messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[3, 8, -5, 0],\n [2, -5, 5, -6],\n [8, -10, -11, -9],\n [-9, -9, -12, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -28 | 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[[4, 2, -12, 6],\n [0, -9, 12, 11],\n [0, 0, 8, 4],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -71 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-6, -7, 0, -11],\n [-7, 3, 5, 2],\n [0, 5, -7, 4],\n [-11, 2, 4, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | 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, -4, -2, 7],\n [-4, -11, -1, 1],\n [-2, -1, 0, 1],\n [7, 1, 1, 2]]\n\nPresent the answer in LaTex format: ... | 55 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-2, -1, -6, 10],\n [0, -1, 2, 0],\n [0, 0, 3, 8],\n [0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | -137 | 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[[12, 5, -6, 1],\n [-2, 12, -6, 11],\n [-1, 1, 11, 5],\n [-3, 1, -1, -12]]\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 sum of all entries rounded to the nearest integer?\n[[-1, -11, -1, -5],\n [3, -10, 4, 12],\n [-1, -4, 11, 3],\n [1, 0, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -47 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[1, -2, 10, 4],\n [0, 10, 1, -10],\n [-11, 4, -8, 0],\n [6, -12, 1, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -15 | MATH |
[
{
"content": "Find the value at position (3, 4) of the inverse of matrix 1/96 * A where A =\n[[-10, 3, -11, -10],\n [0, -3, -4, -10],\n [0, 0, 6, 2],\n [0, 0, 0, 5]]\nRound your answer to the nearest integer.\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[[6, -2, 11, -3],\n [0, 4, -9, 3],\n [0, 0, -3, -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"
}
] | -93 | 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[[-4, -12, 2, 8],\n [0, -2, -8, 4],\n [0, 0, 6, 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 sum of absolute values of all entries rounded to the nearest integer?\n[[-4, 3, 5, 0],\n [3, 0, 9, 0],\n [5, 9, 5, -1],\n [0, 0, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 93 | 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, 10, 8, 4],\n [5, 3, -3, 9],\n [0, -9, -9, -6],\n [7, -1, 12, -7]]\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[[3, -11, -2, -11],\n [0, -10, 0, 10],\n [0, 0, -2, 9],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your ans... | -198 | 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[[12, -7, -5, 4],\n [-7, -1, 0, 2],\n [-5, 0, 0, 6],\n [4, 2, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | -37 | MATH |
[
{
"content": "Find the value at position (2, 4) of the inverse of matrix 1/96 * A where A =\n[[10, 11, 0, -6],\n [0, -2, 11, 0],\n [0, 0, -5, 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"
}
] | 176 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, 10, 5, -5],\n [0, 3, 5, 2],\n [0, 0, 10, -7],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your... | -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[[-4, -10, 4, -12],\n [-9, -4, 10, 5],\n [0, -5, 10, 7],\n [0, -6, -5, 3]]\n\nPresent the an... | -11 | 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, 2, 3, -3],\n [0, 4, 8, 11],\n [0, 0, 6, -9],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex forma... | 237 | 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, 0, 7, 6],\n [0, -3, 12, -4],\n [7, 12, 3, -4],\n [6, -4, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your a... | 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[[-2, -8, -1, 8],\n [-8, 11, -7, 2],\n [-1, -7, -8, -4],\n [8, 2, -4, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 7 | 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, -6, 0, 0],\n [-6, -3, 2, 1],\n [0, 2, -1, -1],\n [0, 1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answe... | -54 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[11, -3, 4, -6],\n [-3, 6, 0, 9],\n [4, 0, 6, -4],\n [-6, 9, -4, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 129 | 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, 6, 10, 2],\n [6, 0, -1, 8],\n [10, -1, 6, -12],\n [2, 8, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{You... | 40 | 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, -11, 6, -4],\n [0, -5, -7, 11],\n [0, 0, -10, -7],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex f... | 367 | 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[[10, 4, 0, -2],\n [0, -1, -1, 4],\n [0, 0, 1, -1],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -42 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-5, 0, 5, 1],\n [0, -5, 0, 11],\n [-10, -8, -7, 3],\n [3, -2, 6, 8]]\nRound your answer to the nearest integer.\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[[8, -1, 9, -8],\n [0, -5, -8, 2],\n [0, 0, 7, 4],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | 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[[-12, 7, 1, 7],\n [0, 11, 7, 11],\n [0, 0, -3, 11],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 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[[-5, -11, -4, -10],\n [0, -1, 6, 6],\n [0, 0, -7, 7],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -137 | 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, -10, -2],\n [6, 5, 0, 0],\n [-10, 0, 3, -8],\n [-2, 0, -8, -2]]\n\nPresent the answer in LaTex f... | 245 | 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, -5, 5, 2],\n [0, 1, -11, -7],\n [0, 0, -11, 4],\n [0, 0, 0, -6]]\n\nPresent the answer ... | -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[[-10, 9, -6, -3],\n [0, -7, 1, -8],\n [0, 0, 7, 4],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your