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 value at position (3, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -4, 11, -6],\n [10, -1, -5, 8],\n [11, 3, -4, 3],\n [-10, 12, -9, -7]]\n\nPresent the answer in LaTex format: \\b... | -48 | 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, 6, -12],\n [1, -8, -8, -2],\n [8, 4, 6, -11],\n [-9, 8, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your ans... | -34 | 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, 2, -6],\n [8, -9, -8, -4],\n [2, -8, -2, -6],\n [-6, -4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{You... | -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[[-3, -12, -7, -9],\n [-3, 9, 5, -2],\n [-11, 5, -7, 2],\n [-2, 2, 2, 10]]\n\nPresent the answer in LaTex... | 120 | 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, 7, 10, 6],\n [0, -3, 8, -6],\n [0, 0, 9, -11],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 67 | MATH |
[
{
"content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[-2, 6, 0, 4],\n [6, 8, 2, 0],\n [0, 2, 4, -5],\n [4, 0, -5, 2]]\nRound your answer to the nearest integer.\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, 3) rounded to the nearest integer?\n[[0, 11, -11, 2],\n [-9, 4, 0, 1],\n [2, -6, 10, -1],\n [3, -2, -5, 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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[6, 7, -10, -2],\n [6, 5, 12, -7],\n [-10, -5, -12, 1],\n [10, -4, -9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | -15 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[12, -6, -2, 0],\n [-6, -12, -2, -8],\n [-2, -2, -6, -1],\n [0, -8, -1, 8]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 12, 0, -1],\n [12, 2, 6, 2],\n [0, 6, 5, 6],\n [-1, 2, 6, -6]]\n\nPresent the answer in LaTex format: \\... | 12 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[2, -3, -9, 9],\n [5, -3, -12, 12],\n [-4, 10, 0, 8],\n [7, 6, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 25 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-5, -2, -8, 2],\n [-2, -4, 5, -2],\n [-8, 5, 6, -7],\n [2, -2, -7, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -75 | 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, -8, -7, -11],\n [0, 4, -11, 6],\n [0, 0, 2, -1],\n [0, 0, 0, -9]]\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 at position (4, 2) rounded to the nearest integer?\n[[-11, 9, -5, 1],\n [0, 12, -10, 11],\n [0, 0, -8, 9],\n [0, 0, 0, -10]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[0, -5, 12, -12],\n [0, -11, -2, 12],\n [-1, -12, -12, 0],\n [8, -6, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -12 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, 7, -1, -8],\n [0, 2, -1, -11],\n [0, 0, 2, -4],\n [0, 0, 0, 6]]\n\nPresent the answer... | 104 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -4, 4, 0],\n [-4, -2, -6, 0],\n [4, -6, -7, -10],\n [0, 0, -10, 7]]\n\nPresent the answer in LaTex format: \\box... | -38 | 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, -2, -6, -8],\n [-2, 5, -4, 2],\n [-6, -4, -10, -10],\n [-8, 2, -10, 4]]\n\nPresent the answer in LaTex f... | -2108 | 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, 3, -7, -12],\n [-8, -6, 10, -4],\n [8, -8, 12, -11],\n [-12, 4, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 289 | MATH |
[
{
"content": "Find the value at position (2, 1) of the inverse of matrix 1/96 * A where A =\n[[7, 0, 1, 12],\n [3, -6, 12, -7],\n [-6, 5, -10, -7],\n [-1, -6, 10, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1560 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, 4, -7, 1],\n [0, 4, 7, 12],\n [0, 0, 9, 4],\n [0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | 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[[-1, 11, -7, 6],\n [0, -4, -8, -7],\n [0, 0, 12, 9],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -787 | 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, 1, -8],\n [12, 6, 4, 10],\n [11, -5, 1, 5],\n [-12, 4, -5, 11]]\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 at position (4, 4) of the inverse. Round your answer to the nearest integer:\n[[-6, -10, -2, 10],\n [0, 10, 7, -2],\n [0, 0, 10, -2],\n [0, 0, 0, 12]]\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[[0, 6, 1, -1],\n [-3, -7, -6, -11],\n [-5, 3, 1, -6],\n [3, 3, -7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 166 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[-8, -1, -9, 12],\n [4, -1, -5, -4],\n [10, 1, 12, 1],\n [11, 11, 9, -2]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 3, 6, -1],\n [-1, -11, 10, 2],\n [-2, -12, -5, -6],\n [-8, 11, -11, 7]]\n\nPresent the answer in LaTex fo... | -77 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 4) rounded to the nearest integer?