6, 26, 8, -1],\n [-14, 14, -4, 5, 1, -3, 5, -14, -4, 12, -15, -4],\n [-18, -4, -28, 26, -3, 4, -5, 8, 8, 2, 4, 0],\n [0, 6, -16, -4, 5, -5, -5, 10, 32, -24, 12, 24],\n [-10, 12, 14, 2, -14, 8, 10, -14, 8, -14, -14, 14],\n [-24, 6, 8, -6, -4, 8, 32, 8, 12, 18, 10, 22],\n [8, -8, 24, 26, 12, 2, -24, -14, 18, 35, -26, -11],\n [-6, -32, 4, 8, -15, 4, 12, -14, 10, -26, 1, -6],\n [-6, 20, -17, -1, -4, 0, 24, 14, 22, -11, -6, 34]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1643", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (11, 12) of the inverse. Round your answer to the nearest integer:\n[[-15, 26, 5, -20, -16, -33, -20, -18, -16, -6, -20, -12],\n [-35, 3, 4, -1, 27, 1, -23, 33, 12, 16, 28, -28],\n [-22, 23, -32, -23, -34, -9, 3, -19, 29, 34, -14, -33],\n [-16, -17, -19, -32, 0, -28, 31, -7, -29, 6, -29, -27],\n [-10, -18, -28, -7, 2, -11, 35, 15, -17, -27, -21, 35],\n [-24, -17, 2, 9, 7, 19, 26, 24, -34, 4, 1, 13],\n [6, 7, 26, 22, 6, -14, -31, -1, 23, 7, 23, 6],\n [7, 16, -9, 5, -23, 23, -9, 32, -35, -3, 8, -10],\n [29, -31, 18, 10, -11, 22, -6, -6, 6, 25, 30, -4],\n [-26, 27, -26, -18, 0, 0, -9, -31, 1, 14, 31, -6],\n [-15, 6, 30, -20, -30, -8, 27, 2, -17, 33, 14, 1],\n [30, -34, 24, -35, 0, -17, 14, 10, 16, -1, -30, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[-8, -33, 14, 1, -23, -3, 17, 24, 15, -20, -21, -24],\n [-16, 31, -26, 35, -26, -33, -17, 26, -13, -29, -34, -32],\n [35, 19, -10, 19, 30, -12, 8, 8, 33, -2, -4, 19],\n [22, -21, -17, -22, 30, 9, -29, 12, -22, -10, 3, -19],\n [-22, -32, -19, 7, -3, -17, 35, 33, 19, -31, 13, 4],\n [-33, 20, -5, 14, 1, 1, -11, -11, 25, 27, 9, 23],\n [-26, 2, 8, -1, -18, -11, -1, 35, 16, -12, 1, -17],\n [-1, 10, 17, 18, 15, 21, 20, -29, 13, -10, -1, -8],\n [17, -7, -17, -7, 31, -27, 12, 19, 35, 8, 12, -11],\n [2, 17, -15, 18, 16, -27, -35, 34, -6, -17, 5, 28],\n [23, -13, 12, -8, -4, -14, -19, 19, 19, 7, 4, -12],\n [32, -7, 22, -10, 18, -22, -14, 21, -32, 27, 16, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[14, 17, 19, 5, 20, -13, 0, 28, -14, 21, -31, 18],\n [4, 3, -7, 18, 8, 8, -17, 19, -5, 32, 25, 6],\n [-32, 15, -6, -10, 13, -4, 4, -6, -31, -34, -2, -5],\n [-6, -10, 18, -27, -22, -5, -28, 20, 27, -8, -13, -13],\n [3, 17, -14, -2, -30, 23, -32, -24, -31, 34, -11, -31],\n [23, -20, 3, 24, -5, 16, 31, 6, 26, -30, -13, 5],\n [25, -30, 14, 32, 21, 21, -1, 27, -1, -19, 2, 6],\n [6, -11, 23, -7, -30, -22, 8, 12, -1, 34, 20, -28],\n [-6, -8, -9, 9, -20, -22, 27, 24, 21, 24, 15, 29],\n [10, -14, -12, 14, 