messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[11, 7, -6, 6],\n [-9, -12, -1, -3],\n [-11, -12, -1, 7],\n [6, -7, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-5, 4, 3, 10],\n [-12, 12, -10, 0],\n [-5, -7, 10, -2],\n [1, 11, -7, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, -8, -7, 6],\n [0, 1, 8, -10],\n [0, 0, 10, -11],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 108 | MATH |
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/96 * A where A =\n[[11, -11, -1, 11],\n [0, 9, 0, -7],\n [0, 0, -1, 9],\n [0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-3, 4, 9, -1],\n [1, 6, 3, -8],\n [12, 2, -5, 2],\n [-9, 6, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-10, -4, -8, 8],\n [-4, -8, 2, 2],\n [-8, 2, -7, -2],\n [8, 2, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[-1, 0, -10, -9],\n [-3, 2, -4, 1],\n [-3, -5, 9, 6],\n [-7, -1, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -17 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[2, -8, 8, -2],\n [-8, -4, -6, -6],\n [8, -6, 7, 3],\n [-2, -6, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -401 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-10, 0, -10, -6],\n [0, -2, 4, -1],\n [-10, 4, 8, 0],\n [-6, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-6, -6, -9, 10],\n [0, -11, 4, 8],\n [0, 0, 5, 1],\n [0, 0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 9, -6, 4],\n [9, 0, 8, 2],\n [-6, 8, 12, 4],\n [4, 2, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[1, 2, 6, 6],\n [2, 9, -6, -4],\n [6, -6, -9, 6],\n [6, -4, 6, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -41 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-3, -12, -11, -1],\n [-3, -11, -5, 8],\n [8, -2, 9, -5],\n [5, -9, 3, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[7, 5, -11, 9],\n [10, 10, 2, 6],\n [-3, -9, -11, -2],\n [-10, 2, -7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -21 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[8, 0, 8, -5],\n [0, -1, 5, 12],\n [0, 0, 2, 0],\n [0, 0, 0, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[6, 2, -10, 6],\n [0, 9, -12, 11],\n [0, 0, -6, 11],\n [0, 0, 0, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[11, -3, -1, -2],\n [-3, -6, -10, -6],\n [-1, -10, 9, 4],\n [-2, -6, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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, -3, -12, -5],\n [11, 12, -2, -4],\n [10, -11, -7, 4],\n [8, -1, -5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 1) rounded to the nearest integer?\n[[11, 4, 0, 6],\n [4, 11, -2, 5],\n [0, -2, 2, 0],\n [6, 5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -6, 4, -1],\n [-6, -7, 9, 2],\n [4, 9, -9, 1],\n [-1, 2, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[8, 1, -9, 12],\n [0, -3, 6, -2],\n [0, 0, -6, -8],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -45 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-7, 10, 7, 6],\n [10, -1, -7, -8],\n [7, -7, 0, -7],\n [6, -8, -7, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Find the value at position (1, 1) of the inverse of matrix 1/96 * A where A =\n[[5, 6, 10, -9],\n [-1, 4, -3, 0],\n [-8, -7, -7, 12],\n [-9, 3, -7, -11]]\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 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, -11, 8, -4],\n [0, 11, -3, 9],\n [0, 0, -8, 10],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 263 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-3, 7, 7, -1],\n [0, -1, 9, 1],\n [0, 0, -7, 3],\n [0, 0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -320 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[10, -9, 12, -5],\n [12, -7, -1, -11],\n [-4, 1, 11, -3],\n [11, -9, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, -2, 4, 1],\n [-2, -9, -2, 6],\n [4, -2, 10, -4],\n [1, 6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -89 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[5, 7, -2, -6],\n [7, -11, 5, -6],\n [-2, 5, 7, -4],\n [-6, -6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-1, -9, 8, -9],\n [-6, -4, 10, -12],\n [-8, -6, -11, -1],\n [9, 11, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the inverse of 1/96 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, 4, -11, 0],\n [-12, -3, 7, 0],\n [-11, -9, -7, 8],\n [0, -8, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -45 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[12, 6, -10, 7],\n [0, 2, 11, 5],\n [0, 0, 4, -5],\n [0, 0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[0, 7, -3, -3],\n [9, 11, 9, 5],\n [-11, -11, -7, -12],\n [7, -3, 10, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 176 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 7, 8, -4],\n [0, -4, 6, 1],\n [0, 0, -8, -5],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 691 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-6, -10, 8, 11],\n [-6, 11, -1, -6],\n [-4, -3, -5, 4],\n [-12, 2, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-3, -11, 3, -7],\n [-2, 7, -1, 10],\n [11, -2, -2, -9],\n [-7, -1, -7, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 3, 10, -7],\n [-12, 1, -1, 4],\n [7, -9, 7, 10],\n [8, -4, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 