\n[[12, -1, 7, 4],\n [-1, 0, -11, 0],\n [7, -11, 4, 6],\n [4, 0, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 0, -11, -12],\n [0, 1, 3, 11],\n [0, 0, -10, 0],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex fo... | 1456 | 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, 8, 7, -11],\n [8, -9, -2, -12],\n [7, -2, -5, -2],\n [-11, -12, -2, 9]]\n\nPresent the answer in LaT... | 446 | 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, -5, -4, -9],\n [-5, 1, 4, 1],\n [-4, 4, 3, -6],\n [-9, 1, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -44 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[10, -3, 10, 3],\n [0, 9, 3, 7],\n [0, 0, 3, 9],\n [0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 63 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (4, 3) rounded to the nearest integer?\n[[-8, -12, 11, -1],\n [7, 9, -3, 6],\n [-7, 10, -5, 10],\n [4, -12, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -10, 3, 6],\n [-10, -7, 6, 7],\n [-2, 12, 8, -4],\n [-7, -8, 8, -6]]\n\nPresent the ans... | 9 | 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[[8, -7, -2, -7],\n [0, -8, 2, -7],\n [0, 0, 6, 7],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex forma... | 107 | 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[[-1, 0, 10, -5],\n [0, -6, 4, -8],\n [10, 4, -10, 0],\n [-5, -8, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 8 | 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, -7, 7, -2],\n [-7, 7, 2, 1],\n [7, 2, -11, -2],\n [-2, 1, -2, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 21 | 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, -6, -8, 2],\n [0, 2, 9, 7],\n [0, 0, 3, 10],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -608 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[2, -6, -3, -11],\n [-6, 12, 5, 7],\n [-3, 5, 6, 3],\n [-11, 7, 3, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "Find the value at position (2, 3) of the inverse of matrix 1/96 * A where A =\n[[8, 10, -5, 1],\n [10, 10, -4, -11],\n [-5, -4, 11, -6],\n [1, -11, -6, -12]]\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 sum of all entries rounded to the nearest integer?\n[[-2, -6, -9, 11],\n [0, -2, 4, 3],\n [0, 0, 5, 7],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 352 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-7, -6, -12, -7],\n [12, -5, -3, -12],\n [-2, 3, -2, 12],\n [5, -10, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | -5 | 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, -10, -2, 11],\n [-10, 5, 8, -10],\n [6, -9, 12, -6],\n [0, -2, 8, 0]]\n\nPresent the an... | 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[[-3, -11, -9, -9],\n [0, -12, 9, -4],\n [0, 0, 12, 9],\n [0, 0, 0, 8]]\n\nPresent the answe... | -46 | MATH |
[
{
"content": "Find the value at position (3, 1) of the inverse of matrix 1/96 * A where A =\n[[-5, 4, -8, 10],\n [-6, -9, 8, -1],\n [-7, 3, 1, -12],\n [0, -11, -3, -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 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, -12, 6, -6],\n [0, -6, -1, -11],\n [0, 0, 10, 7],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 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[[-1, -4, -6, 8],\n [-6, -5, -10, -7],\n [7, 2, 2, 2],\n [-12, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 130 | 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, 9, -11, 9],\n [9, -8, -10, 11],\n [-2, 8, -9, -10],\n [5, 5, 5, -8]]\n\nPresent the answer in LaTex format: \\bo... | 0 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-12, -3, -7, -6],\n [-4, 11, -10, -11],\n [-4, 3, 11, -10],\n [1, 10, -10, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 70 | 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, 8, 11, -10],\n [-2, 9, 9, 5],\n [-4, -11, 5, 4],\n [-3, 6, 10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 105 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[1, 10, 4, -5],\n [10, -11, -6, -4],\n [4, -6, 1, 6],\n [-5, -4, 6, 10]]\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 value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[-1, -4, -3, 4],\n [0, -12, -9, -11],\n [0, 0, -7, -11],\n [0, 0, 0, 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 sum of all entries rounded to the nearest integer?