messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-9, 2, 3, 6],\n [0, 7, 6, -6],\n [0, 0, -10, -11],\n [0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 16 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[9, -4, 0, 10],\n [-4, 5, 9, -2],\n [0, 9, -6, -4],\n [10, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 6 | 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[[11, -8, 6, 6],\n [-8, 9, -10, -5],\n [6, -10, 8, -4],\n [6, -5, -4, -3]]\n\nPresent the answer in LaTex format: \\bo... | 21 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[9, -10, 11, 7],\n [0, 7, -8, -4],\n [0, 0, 12, 7],\n [0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | 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, -4, -5, 2],\n [-4, 3, -2, 6],\n [-5, -2, 0, 2],\n [2, 6, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -176 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[7, -3, -6, -7],\n [7, 7, 4, -12],\n [1, 10, -7, 10],\n [11, -2, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 126 | 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, -10, -8, -11],\n [0, -11, 1, 5],\n [0, 0, -10, 11],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | -8 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[6, -4, -3, 3],\n [0, -9, -7, 7],\n [0, 0, -2, -11],\n [0, 0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, 10, 12, 9],\n [0, 2, -5, -3],\n [0, 0, 9, -6],\n [0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 452 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-9, 2, -6, 9],\n [1, 5, 7, -9],\n [-1, 9, 8, -12],\n [-4, 10, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | -98 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[7, -9, -9, -1],\n [0, -10, 9, -1],\n [0, 0, -1, -2],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 557 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[8, 0, 0, 10],\n [0, -6, 4, 9],\n [0, 4, -1, -2],\n [10, 9, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 37 | MATH |
[
{
"content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[2, 0, -4, -5],\n [2, -4, -10, 5],\n [9, 9, 7, 1],\n [-11, -5, 6, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -264 | 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[[-7, 9, -6, -1],\n [0, -2, 2, -2],\n [0, 0, -8, 8],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -83 | 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, 9, -6, -9],\n [0, -4, -1, 1],\n [0, 0, 4, 6],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -24 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-2, 7, -10, 5],\n [0, 12, -9, 5],\n [0, 0, 6, -5],\n [0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -7, -1, -12],\n [0, -12, 12, 3],\n [0, 0, 8, 3],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format... | -25 | MATH |
[
{
"content": "Find the value at position (4, 3) of the inverse of matrix 1/96 * A where A =\n[[-7, -9, -10, 2],\n [1, -5, -12, 4],\n [-3, -5, -7, -7],\n [-4, -10, -4, 2]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[1, -7, -6, -5],\n [0, 7, -6, -12],\n [0, 0, 6, -10],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 117 | 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, -9, 8, -9],\n [11, 1, -5, -2],\n [-4, 8, 7, 9],\n [2, 9, 0, -8]]\n\nPresent the answer in LaTex format: \... | 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[[-11, -8, 4, 1],\n [-6, 12, -12, 12],\n [4, -12, -10, 3],\n [12, 9, -6, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | -10 | 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[[-2, -12, 5, 11],\n [0, -8, -3, -6],\n [0, 0, -11, -8],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | -53 | 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[[2, 8, -3, -12],\n [-8, -3, 6, -5],\n [-1, -8, -12, -8],\n [-11, -2, -7, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 7 | MATH |
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/96 * A where A =\n[[-3, 2, -12, 10],\n [0, -6, 12, -1],\n [0, 0, -2, -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"
}
] | -48 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[7, 6, 0, -1],\n [6, -8, -4, -6],\n [0, -4, -4, -6],\n [-1, -6, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 117 | 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, 5, -6],\n [0, 8, 3, -2],\n [0, 0, 7, 5],\n [0, 0, 0, 11]]\n\nPresent the answer in... | 60 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-4, 8, -12, -7],\n [0, -8, 11, -6],\n [0, 0, 7, 8],\n [0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 334 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-1, 6, -7, 12],\n [9, 5, 10, -7],\n [-7, 3, 10, 9],\n [0, -11, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 46 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -1, -2, 4],\n [-1, 3, -11, 10],\n [-2, -11, -9, 4],\n [4, 10, 4, -6]]\n\nPresent the answer in LaTex format: \\bo... | 5 | 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[[-1, -1, 8, -2],\n [-1, 0, -8, -1],\n [8, -8, -12, -7],\n [-2, -1, -7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -29 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-5, 1, 6, 12],\n [0, 10, -2, -2],\n [0, 0, -6, 6],\n [0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -42 | 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, -11, -12, 9],\n [9, -10, -8, -10],\n [-6, 6, -7, 11],\n [6, 3, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, -7, -6, 0],\n [-7, 12, -2, -3],\n [-6, -2, 2, -5],\n [0, -3, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 111 | 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, 8, -4, 4],\n [8, 8, -5, -6],\n [-4, -5, 12, 1],\n [4, -6, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -158 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-6, -11, -11, -7],\n [0, 1, 9, -11],\n [0, 0, -2, -7],\n [0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12960 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 2, 2, -1],\n [3, -10, -12, 9],\n [2, 12, -9, 2],\n [0, -1, -5, -10]]\n\nPresent the a... | -10 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[0, -2, 2, -10],\n [-2, -5, 8, 4],\n [2, 8, -3, 0],\n [-10, 4, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 15 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[12, 12, -3, -4],\n [0, 2, -9, -4],\n [0, 0, 1, 5],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your ans... | -344 | 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, 5, 4, -9],\n [5, 2, 4, 7],\n [4, 4, -1, -6],\n [-9, 7, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | -17 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[1, 2, 5, -11],\n [10, -9, -2, -1],\n [8, 7, 3, 3],\n [2, -8, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | -76 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -7, -3, 3],\n [5, 9, 7, 0],\n [-9, -5, -6, -7],\n [-2, -8, 1, -6]]\n\nPresent the answer in LaTex format:... | 31 | 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[[0, 1, 11, 9],\n [11, 6, 11, 0],\n [0, -4, -9, -4],\n [-2, -11, -10, 8]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, 8, -4, -8],\n [8, -7, 2, -8],\n [-4, 2, -2, -5],\n [-8, -8, -5, 9]]\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 absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, 3, -1, 2],\n [-7, -12, 11, 2],\n [6, -11, -3, 4],\n [11, -8, -6, 3]]\n\nPresent the answer in LaTex... | 1148 | 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, 10, 9, -9],\n [0, 12, -9, 4],\n [0, 0, 3, -2],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 155 | 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, 6, 9, 0],\n [6, -11, -4, 0],\n [9, -4, 4, 5],\n [0, 0, 5, -12]]\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[[-3, 12, -6, 0],\n [0, -9, 8, -5],\n [0, 0, -5, 0],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -4, -6, -2],\n [-4, 7, -8, 6],\n [-6, -8, 11, -9],\n [-2, 6, -9, -9]]\n\nPresent the answer in LaTex for... | 11 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-4, 5, -2, 5],\n [0, 4, 6, 5],\n [0, 0, 5, -1],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, -3, -4, -3],\n [0, 3, 6, 2],\n [0, 0, -9, 9],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\b... | 69 | 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, -8, -3, 8],\n [-8, -3, 1, -3],\n [-3, 1, -9, 3],\n [8, -3, 3, 1]]\n\nPresent the answer... | -25 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-1, 5, -9, 6],\n [0, -12, -5, -9],\n [0, 0, 5, -9],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 283 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[8, -6, 9, 6],\n [7, -4, -3, 1],\n [1, -3, -9, -1],\n [-1, 4, 5, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 285 | 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, -12, 6, -6],\n [-12, 2, 1, 1],\n [6, 1, 3, -6],\n [-6, 1, -6, -1]]\n\nPresent the answe... | -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[[-10, 2, 0, 8],\n [2, 1, -4, -1],\n [0, -4, 3, 1],\n [8, -1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | -31 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-12, 6, -4, -1],\n [6, -2, -2, -2],\n [-4, -2, 3, 6],\n [-1, -2, 6, 8]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries rounded to the nearest integer?\n[[-12, 10, 8, 12],\n [0, -3, -9, 10],\n [0, 0, -3, 9],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 410 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-11, -11, 9, 9],\n [8, 10, -10, 9],\n [-3, -11, 3, -2],\n [-1, 6, 10, 11]]\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 all entries rounded to the nearest integer?\n[[6, 4, -8, 2],\n [4, -10, -8, 0],\n [-8, -8, -6, -3],\n [2, 0, -3, 2]]\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 value at position (3, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, 0, -5, -6],\n [0, 10, 8, -8],\n [-5, 8, -6, 7],\n [-6, -8, 7, 3]]\n\nPresent the answer in LaTex format: \\boxed... | -1 | 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, 5, -1, 1],\n [0, -3, -3, 7],\n [0, 0, -9, -5],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -136 | 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[[6, 6, -10, 3],\n [-12, 10, -12, -7],\n [-2, -2, 4, 6],\n [-6, -8, 5, -11]]\n\nPresent the answer in LaTex format: \\... | -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[[8, 7, 12, 6],\n [0, 3, -1, 12],\n [0, 0, 4, -4],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 238 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[6, 1, 0, 1],\n [11, -5, -10, 7],\n [-9, -12, 4, -1],\n [-5, 1, -12, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -49 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-11, 1, -10, 6],\n [-8, 0, -3, 11],\n [8, -5, 8, -8],\n [0, 5, 2, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -16 | 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[[3, 3, -3, -9],\n [2, 7, 5, 5],\n [-7, 8, 1, -6],\n [-3, 4, -6, -9]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, -7, -1, -1],\n [0, -9, 0, 8],\n [0, 0, -7, -2],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 