messages
listlengths 1
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| ground_truth
stringlengths 1
9
| dataset
stringclasses 1
value |
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[
{
"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"
}
] |
-102
|
MATH
|
[
{
"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"
}
] |
117288
|
MATH
|
[
{
"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"
}
] |
7
|
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[[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"
}
] |
-16836
|
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, -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"
}
] |
-331
|
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[[-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"
}
] |
124
|
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[[-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"
}
] |
-281
|
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[[-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"
}
] |
777
|
MATH
|
[
{
"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"
}
] |
16
|
MATH
|
[
{
"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"
}
] |
-14
|
MATH
|
[
{
"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"
}
] |
221
|
MATH
|
[
{
"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"
}
] |
264
|
MATH
|
[
{
"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"
}
] |
37
|
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[[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"
}
] |
43
|
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[[-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"
}
] |
19876
|
MATH
|
[
{
"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"
}
] |
2115
|
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[[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"
}
] |
45
|
MATH
|
[
{
"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"
}
] |
51
|
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[[-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"
}
] |
-48
|
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[[-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"
}
] |
13485
|
MATH
|
[
{
"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"
}
] |
900
|
MATH
|
[
{
"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"
}
] |
-41
|
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[[-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"
}
] |
-10745550
|
MATH
|
[
{
"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"
}
] |
-1409
|
MATH
|
[
{
"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"
}
] |
-58
|
MATH
|
[
{
"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"
}
] |
-176
|
MATH
|
[
{
"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"
}
] |
-469
|
MATH
|
[
{
"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"
}
] |
-3224
|
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, 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"
}
] |
-97
|
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[[-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"
}
] |
-6191
|
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[[-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"
}
] |
3085
|
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[[-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"
}
] |
18
|
MATH
|
[
{
"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"
}
] |
2069
|
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[[-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"
}
] |
-295
|
MATH
|
[
{
"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"
}
] |
-220
|
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, -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"
}
] |
11
|
MATH
|
[
{
"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"
}
] |
39
|
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[[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"
}
] |
27983
|
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[[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"
}
] |
-473571
|
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[[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"
}
] |
6844
|
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[[-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"
}
] |
1454
|
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[[-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"
}
] |
-172141
|
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[[-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"
}
] |
-28
|
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, -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"
}
] |
1618
|
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, -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"
}
] |
5856
|
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[[-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"
}
] |
-386
|
MATH
|
[
{
"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"
}
] |
-98
|
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[[-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"
}
] |
-26
|
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, -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"
}
] |
11849
|
MATH
|
[
{
"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"
}
] |
7491
|
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[[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"
}
] |
-1021
|
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[[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"
}
] |
33952
|
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[[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"
}
] |
-16657
|
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[[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"
}
] |
13
|
MATH
|
[
{
"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"
}
] |
7
|
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[[-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"
}
] |
144
|
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[[-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"
}
] |
-209
|
MATH
|
[
{
"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"
}
] |
120
|
MATH
|
[
{
"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"
}
] |
-58660
|
MATH
|
[
{
"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"
}
] |
-3
|
MATH
|
[
{
"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"
}
] |
-193975
|
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[[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"
}
] |
1595175
|
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, -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"
}
] |
-36
|
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[[-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"
}
] |
55
|
MATH
|
[
{
"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"
}
] |
-4674
|
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[[-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"
}
] |
1088
|
MATH
|
[
{
"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"
}
] |
981
|
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[[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"
}
] |
19733
|
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, 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"
}
] |
991
|
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[[-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"
}
] |
-316
|
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[[-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"
}
] |
102
|
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[[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"
}
] |
-1110
|
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[[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"
}
] |
76
|
MATH
|
[
{
"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"
}
] |
-19320
|
MATH
|
[
{
"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"
}
] |
3125
|
MATH
|
[
{
"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"
}
] |
8
|
MATH
|
[
{
"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"
}
] |
29
|
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[[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"
}
] |
-167
|
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[[-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"
}
] |
7998
|
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[[-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"
}
] |
88
|
MATH
|
[
{
"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"
}
] |
-13
|
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[[-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"
}
] |
181
|
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[[-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"
}
] |
1003771
|
MATH
|
[
{
"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"
}
] |
16
|
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[[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"
}
] |
-34
|
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[[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"
}
] |
-234
|
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[[-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"
}
] |
56
|
MATH
|
[
{
"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"
}
] |
-6
|
MATH
|
[
{
"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"
}
] |
70
|
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[[-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"
}
] |
-156
|
MATH
|
[
{
"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"
}
] |
1643
|
MATH
|
[
{
"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"
}
] |
-24
|
MATH
|
[
{
"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"
}
] |
-12
|
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[[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"
}
] |
-343
|
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[[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"
}
] |
57
|
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[[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"
}
] |
66
|
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[[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"
}
] |
172
|
MATH
|
[
{
"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"
}
] |
211
|
MATH
|
[
{
"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"
}
] |
89
|
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, 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"
}
] |
5088
|
MATH
|
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