\n[[2, -6, 6, 0],\n [-6, -6, 12, 4],\n [6, 12, -2, -2],\n [0, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 870 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-12, -10, -9, 11],\n [0, 8, -8, 8],\n [0, 0, 3, -3],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -51 | 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[[-1, 12, -7, 1],\n [0, -9, -8, 1],\n [0, 0, 8, -7],\n [0, 0, 0, 5]]\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[[-9, -8, 3, 7],\n [0, 9, -4, -8],\n [0, 0, -11, 9],\n [0, 0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -54 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-11, 2, -6, -12],\n [-5, 1, 1, -9],\n [-4, -7, 1, 0],\n [8, 10, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 184 | 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, -6, 0, 2],\n [-6, 5, 4, 0],\n [0, 4, 7, 11],\n [2, 0, 11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87 | 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, 6, -5, 11],\n [0, -9, 0, 10],\n [0, 0, 2, 1],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | -59 | 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, 4, 5, -3],\n [0, 4, 0, -8],\n [0, 0, 4, 1],\n [0, 0, 0, -9]]\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 all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -9, 0, 7],\n [0, 12, -1, 10],\n [0, 0, -3, -11],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your... | -300 | 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, -3, -4, 9],\n [-9, -8, -8, 11],\n [3, 7, 4, 8],\n [5, -9, 11, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 6 | 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, 8, -12, 5],\n [0, -6, -9, -1],\n [0, 0, 3, -2],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex forma... | 1379 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (1, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, -9, 12, -9],\n [8, 12, 7, 10],\n [4, 7, 2, 12],\n [-7, -11, -7, 12]]\n\nPresent the answer in LaTex format: \\bo... | 96 | 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[[-12, 3, -2, 4],\n [3, 10, 4, 12],\n [-2, 4, 9, 0],\n [4, 12, 0, -9]]\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 absolute values of all entries rounded to the nearest integer?\n[[11, 9, 4, 5],\n [11, 12, -8, 10],\n [-2, 6, 2, 11],\n [5, 1, 10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 97 | MATH |
[
{
"content": "Find the value at position (2, 1) of the inverse of matrix 1/96 * A where A =\n[[0, 2, 0, 5],\n [2, -5, -1, -2],\n [0, -1, -12, 6],\n [5, -2, 6, -5]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -2, -5, 4],\n [10, -11, -11, -3],\n [3, -1, 7, 2],\n [-11, 8, 8, -10]]\n\nPresent the answer in LaTex for... | 13 | 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, -1, -9, 6],\n [9, -7, 2, -5],\n [-7, -8, 11, 7],\n [11, 1, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 88 | 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, 12, -9, 1],\n [0, -10, -7, -8],\n [0, 0, -3, 2],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -139 | 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, 6, 0],\n [-4, 4, -4, 0],\n [6, -4, -1, 0],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\b... | 112 | 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, 2, -1],\n [-1, -10, -7, 4],\n [2, -7, -10, -2],\n [-1, 4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{... | 271 | 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[[9, -1, -10, 4],\n [-2, 1, -1, 9],\n [-1, 8, -1, 11],\n [12, 11, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2096 | MATH |
[
{
