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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[2, -6, 4, 6],\n [-6, -3, -4, -2],\n [4, -4, 1, -6],\n [6, -2, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 104 | 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[[-3, -8, 5, 12],\n [1, 10, -7, 4],\n [-8, -8, 7, 4],\n [-8, -11, -7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | 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, 12, 2, 4],\n [0, 8, -12, 8],\n [0, 0, -4, -12],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | 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[[-12, -6, 6, -2],\n [-6, 1, -2, 4],\n [6, -2, -11, -11],\n [-2, 4, -11, -9]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, -2, 7, -4],\n [-2, -12, -2, 2],\n [7, -2, -10, 4],\n [-4, 2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 608 | 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[[-5, 7, 3, 4],\n [0, -11, -10, 6],\n [0, 0, -4, 12],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -76 | 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[[4, 6, 7, -3],\n [-9, 9, -9, -9],\n [-1, -3, 6, 11],\n [4, 6, -1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | 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[[-6, -8, 6, -7],\n [7, 8, -12, -5],\n [8, -9, -8, 11],\n [-12, -1, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-12, -4, 8, 0],\n [-4, 6, 5, -2],\n [8, 5, -2, 2],\n [0, -2, 2, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 133 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (1, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 0, 3, 7],\n [0, -12, 3, -11],\n [0, 0, 4, 1],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | 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, 9, -7, -5],\n [0, 12, -7, 9],\n [0, 0, -4, 3],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | 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[[-2, -2, 4, -6],\n [-2, 1, 1, 2],\n [4, 1, 10, -4],\n [-6, 2, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -23 | 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[[-3, -8, 7, -8],\n [-10, 4, 5, -5],\n [-9, 8, -8, 6],\n [10, -6, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -268 | 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[[11, 6, 4, 0],\n [0, -6, -7, 6],\n [0, 0, -6, -11],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | 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[[3, 0, -1, 0],\n [0, -7, 0, -6],\n [-1, 0, 2, 10],\n [0, -6, 10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[11, 2, 8, 7],\n [2, 6, 2, -2],\n [8, 2, -3, 0],\n [7, -2, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[3, -1, 8, -1],\n [0, 9, -1, 6],\n [0, 0, 10, -3],\n [0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | 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[[-8, 3, 0, 2],\n [0, 4, 6, -8],\n [0, 0, -7, 12],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | 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[[-12, -1, 7, 10],\n [3, 6, -9, 1],\n [-5, 12, -4, 3],\n [-4, -1, 7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 119 | 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[[-12, 6, 0, 6],\n [6, -10, 8, 2],\n [0, 8, 3, -8],\n [6, 2, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-3, -8, 4, -4],\n [-10, 12, -2, 6],\n [-10, -11, -10, 11],\n [-9, -11, 3, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 145 | 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[[-7, -6, -4, -1],\n [-6, 1, -4, -7],\n [-4, -4, 2, -7],\n [-1, -7, -7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -22 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[1, 2, 0, 10],\n [2, -10, -4, -2],\n [0, -4, 8, 6],\n [10, -2, 6, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71 | 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[[9, -11, -8, -8],\n [0, 4, -7, -4],\n [0, 0, -2, -9],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -145 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 3, 12, -1],\n [1, -2, 3, 11],\n [8, 4, 12, 2],\n [-9, 3, -4, 0]]\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 at position (4, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -2, -5, 6],\n [2, 1, 5, -3],\n [-6, -3, 1, 6],\n [-11, -10, 3, -7]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 10, 2, 3],\n [10, 5, -1, 7],\n [2, -1, -3, -5],\n [3, 7, -5, 10]]\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 value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[-12, 1, 11, -4],\n [4, 10, -3, 5],\n [11, 4, 2, -4],\n [-5, 7, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | 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, -6, -3, 9],\n [5, 11, 6, 5],\n [-8, 4, 1, -3],\n [3, 12, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -33 | 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[[8, 0, 6, 0],\n [0, 12, 10, -6],\n [6, 10, 4, -5],\n [0, -6, -5, -6]]\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[[12, 3, -11, -2],\n [0, 4, 6, -4],\n [0, 0, -9, -7],\n [0, 0, 0, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | 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, -1, 3, -11],\n [0, 2, 11, -5],\n [0, 0, 10, 10],\n [0, 0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 192 | 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[[8, 2, 2, 8],\n [-12, -8, -2, 0],\n [-8, 1, -3, 3],\n [-3, 11, 12, 0]]\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, 11, -5, 6],\n [0, 1, -4, -5],\n [0, 0, 4, 9],\n [0, 0, 0, -8]]\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[[-2, -4, 4, 8],\n [-4, -7, -4, -1],\n [4, -4, 9, -4],\n [8, -1, -4, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | 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, -3, -9, -5],\n [-11, -5, 2, -9],\n [-9, -11, 6, -9],\n [-3, 7, -9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -27 | 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, -3, 0, 12],\n [11, 6, 5, 11],\n [-6, 2, -3, 6],\n [7, 3, -1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 118 | MATH |