224 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[2, 6, -4, 0],\n [6, 11, -6, 6],\n [-4, -6, -10, 0],\n [0, 6, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 665 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[2, 5, 7, -7],\n [0, -7, -8, 2],\n [-8, 1, 6, 10],\n [1, 5, -8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -229 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[-4, -4, -3, 11],\n [11, -7, 6, -10],\n [-3, 5, -8, 3],\n [-2, -3, 12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -226 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[-6, 11, -8, 12],\n [0, -2, -2, -2],\n [0, 0, 11, -3],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 232 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-2, -5, -10, -7],\n [0, -5, 8, 4],\n [0, 0, -7, 2],\n [0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -72 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, -3, -8, -1],\n [-3, -11, -8, -3],\n [-8, -8, -8, -3],\n [-1, -3, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 150 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, -6, 1, 4],\n [-6, 10, 5, 1],\n [1, 5, -10, 4],\n [4, 1, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Find the inverse of 1/96 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, 3, 8, 2],\n [3, -3, 1, 1],\n [8, 1, 2, -2],\n [2, 1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 111 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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, 2, 6, -8],\n [0, 4, -11, -10],\n [0, 0, -1, 2],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -67 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 1) rounded to the nearest integer?\n[[5, -5, -4, -2],\n [-5, -5, 8, -5],\n [-4, 8, 12, -4],\n [-2, -5, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -5, -12, 8],\n [9, 10, -2, 8],\n [-8, -9, 0, -3],\n [-5, -6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4328 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, -10, -8, 6],\n [-10, 0, 9, -11],\n [-8, 9, -7, -4],\n [6, -11, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -44 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[11, -9, 1, 3],\n [3, -3, 2, -5],\n [7, 3, -3, -1],\n [-5, 8, -9, 1]]\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 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, 2, -4, 1],\n [0, -7, -4, -4],\n [0, 0, 6, 1],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, 6, 0, 8],\n [6, 2, -3, -7],\n [0, -3, 4, 0],\n [8, -7, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 134 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-10, -2, -7, -6],\n [-2, 2, 0, -3],\n [6, 2, -12, -4],\n [-12, 7, -12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[0, 0, -7, -10],\n [8, -3, 12, 2],\n [12, -4, 12, -1],\n [2, 2, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 246 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 4) rounded to the nearest integer?\n[[12, 5, -11, 1],\n [11, 12, -7, 12],\n [-2, 2, -9, -6],\n [-8, -7, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -1, 0, -2],\n [-1, -10, -8, 4],\n [0, -8, -7, 2],\n [-2, 4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 429 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[7, -8, 0, -6],\n [-8, 11, 0, -2],\n [0, 0, 7, 0],\n [-6, -2, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 95 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-1, -11, -12, -2],\n [0, -8, -8, -7],\n [0, 0, 10, -6],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -89 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-9, 10, -2, -1],\n [0, -8, -5, -1],\n [0, 0, 2, -10],\n [0, 0, 0, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-2, 7, 2, -11],\n [-8, -1, -1, -2],\n [-10, -3, 10, -7],\n [-5, 6, 1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -31 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[12, -3, -7, -1],\n [0, -4, -6, -1],\n [0, 0, 10, -3],\n [0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 264 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -10, 10, -1],\n [-5, -3, -11, 1],\n [4, 7, 7, -3],\n [-9, -6, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 970 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[8, -6, 2, 2],\n [-6, 2, -9, 2],\n [2, -9, -12, 10],\n [2, 2, 10, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 350 | MATH |
[
{
"content": "Find the value at position (1, 1) of the inverse of matrix 1/96 * A where A =\n[[-8, -7, 7, -10],\n [0, 1, 4, -5],\n [0, 0, 7, -11],\n [0, 0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[0, 2, 10, 2],\n [2, 10, 6, -4],\n [10, 6, -8, -8],\n [2, -4, -8, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 293 | MATH |
[
{