ans... | -56 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, -2, 6, 0],\n [-2, 6, 0, 8],\n [6, 0, 10, 0],\n [0, 8, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | 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, -1, -4, -7],\n [-1, 0, -4, -2],\n [-4, -4, -5, 2],\n [-7, -2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 29 | 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[[-12, -12, 5, -2],\n [0, -4, -4, -7],\n [0, 0, 3, 7],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex fo... | 225 | 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, -7, 1],\n [0, -6, -2, 2],\n [0, 0, 5, 6],\n [0, 0, 0, 8]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-12, 12, -6, -11],\n [-8, 10, -6, 5],\n [6, -3, -8, 6],\n [-2, -1, 7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | -57 | 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, -1, -6, -12],\n [-12, -10, -5, -1],\n [1, 10, 7, 3],\n [2, 6, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 13 | 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, -10, -6, -4],\n [-10, 7, -5, 3],\n [-6, -5, 6, 4],\n [-4, 3, 4, 4]]\n\nPresent the answ... | 57 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[2, 4, 2, 1],\n [4, -12, -1, 11],\n [2, -1, -12, 6],\n [1, 11, 6, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "Find the value at position (1, 2) of the inverse of matrix 1/96 * A where A =\n[[-12, 8, 8, -10],\n [0, -6, 0, -4],\n [0, 0, -12, 4],\n [0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, -4, 8, 2],\n [-4, 1, -4, 1],\n [8, -4, -10, 2],\n [2, 1, 2, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 108 | 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, -7, -2, 0],\n [-10, 10, -12, -1],\n [-1, 9, -3, -8],\n [11, -11, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 2) rounded to the nearest integer?\n[[-12, -3, 10, 3],\n [0, 2, -7, -2],\n [0, 0, 9, -3],\n [0, 0, 0, -3]]\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 (4, 4) rounded to the nearest integer?\n[[-6, -4, -10, -5],\n [-1, 9, 4, 6],\n [-3, -12, 0, 11],\n [-5, 12, -12, 9]]\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, 3, 6, 2],\n [3, -5, -1, 1],\n [6, -1, 4, -6],\n [2, 1, -6, -9]]\n\nPresent the answer ... | -34 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-1, 8, 0, -2],\n [8, -3, -6, 8],\n [0, -6, 0, 8],\n [-2, 8, 8, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -40 | 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[[-11, 2, -2, -12],\n [2, -12, 5, -4],\n [-2, 5, -7, 4],\n [-12, -4, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -53 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-6, 8, -9, -10],\n [0, -1, -12, -3],\n [0, 0, -5, 2],\n [0, 0, 0, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1245 | MATH |
[
{
"content": "Find the value at position (4, 1) of the inverse of matrix 1/96 * A where A =\n[[4, 12, -3, 12],\n [0, -1, -12, -12],\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"
}
] | 0 | 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, -6, -2, -4],\n [-6, 1, 4, -4],\n [-2, 4, -10, -1],\n [-4, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your a... | 11 | 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, 9, 11, 6],\n [8, -10, -3, -4],\n [-11, -6, -9, -5],\n [8, -9, -7, 11]]\n\nPresent the answer in LaTex fo... | -13 | 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[[7, -10, -3, -2],\n [-10, 1, 10, 4],\n [-3, 10, 3, -2],\n [-2, 4, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | 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, -2, 1, 7],\n [0, 4, 7, -1],\n [0, 0, 3, 0],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -56 | 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[[-2, -1, -1, -9],\n [0, -12, -1, -9],\n [0, 0, -4, -8],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxe... | 16 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-7, 9, 8, 0],\n [0, -10, -10, 1],\n [0, 0, 8, 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"
}
] | -35 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[6, 10, -1, 8],\n [0, 4, -4, -3],\n [0, 0, -11, 10],\n [0, 0, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 183 | 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[[6, 12, 0, -2],\n [0, 2, 4, -11],\n [0, 0, 5, -1],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 488 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[10, 8, 8, -10],\n [8, 6, 7, 4],\n [8, 7, 10, -5],\n [-10, 4, -5, 3]]\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[[7, -3, -3, -2],\n [-3, 7, 0, 3],\n [-3, 0, 0, 2],\n [-2, 3, 2, 6]]\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[[-7, 0, -3, -2],\n [0, -9, -9, 0],\n [0, 0, 9, 2],\n [0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -13 | 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, 1, -9, -8],\n [-11, -1, 11, -3],\n [8, 11, 1, 0],\n [6, 8, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 13 | 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[[11, -5, 4, -6],\n [-3, -5, 7, -9],\n [-7, 9, -1, -7],\n [-7, 12, 10, 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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, -9, 12, 11],\n [3, -1, -10, 7],\n [2, 10, -5, 8],\n [-8, -5, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Y... | -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[[9, 2, -8, -3],\n [0, -4, 6, 2],\n [0, 0, -4, 4],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\... | -46 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[5, -9, 1, 0],\n [-4, -8, 6, -7],\n [-9, 12, -8, -10],\n [6, 7, 4, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | 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, -4, 11, 0],\n [0, -2, -6, 3],\n [0, 0, -12, -2],\n [0, 0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -48 | 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, -10, 6, -8],\n [-7, -1, -11, 2],\n [-5, 2, 12, 2],\n [9, -10, -7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 9 | 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, 2, -8, -4],\n [2, -8, 1, 11],\n [-8, 1, 2, -2],\n [-4, 11, -2, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 11 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[11, 0, -6, 11],\n [0, 0, 4, 10],\n [-6, 4, 11, -1],\n [11, 10, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | -85 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 3) rounded to the nearest integer?