[
{
"content": "Find the value at position (4, 1) of the inverse of matrix 1/96 * A where A =\n[[10, 6, 10, 2],\n [0, 2, 9, 12],\n [0, 0, -1, 8],\n [0, 0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the value at position (4, 1) of the inverse of matrix 1/96 * A where A =\n[[-7, 2, 0, 1],\n [2, -7, -10, 2],\n [0, -10, 1, -4],\n [1, 2, -4, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-4, 0, -4, 11],\n [-11, 10, 12, 7],\n [-9, -3, 9, 4],\n [8, -4, -10, -12]]\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, -8, 0, 5],\n [-8, -10, -2, 2],\n [0, -2, -2, 1],\n [5, 2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[7, 5, -2, 0],\n [5, 6, 0, 1],\n [-2, 0, 7, -4],\n [0, 1, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | 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[[-10, -7, 1, -12],\n [-7, 12, -6, -2],\n [1, -6, 1, -2],\n [-12, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -95 | 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[[-9, -1, -10, 1],\n [-11, 6, 7, -11],\n [-12, -5, -9, 11],\n [2, 7, 9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 89 | MATH |
[
{
"content": "Find the value at position (1, 1) of the inverse of matrix 1/96 * A where A =\n[[4, -7, 2, 0],\n [-7, -9, 4, 4],\n [2, 4, -11, 2],\n [0, 4, 2, -9]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries rounded to the nearest integer?\n[[-2, -2, -4, 2],\n [-2, -9, 10, 1],\n [-4, 10, -1, 6],\n [2, 1, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 137 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 2) rounded to the nearest integer?\n[[-5, 1, -11, -9],\n [0, 6, 4, -8],\n [0, 0, -9, -1],\n [0, 0, 0, -2]]\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 1/96 * A where A =\n[[11, -10, -6, 2],\n [-10, -9, -2, -2],\n [-6, -2, -12, 9],\n [2, -2, 9, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | 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[[-12, -1, -7, 7],\n [5, 0, 5, -8],\n [-4, 1, -7, -11],\n [-8, 6, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -24 | 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, 6, -11, -7],\n [-6, 6, -12, -2],\n [-3, 6, -6, 9],\n [8, -9, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-5, 7, -6, 0],\n [7, 8, 1, -10],\n [-6, 1, 0, 0],\n [0, -10, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -17 | 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[[8, 6, -1, 4],\n [6, -9, -4, 1],\n [-1, -4, 9, -2],\n [4, 1, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 7, -1, 2],\n [7, 0, -4, 6],\n [-1, -4, 12, 2],\n [2, 6, 2, 6]]\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -8, 2, -8],\n [7, 6, 9, -10],\n [-12, 3, 1, -9],\n [0, 5, 7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-7, 8, -4, 4],\n [-8, -11, -8, -5],\n [-8, 6, 7, -8],\n [8, 3, -10, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-6, -3, -7, -1],\n [-6, -6, -2, 9],\n [11, -8, 12, -12],\n [-2, 9, -12, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 125 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[3, -4, 7, -6],\n [0, 4, 3, 5],\n [0, 0, -3, -6],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | 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[[7, 11, -4, -5],\n [-2, 5, -10, -9],\n [8, -11, -3, -7],\n [-6, 5, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | 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, -10, 9, 7],\n [0, 3, -11, -5],\n [0, 0, 2, -9],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2576 | 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[[9, -8, 0, -1],\n [-8, -8, -9, 5],\n [10, -7, 6, 4],\n [-8, 12, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | 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, 4, 3, 0],\n [0, 5, -12, 7],\n [0, 0, 10, 4],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 225 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[9, -5, -6, 4],\n [-5, -8, 2, -6],\n [-6, 2, -4, -2],\n [4, -6, -2, -4]]\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[[-2, -6, 2, -10],\n [0, -5, 2, 1],\n [0, 0, -5, 12],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -46 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-5, 2, -8, 2],\n [0, 7, 12, 11],\n [0, 0, -10, -11],\n [0, 0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -26 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[4, -2, 4, -1],\n [0, -3, -12, 1],\n [0, 0, -8, -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"
}
