messages
listlengths 1
1
| ground_truth
stringlengths 1
9
| dataset
stringclasses 1
value |
|---|---|---|
[
{
"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"
}
] |
-4811
|
MATH
|
[
{
"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"
}
] |
791
|
MATH
|
[
{
"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"
}
] |
1645
|
MATH
|
[
{
"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"
}
] |
8679
|
MATH
|
[
{
"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"
}
] |
5779
|
MATH
|
[
{
"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"
}
] |
1324
|
MATH
|
[
{
"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"
}
] |
683589
|
MATH
|
[
{
"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"
}
] |
-1733
|
MATH
|
[
{
"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"
}
] |
2050
|
MATH
|
[
{
"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"
}
] |
-112
|
MATH
|
[
{
"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"
}
] |
-109
|
MATH
|
[
{
"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"
}
] |
-134
|
MATH
|
[
{
"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"
}
] |
580
|
MATH
|
[
{
"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"
}
] |
-59
|
MATH
|
[
{
"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"
}
] |
125
|
MATH
|
[
{
"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"
}
] |
-24
|
MATH
|
[
{
"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"
}
] |
104347
|
MATH
|
[
{
"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"
}
] |
248736411
|
MATH
|
[
{
"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"
}
] |
6203
|
MATH
|
[
{
"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"
}
] |
144
|
MATH
|
[
{
"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"
}
] |
191
|
MATH
|
[
{
"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"
}
] |
-2134
|
MATH
|
[
{
"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"
}
] |
-39
|
MATH
|
[
{
"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"
}
] |
563456
|
MATH
|
[
{
"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"
}
] |
-627
|
MATH
|
[
{
"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"
}
] |
723
|
MATH
|
[
{
"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"
}
] |
1399
|
MATH
|
[
{
"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"
}
] |
-271
|
MATH
|
[
{
"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"
}
] |
3074
|
MATH
|
[
{
"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"
}
] |
-331
|
MATH
|
[
{
"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"
}
] |
-11138
|
MATH
|
[
{
"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"
}
] |
2431
|
MATH
|
[
{
"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"
}
] |
0
|
MATH
|
[
{
"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"
}
] |
149744
|
MATH
|
[
{
"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"
}
] |
1594
|
MATH
|
[
{
"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"
}
] |
343
|
MATH
|
[
{
"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"
}
] |
7723
|
MATH
|
[
{
"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"
}
] |
-338783
|
MATH
|
[
{
"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"
}
] |
15
|
MATH
|
[
{
"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"
}
] |
-119588
|
MATH
|
[
{
"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"
}
] |
162
|
MATH
|
[
{
"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"
}
] |
21
|
MATH
|
[
{
"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"
}
] |
-43
|
MATH
|
[
{
"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"
}
] |
-386
|
MATH
|
[
{
"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"
}
] |
245479
|
MATH
|
[
{
"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"
}
] |
0
|
MATH
|
[
{
"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"
}
] |
6725
|
MATH
|
[
{
"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"
}
] |
423
|
MATH
|
[
{
"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"
}
] |
-67
|
MATH
|
[
{
"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"
}
] |
5989
|
MATH
|
[
{
"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"
}
] |
-89
|
MATH
|
[
{
"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"
}
] |
32
|
MATH
|
[
{
"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"
}
] |
3380
|
MATH
|
[
{
"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"
}
] |
0
|
MATH
|
[
{
"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"
}
] |
1093
|
MATH
|
[
{
"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"
}
] |
562
|
MATH
|
[
{
"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"
}
] |
-9388406
|
MATH
|
[
{
"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"
}
] |
4644
|
MATH
|
[
{
"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"
}
] |
93
|
MATH
|
[
{
"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"
}
] |
3459621
|
MATH
|
[
{
"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"
}
] |
-194
|
MATH
|
[
{
"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"
}
] |
12889
|
MATH
|
[
{
"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"
}
] |
-13
|
MATH
|
[
{
"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"
}
] |
2
|
MATH
|
[
{
"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"
}
] |
45
|
MATH
|
[
{
"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"
}
] |
215
|
MATH
|
[
{
"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"
}
] |
-128542
|
MATH
|
[
{
"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"
}
] |
63
|
MATH
|
[
{
"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"
}
] |
618422
|
MATH
|
[
{
"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"
}
] |
37
|
MATH
|
[
{
"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"
}
] |
5103
|
MATH
|
[
{
"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"
}
] |
-13
|
MATH
|
[
{
"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"
}
] |
-16
|
MATH
|
[
{
"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"
}
] |
192
|
MATH
|
[
{
"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"
}
] |
32384
|
MATH
|
[
{
"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"
}
] |
118
|
MATH
|
[
{
"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"
}
] |
257
|
MATH
|
[
{
"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"
}
] |
3717
|
MATH
|
[
{
"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"
}
] |
1964
|
MATH
|
[
{
"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"
}
] |
-188
|
MATH
|
[
{
"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"
}
] |
-135
|
MATH
|
[
{
"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"
}
] |
62
|
MATH
|
[
{
"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"
}
] |
1535
|
MATH
|
[
{
"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"
}
] |
-130
|
MATH
|
[
{
"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"
}
] |
-562
|
MATH
|
[
{
"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"
}
] |
-5
|
MATH
|
[
{
"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"
}
] |
14
|
MATH
|
[
{
"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"
}
] |
-5329
|
MATH
|
[
{
"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"
}
] |
-145
|
MATH
|
[
{
"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"
}
] |
2122
|
MATH
|
[
{
"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"
}
] |
-18
|
MATH
|
[
{
"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"
}
] |
1865
|
MATH
|
[
{
"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"
}
] |
-70
|
MATH
|
[
{
"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"
}
] |
-26
|
MATH
|
[
{
"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"
}
] |
1391
|
MATH
|
[
{
"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"
}
] |
165
|
MATH
|
[
{
"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"
}
] |
91065
|
MATH
|
[
{
"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"
}
] |
512
|
MATH
|
[
{
"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"
}
] |
278
|
MATH
|
[
{
"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"
}
] |
-107
|
MATH
|
End of preview. Expand
in Data Studio
No dataset card yet
- Downloads last month
- 6