"content": "Find the inverse of 1/96 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[[0, -12, -10, 8],\n [4, -9, -6, -11],\n [2, -3, 2, -10],\n [-4, 7, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[12, -4, 9, 10],\n [0, -5, 7, 0],\n [0, 0, -10, -12],\n [0, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 4) rounded to the nearest integer?\n[[1, -1, 3, 3],\n [1, 2, 1, 7],\n [4, 2, 1, 2],\n [-3, -12, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -25 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-8, -6, -12, -12],\n [-10, 5, 3, -11],\n [1, 10, 3, -12],\n [-6, 3, -10, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -2, -8, 3],\n [0, 7, -2, 1],\n [0, 0, -9, -4],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[4, 7, 12, -4],\n [0, -10, 11, -10],\n [0, 0, -6, 9],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, -5, 4, -5],\n [0, 7, 2, -3],\n [0, 0, 5, -4],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "Find the value at position (1, 1) of the inverse of matrix 1/96 * A where A =\n[[6, -8, -6, 4],\n [-8, -8, -4, 2],\n [-6, -4, 10, 0],\n [4, 2, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the value at position (3, 4) of the inverse of matrix 1/96 * A where A =\n[[1, 0, -2, 0],\n [0, 3, -2, -4],\n [-2, -2, -2, -10],\n [0, -4, -10, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (4, 4) rounded to the nearest integer?\n[[-12, 5, -12, -11],\n [1, -9, -6, 4],\n [-10, 12, -8, 9],\n [-1, 0, -7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 4, 2, 1],\n [4, -8, 10, 6],\n [2, 10, -4, 8],\n [1, 6, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -409 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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, -1, 2],\n [-8, -3, 0, 4],\n [-1, 0, -9, 5],\n [2, 4, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[-4, -2, -6, 8],\n [-2, 2, -4, -3],\n [-6, -4, 3, 0],\n [8, -3, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-4, -7, -11, -10],\n [0, 6, -12, -9],\n [0, 0, 7, 3],\n [0, 0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -86 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[7, 7, 1, 12],\n [0, -2, 1, -10],\n [0, 0, 3, 11],\n [0, 0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -98 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[12, -11, 0, -11],\n [0, -6, -12, 12],\n [0, 0, 6, -2],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 162 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-10, -3, 6, 1],\n [-3, 7, -1, -4],\n [6, -1, -11, 1],\n [1, -4, 1, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 93 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[11, -11, 12, 11],\n [-12, 6, -4, 10],\n [8, 2, -5, -10],\n [5, -12, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -19 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, -7, -2, -10],\n [0, -4, 10, -7],\n [0, 0, 11, 5],\n [0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -17 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -9, -11, -9],\n [11, 10, 2, -12],\n [1, -11, -1, -11],\n [-2, -2, 10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[5, 12, -4, 3],\n [12, -7, 8, 2],\n [-4, 8, -2, 6],\n [3, 2, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -33 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-8, 0, 3, 5],\n [0, 5, -2, -4],\n [3, -2, -7, 2],\n [5, -4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2980 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[11, 2, -12, 10],\n [0, -7, -9, -4],\n [0, 0, -1, 5],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -127 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-8, -3, -6, -6],\n [1, 8, 4, -11],\n [5, 1, -9, 0],\n [2, -7, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -30 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-9, 1, -1, -1],\n [9, -7, -12, -7],\n [-6, 1, 10, -3],\n [-9, -3, 2, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -22 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[7, -2, 7, 10],\n [12, -10, 9, 5],\n [-12, -5, 7, 10],\n [-5, 9, -2, 12]]\nRound your answer to the nearest integer.\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 1/96 * A where A =\n[[-4, -5, 8, 9],\n [-5, 7, -6, 4],\n [8, -6, 10, -1],\n [9, 4, -1, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 147 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[12, -10, -11, -3],\n [0, -11, -7, 9],\n [0, 0, -3, 10],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, -12, 0, -6],\n [-6, -1, 4, 12],\n [3, 7, 8, 10],\n [10, 2, 7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 105 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[6, -1, 0, -9],\n [-1, 5, 3, 3],\n [0, 3, -6, -4],\n [-9, 3, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-7, 1, -9, 1],\n [-1, 11, 1, 0],\n [-10, 4, -9, 8],\n [-5, -2, -7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -18 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, -6, 7, 2],\n [0, 3, 11, 8],\n [0, 0, -1, 1],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 869 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[1, -8, 7, -1],\n [-11, -6, 2, -7],\n [8, -12, -10, -1],\n [9, -11, -3, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, 11, 11, 10],\n [0, 5, -2, -7],\n [0, 0, -1, -10],\n [0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 733 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[-8, 12, 2, 5],\n [1, -11, 12, -9],\n [5, -4, 2, -9],\n [-11, 1, -8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -19 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, 6, -10, 0],\n [1, 9, -6, 4],\n [1, 11, 11, -11],\n [8, -4, -7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71 | MATH |
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