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[[12, -5, -3, 10],\n [0, -3, 11, 4],\n [0, 0, -6, 10],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | -72 | 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[[5, 6, 1, -11],\n [0, 5, 6, 1],\n [0, 0, -2, 6],\n [0, 0, 0, 6]]\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[[-5, -1, -10, -4],\n [-1, 2, -4, -3],\n [-10, -4, 8, 8],\n [-4, -3, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 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, 9, -2, -4],\n [9, 9, -6, 8],\n [-2, -6, 9, 6],\n [-4, 8, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[9, -5, 11, -7],\n [8, -2, 10, 11],\n [-1, 11, -10, -10],\n [-7, 9, -4, 1]]\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 (2, 4) of the inverse. Round your answer to the nearest integer:\n[[-5, 0, -7, 2],\n [0, -3, 1, -2],\n [0, 0, 9, 5],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 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[[5, 0, -2, 2],\n [0, -9, -2, 2],\n [-2, -2, -12, 4],\n [2, 2, 4, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | -34 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 10, -7, -4],\n [10, -2, 5, -6],\n [-7, 5, 5, 4],\n [-4, -6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed... | 29 | 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, 2, -5],\n [-2, 0, 7, -8],\n [7, 2, -4, -9],\n [2, 8, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | -1 | 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, -4, -11],\n [-10, -7, -4, -8],\n [-9, -10, 1, 6],\n [-9, 4, -3, 1]]\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 all entries of the inverse. Round your answer to the nearest integer:\n[[-1, 6, 6, -4],\n [6, -8, 5, -6],\n [6, 5, -2, 1],\n [-4, -6, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -2, 4, 9],\n [0, 4, 11, -3],\n [0, 0, -8, -4],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex for... | 130 | 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[[9, 0, 3, -1],\n [0, 11, 3, -5],\n [3, 3, 12, -4],\n [-1, -5, -4, -8]]\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[[7, 9, 6, -4],\n [0, 3, 7, 9],\n [0, 0, -6, 5],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\box... | 38 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[11, 1, 3, 7],\n [0, -8, -5, 4],\n [0, 0, 3, -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"
}
] | 25 | 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, -10, -11, 6],\n [0, 8, -8, 6],\n [0, 0, -11, -11],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format... | 3 | 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, -11, 3, 8],\n [6, -11, 11, -1],\n [-9, 7, -11, 12],\n [-12, -6, -7, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 24 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-9, -7, -10, 3],\n [0, 8, 8, 10],\n [0, 0, 3, 11],\n [0, 0, 0, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -37 | 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, 1, -4, -1],\n [1, 5, -8, 11],\n [-4, -8, -1, 4],\n [-1, 11, 4, -4]]\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 value at position (4, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 2, -4, -4],\n [2, -2, -10, 2],\n [-4, -10, 2, 8],\n [-4, 2, 8, -2]]\n\nPresent the answer in LaTex format: \\boxe... | -35 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, -12, -8, -8],\n [4, -1, 12, 0],\n [11, -12, 11, 0],\n [0, 1, 3, -10]]\n\nPresent the answer in LaTex format: \\bo... | 46 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-12, 9, -4, 3],\n [0, 3, -12, 10],\n [0, 0, 3, -2],\n [0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 343 | 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, 4, -11, -1],\n [0, 12, -10, 6],\n [0, 0, -12, 2],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, -7, 8, 3],\n [2, -1, -6, 1],\n [-2, -10, -8, 0],\n [9, -4, 6, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 307 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -10, 2, 11],\n [-7, -1, 8, -10],\n [-3, -1, 6, -11],\n [2, -4, -7, -9]]\n\nPresent the answer in LaTex format: ... | 2 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[3, 0, -10, 3],\n [0, -5, -3, 3],\n [0, 0, -10, -4],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 32 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[6, 7, -5, -5],\n [0, -10, -9, -10],\n [0, 0, 2, -3],\n [0, 0, 0, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65 | 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, -4, -6, 2],\n [-4, 1, 8, 10],\n [-6, 8, 5, -2],\n [2, 10, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 193 | 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[[5, 12, 11, 3],\n [0, -5, 6, -9],\n [0, 0, -3, 2],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -32 | 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[[5, -7, 0, 0],\n [2, 3, 0, -8],\n [-1, -5, -4, -10],\n [4, -1, 7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 126 | 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, 8, -7, -8],\n [8, 10, 1, -3],\n [-7, 1, -5, 0],\n [-8, -3, 0, 8]]\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 value at position (3, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, -3, -4, 2],\n [-3, 6, 0, 4],\n [-4, 0, -6, 9],\n [2, 4, 9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | -3 | 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, 2, -11, -11],\n [0, -6, 9, -5],\n [0, 0, 5, 1],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -2 | MATH |
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