30, -30, -35, 1, -35, -11, 14, 21],\n [30, 5, -30, 8, 32, 2, -20, 6, 22, 11, 29, -16],\n [25, 6, -9, 11, -33, -4, 35, 18, 28, -18, 5, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-343", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -8, 11, -8, -6, -16, 2, -2, 5, -32, -12, 28],\n [-8, -17, -10, -13, -4, 4, 28, -11, 25, -15, -4, 28],\n [11, -10, 23, -18, 6, 10, 24, 16, 19, 1, 5, -28],\n [-8, -13, -18, -10, 16, -8, -2, -18, -21, 14, 28, -14],\n [-6, -4, 6, 16, -31, -6, -6, -8, -14, 2, -22, 0],\n [-16, 4, 10, -8, -6, 8, 9, 8, -32, 5, -16, -5],\n [2, 28, 24, -2, -6, 9, -11, -29, -12, 8, 11, 6],\n [-2, -11, 16, -18, -8, 8, -29, -22, -2, -1, -16, 5],\n [5, 25, 19, -21, -14, -32, -12, -2, 17, -22, 4, -24],\n [-32, -15, 1, 14, 2, 5, 8, -1, -22, 25, 28, -4],\n [-12, -4, 5, 28, -22, -16, 11, -16, 4, 28, -33, -24],\n [28, 28, -28, -14, 0, -5, 6, 5, -24, -4, -24, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "For the inverse of 1/839 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[25, -30, 5, -19, -26, 34, 27, 9, -24, 13, -34, -19],\n [23, -29, -16, 24, 25, 25, -20, -19, -15, 7, -35, -25],\n [-5, 29, 6, -4, -29, -3, -23, -29, 4, 33, -29, -33],\n [-19, -25, -34, -6, 15, 31, 18, 2, -7, 32, -4, 15],\n [-20, -14, 19, 21, -1, 6, 16, 17, 34, -21, -15, -23],\n [34, 31, 12, -31, 5, 12, 7, -20, -24, -27, -17, 7],\n [-13, -20, -8, -24, -15, 23, -5, 8, 11, -23, -18, 0],\n [0, -32, 19, -13, 32, -17, 15, -7, 1, 16, -34, -31],\n [-7, -7, 7, 5, 19, -4, 2, 24, 7, -25, 16, -13],\n [-19, 33, 26, 1, 2, 9, 19, -8, -11, -26, 30, -32],\n [-17, 11, -18, 26, 25, 28, -28, 7, -19, 4, -21, 11],\n [13, 14, -5, -10, 22, -24, 6, 6, 11, -32, 32, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Calculate the inverse matrix of 1/839 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 14, -27, -3, 16, 9, -33, -34, -32, 21, 25, -25],\n [-15, 18, -1, 6, -27, -22, -34, 25, -21, -25, 21, 31],\n [-29, -35, 15, 5, 24, -17, 26, -6, -20, -18, -5, -1],\n [-8, -24, -12, 5, 33, 26, 30, 16, -9, 21, -12, 32],\n [28, -16, -27, 27, -11, 25, 6, -33, 21, 25, -27, 7],\n [7, -13, -19, -23, -16, 14, -18, 18, -20, -23, 26, 25],\n [4, 18, 32, 33, 18, 22, -17, -7, -2, -31, -22, 21],\n [-26, 5, -12, 3, -23, 27, -30, 4, 7, 17, -26, -13],\n [-10, 29, 11, -2, -32, -6, -33, 16, 28, -10, -22, -34],\n [22, 9, 14, -32, -27, -26, -28, 23, -17, -14, -11, 17],\n [-11, -21, 32, -9, -31, -16, -11, 32, -9, 2, -27, 27],\n [10, 35, -16, -7, -16, 20, -20, 0, 10, 7, -4, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172", "dataset": "MATH"}
