messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"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, 2, 12, -6],\n [2, -12, 4, -2],\n [12, 4, 2, 8],\n [-6, -2, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[8, 1, 8, 0],\n [-7, 3, -2, -5],\n [2, 2, 7, -4],\n [11, 4, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-6, 9, -5, 5],\n [0, 8, 6, -1],\n [0, 0, -3, -11],\n [0, 0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 381 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (4, 1) rounded to the nearest integer?\n[[-5, -7, -10, -4],\n [-8, -7, 7, 5],\n [-12, 2, 3, -7],\n [7, -4, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-9, -5, 8, 1],\n [-5, -10, -4, 1],\n [8, -4, -11, 0],\n [1, 1, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | 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[[-5, 7, -7, -3],\n [0, -1, 11, 0],\n [0, 0, 12, 8],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 191 | 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[[4, 10, -7, 4],\n [10, 6, 8, 5],\n [-7, 8, 8, -4],\n [4, 5, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | 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[[-1, 5, 0, 9],\n [-12, 9, -2, -9],\n [-3, 10, 5, 12],\n [-2, -7, -6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 299 | 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, -3, -7, 10],\n [0, -7, -9, -7],\n [0, 0, 10, -9],\n [0, 0, 0, -8]]\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 value at position (2, 4) rounded to the nearest integer?\n[[-10, 7, -12, 6],\n [0, 9, -5, -3],\n [0, 0, 10, 1],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[4, 5, -6, -5],\n [5, -3, -9, 2],\n [-6, -9, 2, -6],\n [-5, 2, -6, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 107 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (4, 1) rounded to the nearest integer?\n[[8, 0, 10, 5],\n [0, -10, -4, 3],\n [10, -4, -8, -1],\n [5, 3, -1, 2]]\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 all entries rounded to the nearest integer?\n[[11, 1, 4, 0],\n [1, -6, 3, -6],\n [4, 3, 3, 0],\n [0, -6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 324 | 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[[3, -3, -8, -3],\n [7, -7, 5, -3],\n [-8, 3, 6, -2],\n [-12, -12, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | 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[[-4, -6, -9, 8],\n [2, -7, 2, -2],\n [-9, 3, 11, -7],\n [-6, 12, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | 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[[0, 7, 2, 6],\n [7, -6, 2, 4],\n [2, 2, 7, -7],\n [6, 4, -7, -2]]\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 (1, 3) of the inverse. Round your answer to the nearest integer:\n[[0, 0, 0, 2],\n [0, 12, -6, -2],\n [0, -6, 2, 8],\n [2, -2, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 336 | 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[[-8, 10, -7, -6],\n [10, 2, 5, 5],\n [-7, 5, 4, -6],\n [-6, 5, -6, -8]]\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[[9, -1, 1, -6],\n [-10, -7, -10, 9],\n [-1, 1, 3, 8],\n [8, -4, 1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 791 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-11, 12, 2, 2],\n [4, 2, -3, -7],\n [3, -6, 9, -4],\n [3, 5, -6, -3]]\nRound your answer to the nearest integer.\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[[12, 4, -7, 6],\n [4, 7, -8, 10],\n [-7, -8, -2, 10],\n [6, 10, 10, 1]]\nRound your answer to the nearest integer.\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[[-7, -7, -6, -10],\n [0, -6, 6, 9],\n [0, 0, 10, 1],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 209 | 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[[10, -2, 4, 0],\n [-2, 12, -4, 6],\n [4, -4, 6, 0],\n [0, 6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 816 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-9, 10, -11, -1],\n [0, 6, 10, 2],\n [0, 0, -4, 1],\n [0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | 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[[-12, 7, 4, -1],\n [0, -3, 11, -2],\n [0, 0, -6, 9],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -64 | 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, -4, -10],\n [-2, 11, -1, -8],\n [-4, -1, 5, 6],\n [-10, -8, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 319 | 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, -11, -5, 8],\n [-6, -8, 4, 5],\n [9, -6, 9, -5],\n [3, -9, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | 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, 9, 9, 10],\n [0, 3, 1, -3],\n [0, 0, 5, -2],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 274 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[-9, -10, -10, -11],\n [0, -4, -10, -12],\n [0, 0, -2, 12],\n [0, 0, 0, -11]]\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[[-4, -3, 0, 11],\n [3, -10, -10, 8],\n [-11, 12, 12, 6],\n [-6, 5, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 212 | 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, 12, 1, -9],\n [0, 12, 10, 9],\n [0, 0, 4, -11],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 256 | 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, -9, 11],\n [6, -11, 11, -4],\n [11, 0, 4, -10],\n [4, 1, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[4, 2, -6, 0],\n [2, -5, 10, 6],\n [-6, 10, 10, 2],\n [0, 6, 2, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 472 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 4, 5, 0],\n [4, -2, -2, -6],\n [5, -2, 1, -1],\n [0, -6, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | 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[[-9, -8, -9, 2],\n [-8, -4, -8, -7],\n [-9, -8, -4, -8],\n [2, -7, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Find the value at position (4, 3) of the inverse of matrix 1/96 * A where A =\n[[-4, -8, 11, 1],\n [-6, 8, 9, -7],\n [0, -1, 2, 6],\n [-1, 2, -4, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | 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[[6, -1, -1, -4],\n [0, -11, -3, 4],\n [0, 0, -5, 1],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | 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, -10, 6],\n [-4, 12, -12, -12],\n [-11, -2, -7, 1],\n [-7, 10, -7, 6]]\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[[-5, -11, 10, 9],\n [0, -6, -7, 6],\n [0, 0, -11, 5],\n [0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -56 | 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[[12, -9, 0, -10],\n [0, -5, 11, 8],\n [0, 0, 8, -9],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 187 | 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[[-11, -9, -12, 8],\n [4, 4, 11, 2],\n [-4, 10, 0, 7],\n [3, -4, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | 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, -11, -7, 1],\n [0, 6, 9, -3],\n [0, 0, 5, 6],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | 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, 7, 6],\n [-6, -9, 0, 2],\n [7, 0, -8, 2],\n [6, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14742 | 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[[-10, 10, -4, -6],\n [0, -10, 12, -2],\n [0, 0, -7, -1],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-6, 5, 12, 12],\n [-5, -11, 10, 3],\n [-5, 4, -12, -2],\n [10, 9, -1, 10]]\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 of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-10, 8, 11, 1],\n [0, 4, 6, -11],\n [0, 0, -10, 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"
}
] | 24 | MATH |
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/96 * A where A =\n[[9, -2, -8, -5],\n [-2, -4, -2, 2],\n [-8, -2, -8, 0],\n [-5, 2, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[4, 7, -2, -11],\n [0, -4, -6, -6],\n [0, 0, -11, 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"
}
] | 5 | 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, 12, -9],\n [0, -1, -9, 8],\n [0, 0, -7, -9],\n [0, 0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1879 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (4, 3) of the inverse. Round your answer to the nearest integer:\n[[-2, 2, -1, 7],\n [0, -2, -2, 1],\n [0, 0, -7, 12],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | 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[[-9, -9, 3, 4],\n [-9, 5, 1, 3],\n [3, 1, -2, 4],\n [4, 3, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | 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, 1, 3],\n [6, 9, 1, 10],\n [-2, -7, -1, -7],\n [4, -10, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1510 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[5, 11, -9, -2],\n [10, 5, 7, 1],\n [3, -1, 10, -1],\n [-6, 7, 11, -6]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 10, 2, -9],\n [0, 5, -10, -6],\n [0, 0, -5, 8],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -42 | MATH |
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/96 * A where A =\n[[-6, -10, -11, -10],\n [0, 6, -4, -12],\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"
}
] | -40 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[11, -1, 7, 6],\n [0, 6, 0, 10],\n [0, 0, -12, 6],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | 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, -3, 6],\n [4, -5, -2, 0],\n [-3, -2, -6, 2],\n [6, 0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -325 | 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, 0, 2, 9],\n [0, -9, -12, 2],\n [2, -12, 0, 4],\n [9, 2, 4, -1]]\nRound your answer to the nearest integer.\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 at position (2, 2) of the inverse. Round your answer to the nearest integer:\n[[-9, -1, -9, 6],\n [-4, -2, -7, -4],\n [-3, 10, -2, 4],\n [10, 3, -2, 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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 8, -2, 11],\n [7, -11, -10, 7],\n [-8, -11, -3, 9],\n [12, -2, 9, 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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-6, 4, 6, -5],\n [4, 4, -8, -3],\n [6, -8, 7, 2],\n [-5, -3, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 162 | 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, -4, 2, 4],\n [-4, -5, -5, 6],\n [2, -5, -6, -4],\n [4, 6, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 218 | 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[[-11, -3, -10, 11],\n [-7, 3, -1, -1],\n [7, 1, -1, 11],\n [5, 4, 11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | 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[[6, -3, 0, -6],\n [-3, -6, 6, 0],\n [0, 6, 10, -5],\n [-6, 0, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -221 | 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, -8, 10, -2],\n [-6, 8, -4, -7],\n [-6, -6, -2, -10],\n [-8, 11, -3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | 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, -6, 4, -12],\n [0, 11, 8, 0],\n [-1, 0, 3, -6],\n [-12, -1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -734 | 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[[-5, -7, 4, 10],\n [0, -3, -12, -7],\n [0, 0, -1, -10],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -910 | 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, -4, 8, -6],\n [0, -5, 11, 0],\n [0, 0, 10, 7],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 123 | MATH |