"content": "Find the value at position (1, 2) of the inverse of matrix 1/96 * A where A =\n[[-11, 8, 5, -2],\n [8, 0, -4, 9],\n [5, -4, -6, 7],\n [-2, 9, 7, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, 7, -12, -11],\n [4, -11, 7, 9],\n [7, -4, -9, 11],\n [11, 8, 5, 7]]\n\nPresent the answer in LaTex format... | -5 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 4) of the inverse. Round your answer to the nearest integer:\n[[8, -6, -9, -1],\n [0, 1, 4, 4],\n [1, -10, -10, -2],\n [-3, -7, 3, -2]]\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[[8, 6, 0, 0],\n [6, 10, -2, 6],\n [0, -2, 0, -6],\n [0, 6, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2020 | 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[[-1, -9, -5, 11],\n [0, 7, -6, 12],\n [0, 0, 6, 9],\n [0, 0, 0, -5]]\n\nPresent the answer ... | -874 | 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, -3, -4, 6],\n [-3, -7, 0, 0],\n [-4, 0, -2, 9],\n [6, 0, 9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 118 | MATH |
[
{
"content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[2, 8, -4, -3],\n [-3, 5, -11, 5],\n [-1, -10, 5, -11],\n [-6, 10, -11, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14 | MATH |
[
{
"content": "Find the value at position (2, 2) of the inverse of matrix 1/96 * A where A =\n[[11, -2, -9, -3],\n [-6, 12, -3, 7],\n [-8, -1, 10, 11],\n [9, -9, 7, -4]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[1, 2, 5, -2],\n [2, 10, 1, 1],\n [5, 1, -1, 8],\n [-2, 1, 8, -2]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[-10, -2, 8, -9],\n [-2, -1, -7, 8],\n [8, -7, -11, -5],\n [-9, 8, -5, -9]]\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 all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, -12, 12, -2],\n [-7, 3, 3, -2],\n [11, 11, 5, -3],\n [1, 1, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{You... | -7 | 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, 0, 5],\n [-2, 5, -4, -4],\n [0, -4, 12, 4],\n [5, -4, 4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[6, 4, -4, 10],\n [7, 6, -9, 2],\n [-2, 11, 10, -7],\n [-10, 1, 10, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -15 | 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[[0, -9, -6, 9],\n [-9, 7, -2, -4],\n [-6, -2, 1, 4],\n [9, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 575 | 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, -5, -7, 4],\n [0, 12, -1, 5],\n [0, 0, -6, -8],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -126 | 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, -6, 6, 1],\n [0, -2, -8, -12],\n [0, 0, 8, 10],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 261 | 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, -11, 9, 8],\n [0, -5, 1, -6],\n [0, 0, 5, 12],\n [0, 0, 0, -3]]\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 at position (3, 3) of the inverse. Round your answer to the nearest integer:\n[[9, -6, -1, -7],\n [0, 3, 0, -5],\n [0, 0, -4, 1],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | -24 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[-7, 8, 2, 4],\n [8, -6, -12, -5],\n [2, -12, -5, -2],\n [4, -5, -2, -5]]\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[[-2, 2, 10, -3],\n [0, 7, 10, -5],\n [0, 0, 2, 10],\n [0, 0, 0, 10]]\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[[-11, 3, 10, -6],\n [9, 4, -9, -6],\n [12, 7, -10, -6],\n [-2, -5, -7, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 2823 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 4) of the inverse. Round your answer to the nearest integer:\n[[2, 4, 11, 1],\n [8, 10, 4, -7],\n [11, 7, 1, 7],\n [-11, 12, -5, 10]]\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[[-5, -2, -2, 7],\n [-2, -6, -4, -3],\n [-2, -4, 3, 6],\n [7, -3, 6, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 275 | 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, -12, -4, 3],\n [0, -3, -7, -3],\n [0, 0, -11, -1],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex forma... | -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[[-5, -2, 7, 12],\n [0, 4, 12, -6],\n [0, 0, -1, -12],\n [0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -600 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-8, -11, 1, 6],\n [0, -10, 2, -6],\n [0, 0, -10, 12],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -57 | 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, -10, -6, -11],\n [7, -3, 7, 8],\n [-12, -10, 0, 10],\n [5, 3, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your... | -8 | MATH |
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