{"messages": [{"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/839 * A where A =\n[[-1, 10, 6, -32, 21, -8, -24, -22, 7, 15, -17, 3],\n [10, 0, -22, -10, -4, -6, 3, -1, -1, 10, 23, -10],\n [6, -22, -6, -12, -6, 6, -16, 22, -30, 5, 28, -2],\n [-32, -10, -12, 23, -4, 17, -18, 6, 6, -16, -24, 26],\n [21, -4, -6, -4, -20, 3, -8, 0, 6, -1, 8, 0],\n [-8, -6, 6, 17, 3, -2, 18, 6, -4, -5, 24, -24],\n [-24, 3, -16, -18, -8, 18, -34, -22, 23, -12, 11, -24],\n [-22, -1, 22, 6, 0, 6, -22, -30, -9, -25, -30, 6],\n [7, -1, -30, 6, 6, -4, 23, -9, -25, -14, 10, 14],\n [15, 10, 5, -16, -1, -5, -12, -25, -14, 13, 2, 9],\n [-17, 23, 28, -24, 8, 24, 11, -30, 10, 2, 9, -4],\n [3, -10, -2, 26, 0, -24, -24, 6, 14, 9, -4, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "211", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the value at position (6, 2) of the inverse. Round your answer to the nearest integer:\n[[-22, -7, -32, 13, 0, -25, -24, -32, 25, -21, -25, -2],\n [-33, 3, -4, -15, -1, -21, -15, -34, -17, -20, 2, 11],\n [-1, 33, 9, -30, -22, 15, -13, 28, -32, -1, -11, -1],\n [-2, -33, -27, -12, -11, -29, -29, -18, 26, -6, -27, 14],\n [-30, -16, -18, -7, -35, 2, 7, -10, -27, -32, -1, -3],\n [-19, 30, 25, 8, -26, 19, 11, -13, 33, -18, 31, -14],\n [-16, -35, -3, -20, -33, -25, -25, -33, 12, 10, 1, -16],\n [-25, -5, -35, -30, 7, 0, 35, 10, -34, 35, 4, 2],\n [17, -31, 20, 31, -27, 33, 27, 25, -22, -9, -27, -9],\n [-27, 10, 27, -3, 25, 5, 8, -21, -16, 33, -23, -22],\n [-9, -22, 13, -3, -31, -16, -19, -4, 24, 34, 2, 0],\n [-6, -21, -17, -17, -30, -32, -26, -29, -34, -34, -24, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89", "dataset": "MATH"}
{"messages": [{"content": "Find the inverse of 1/839 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[15, 23, -13, 1, 4, 31, 18, 11, -27, 10, -13, 15],\n [-21, -24, 1, 17, -23, -31, -17, 14, 21, 34, 13, 10],\n [-2, -15, 2, -33, 24, 30, -28, 12, -9, -32, 2, 22],\n [-11, 29, -15, -27, 7, 10, -7, 26, 30, 21, 32, 24],\n [4, -33, -33, 26, 24, -26, 7, -28, 26, 18, -27, -29],\n [-34, -26, -15, 9, 4, 14, 22, -27, 7, -12, 12, 7],\n [17, 11, -13, 9, 11, -7, 26, 5, 9, -7, 23, 19],\n [-35, 26, -12, -26, 8, -10, -2, -32, -23, -31, 12, 12],\n [-1, 29, -10, -7, 0, 25, -28, -11, 17, 9, 4, -16],\n [16, 30, -11, 27, -9, -13, 10, 11, 2, -23, 12, -2],\n [21, 25, -26, 23, 2, 15, 13, 17, 35, 32, 18, 17],\n [33, -34, 18, -1, 12, -7, 25, 16, -26, -24, 5, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5088", "dataset": "MATH"}