] | 14 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, 4, 8, -7],\n [4, 5, -6, 2],\n [8, -6, -12, -2],\n [-7, 2, -2, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -30 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[12, -2, 1, 2],\n [-2, 11, 6, -6],\n [1, 6, 12, 3],\n [2, -6, 3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[10, 5, 2, 3],\n [0, -6, -8, -1],\n [0, 0, 4, 8],\n [0, 0, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-9, 1, -4, 2],\n [1, -11, -1, 6],\n [-4, -1, 3, -6],\n [2, 6, -6, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -28 | 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, 10, -7, 12],\n [-3, -7, 12, -7],\n [6, -10, 8, 9],\n [-2, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | 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[[7, 4, 0, -7],\n [4, 3, -7, -3],\n [0, -7, 0, -3],\n [-7, -3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -26 | 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[[6, -2, -1, 0],\n [-2, 0, 0, -4],\n [-1, 0, 8, 4],\n [0, -4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-3, 1, 0, 2],\n [1, 7, 2, 6],\n [0, 2, -9, -8],\n [2, 6, -8, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | 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, -6, -6, 11],\n [12, -3, 0, 3],\n [11, 7, 3, 3],\n [12, -1, -9, 7]]\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 absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 2, 8, 9],\n [0, 12, -8, 7],\n [0, 0, -11, 4],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 98 | 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[[9, -8, 6, 9],\n [0, 4, -7, -1],\n [0, 0, -10, 3],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[5, 5, 3, 1],\n [-11, 8, 3, -11],\n [12, 8, 2, -8],\n [-4, -4, -8, 6]]\nRound your answer to the nearest integer.\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 absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[11, 4, 0, 5],\n [4, 3, 0, 4],\n [0, 0, 3, 0],\n [5, 4, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 167 | MATH |
[
{
"content": "Find the value at position (3, 1) of the inverse of matrix 1/96 * A where A =\n[[-5, 7, 7, -3],\n [3, 11, -7, 5],\n [-1, 0, 2, -6],\n [12, 8, 1, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[2, 0, -12, 12],\n [3, 8, 12, 12],\n [6, 4, -3, 9],\n [8, -11, 11, 11]]\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 sum of all entries rounded to the nearest integer?\n[[4, 3, 2, 3],\n [0, -7, 6, -3],\n [0, 0, 3, 4],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | 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[[7, 12, 4, -2],\n [0, 7, 9, 1],\n [0, 0, -11, -2],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -24 | 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, 4, -12, -1],\n [-5, 3, 1, 2],\n [10, 7, -6, -12],\n [-12, 2, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1123 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 4) rounded to the nearest integer?\n[[0, 6, 9, -5],\n [-4, 0, 8, 4],\n [-1, -7, 10, 1],\n [4, 8, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -66 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, 12, 7, -6],\n [0, -8, -12, -1],\n [0, 0, -2, 1],\n [0, 0, 0, 5]]\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[[2, -2, -5, 5],\n [-4, -3, -1, 5],\n [6, 11, 6, -8],\n [-9, -11, -10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the value at position (2, 2) of the inverse of matrix 1/96 * A where A =\n[[7, -10, 2, 9],\n [0, 2, 7, 1],\n [0, 0, 11, 6],\n [0, 0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 4) of the inverse. Round your answer to the nearest integer:\n[[-4, -9, 0, 4],\n [-9, -9, 8, 8],\n [0, 8, 1, 3],\n [4, 8, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-9, 1, -8, -4],\n [1, -7, 3, -3],\n [-8, 3, 4, -3],\n [-4, -3, -3, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 273 | 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[[7, -3, 8, 0],\n [5, 4, -5, 8],\n [-10, 0, 12, -2],\n [3, 0, 10, 8]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -1, -12, -3],\n [-7, 8, 7, -3],\n [5, 3, -1, 1],\n [-1, -10, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[7, -9, -7, 3],\n [0, -11, -11, -7],\n [0, 0, 1, -9],\n [0, 0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 308 | 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[[-6, -1, -8, 1],\n [0, 1, 10, -4],\n [0, 0, 8, -3],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[1, 8, 10, 6],\n [-7, 1, 0, 6],\n [-6, 2, -8, -12],\n [-8, 4, -11, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | 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, 6, 9, -11],\n [0, -8, 7, -7],\n [0, 0, -12, -4],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 138 | 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[[10, 1, 11, 10],\n [-8, 12, -4, 9],\n [1, 10, -4, -8],\n [7, -4, -9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | 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[[12, -7, -7, -9],\n [-12, 8, 2, 12],\n [0, -4, -2, -2],\n [3, -1, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 297 | 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, -5, -10, -7],\n [0, 2, -2, 12],\n [0, 0, 3, 0],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -480 | 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[[-2, 11, 0, 3],\n [-3, 10, 6, 6],\n [2, -8, 8, -7],\n [9, -9, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | 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[[-7, 7, 8, 1],\n [0, -12, 6, -5],\n [0, 0, 7, 3],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 102 | MATH |
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