\n[[-7, -4, -12, 1],\n [0, -4, -6, -11],\n [0, 0, 1, 9],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -82 | 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, -11, 4, -2],\n [-12, -12, 9, -8],\n [-6, 5, 1, 11],\n [5, -11, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | -36 | 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, 5, -8, -9],\n [0, 12, 11, -1],\n [0, 0, -10, 12],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 93 | 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, -5, 0, 4],\n [-5, -1, 5, 1],\n [0, 5, 7, -1],\n [4, 1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answe... | -57 | 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, -12, 3, 5],\n [2, -5, -4, 4],\n [-10, 2, -2, 2],\n [-11, 9, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | -288 | 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[[-2, 3, 12, 9],\n [2, -5, -12, -2],\n [-10, -1, 1, -6],\n [8, 12, -11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | 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, -2, 2, 2],\n [-2, 1, -4, 0],\n [2, -4, 9, -10],\n [2, 0, -10, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -20 | 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, -12, -12, -1],\n [2, 3, -1, 6],\n [-12, -5, 11, -8],\n [10, -11, -5, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 27 | 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, 6, -6, -8],\n [0, 8, 5, -1],\n [0, 0, 5, -11],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 166 | 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[[-8, -12, -4, -10],\n [-12, 11, 2, -2],\n [-4, 2, 11, -6],\n [-10, -2, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 2) of the inverse. Round your answer to the nearest integer:\n[[-6, 4, 5, 10],\n [4, 6, -8, 2],\n [5, -8, -10, -1],\n [10, 2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -7 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[12, 9, 8, -12],\n [-7, 4, 5, 5],\n [-8, 8, 0, -6],\n [1, 4, 6, -3]]\nRound your answer to the nearest integer.\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, -4, 2, 6],\n [-4, -12, -8, 0],\n [2, -8, -5, 0],\n [6, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 241 | 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[[-12, -6, -11, 4],\n [-2, -5, -4, 10],\n [1, -10, -5, 1],\n [7, 11, 3, -5]]\n\nPresent the answer in LaTex format: \\... | -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[[-1, -3, -6, 10],\n [-3, -6, 2, -2],\n [-6, 2, 1, 1],\n [10, -2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 140 | 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, 8, -3, 2],\n [0, -9, -3, -7],\n [0, 0, 1, 0],\n [0, 0, 0, -10]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[3, -7, -9, -11],\n [5, -7, -9, -10],\n [3, -6, -6, 2],\n [-6, -9, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your ... | 53 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[1, -12, 4, -7],\n [-10, -2, 9, 11],\n [3, -11, 12, 8],\n [12, -6, -11, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | 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, 1, 10, -4],\n [1, 9, 6, -2],\n [10, 6, 1, 12],\n [-4, -2, 12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your an... | 12 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (1, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -2, 5, -5],\n [0, -11, 11, -1],\n [0, 0, 12, 9],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxe... | 2 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[9, 2, -2, 4],\n [2, 9, 7, 1],\n [-2, 7, -4, 0],\n [4, 1, 0, 5]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, -2, -7, 4],\n [-8, -10, -8, -6],\n [0, -4, 6, -3],\n [7, -1, -9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 94 | 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, 4, -5, 9],\n [4, 0, 4, 1],\n [-5, 4, -1, 2],\n [9, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\b... | -4 | 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[[-9, -6, 0, 6],\n [-6, -7, 2, -7],\n [0, 2, 5, 4],\n [6, -7, 4, 12]]\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[[-9, 11, 7, 12],\n [-8, 11, 10, -12],\n [9, -2, 1, 10],\n [-12, 11, 1, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | 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, 6, -1],\n [-2, -4, 2, -12],\n [-9, 2, -6, -10],\n [-1, -5, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{You... | -13 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[9, -12, 8, 0],\n [0, -6, -9, -6],\n [0, 0, 12, -5],\n [0, 0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -91 | 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, -5, -6, 0],\n [-5, -3, -2, 4],\n [-6, -2, 3, -4],\n [0, 4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 126 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-12, -10, 0, -10],\n [0, 8, -1, 1],\n [0, 0, -8, 2],\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 |
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