[
{
"content": "Find the value at position (2, 3) of the inverse of matrix 1/96 * A where A =\n[[8, 8, -3, 12],\n [0, -9, -4, -3],\n [0, 0, -5, 7],\n [0, 0, 0, 9]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-10, 1, 9, -2],\n [1, 1, -5, -2],\n [9, -5, -11, 3],\n [-2, -2, 3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -22 | 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, -5, -1, 1],\n [0, -5, 11, -10],\n [0, 0, 10, -11],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 137 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[12, 7, 3, 3],\n [2, -9, -1, -5],\n [8, -2, -11, 11],\n [4, -11, 7, 10]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -8, 5, -8],\n [0, -12, -2, 8],\n [0, 0, 1, -12],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 196 | MATH |
[
{
"content": "Find the value at position (2, 1) of the inverse of matrix 1/96 * A where A =\n[[-3, -2, -1, -2],\n [-2, 11, 6, 1],\n [-1, 6, 7, 0],\n [-2, 1, 0, 7]]\nRound your answer to the nearest integer.\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 value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[-2, 12, 6, -5],\n [12, -1, -1, -2],\n [6, -1, 12, -2],\n [-5, -2, -2, 4]]\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[[11, -5, 12, 0],\n [11, -12, 1, 4],\n [7, -5, -10, 11],\n [0, 8, -2, -5]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-2, -1, -2, 4],\n [-1, 7, -3, -2],\n [-2, -3, 4, -1],\n [4, -2, -1, -9]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[6, 3, -12, -3],\n [9, 4, -6, -4],\n [5, -12, -6, -4],\n [-8, -1, 4, 11]]\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 at position (1, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 1, 12, -2],\n [0, -12, 12, -3],\n [0, 0, 4, 2],\n [0, 0, 0, 2]]\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 all entries of the inverse. Round your answer to the nearest integer:\n[[10, -10, 11, -1],\n [0, 10, 12, 0],\n [0, 0, 10, -7],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -26 | 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[[8, 3, 1, 0],\n [0, 10, 7, 0],\n [0, 0, -2, 9],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -48 | 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[[-6, -4, -10, -2],\n [1, -12, -9, 11],\n [1, 12, -11, -11],\n [-6, 3, 11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-5, -11, 10, 4],\n [4, -11, 0, -9],\n [-4, -11, -2, 4],\n [-6, -4, 6, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -40 | 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[[-5, -2, -4, -6],\n [-2, -4, -3, 2],\n [-4, -3, 2, -4],\n [-6, 2, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 265 | 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, -6, -2, 5],\n [-6, 5, -1, 8],\n [-2, -1, -10, -8],\n [5, 8, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (4, 1) rounded to the nearest integer?\n[[6, 2, -2, 6],\n [2, -5, 8, 5],\n [-2, 8, 5, 2],\n [6, 5, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65 | 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, 5, 2, -10],\n [5, -6, 0, 3],\n [2, 0, -12, -4],\n [-10, 3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -47 | 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[[11, 8, -9, -12],\n [0, 12, 12, -12],\n [0, 0, 2, 8],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1711 | 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[[-11, -7, -5, 10],\n [0, 1, 12, -2],\n [0, 0, 11, 9],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 85 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, 9, 3, -3],\n [0, 7, 8, -1],\n [0, 0, 8, 8],\n [0, 0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 173 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, -8, 0, -4],\n [-8, 4, 0, -6],\n [0, 0, -5, 0],\n [-4, -6, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -37 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[1, -10, 11, -8],\n [0, -12, -6, 3],\n [0, 0, -12, -3],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 94 | 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[[4, 4, -2, 4],\n [4, 10, -3, -4],\n [-2, -3, -10, -2],\n [4, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | 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, 2, 3, 7],\n [2, 4, 0, 4],\n [3, 0, -9, 10],\n [7, 4, 10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | 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[[-10, 8, 4, -4],\n [8, 0, -2, 10],\n [4, -2, -11, 6],\n [-4, 10, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[3, 11, -12, 5],\n [-11, -12, 7, -5],\n [8, -12, 4, -7],\n [-4, -2, -5, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 498 | 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, -4, -2, -4],\n [-4, 1, 8, 8],\n [-2, 8, -12, -1],\n [-4, 8, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | 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, 11, -4, 12],\n [0, 7, -12, -8],\n [0, 0, -5, 8],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | 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[[3, -4, 1, 1],\n [0, 12, -10, 9],\n [0, 0, -4, -5],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -50 | 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, 7, -5, 6],\n [8, -12, 8, 1],\n [12, 12, -4, -3],\n [11, -7, -7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
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