messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1
value |
|---|---|---|
[
{
"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, 2, 5, 7],\n [8, -2, 9, 12],\n [-10, 4, 10, -8],\n [-10, 1, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 38 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[2, 6, -2, 6],\n [6, 8, 2, -4],\n [-2, 2, -11, -9],\n [6, -4, -9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "Find the value at position (2, 4) of the inverse of matrix 1/96 * A where A =\n[[-7, -7, -12, 3],\n [0, -12, -7, -11],\n [0, 0, -7, -7],\n [0, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -2, 11, 7],\n [0, -5, -8, -2],\n [0, 0, -12, 4],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your an... | -41 | 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, 4, -6, -1],\n [4, -8, -4, 9],\n [-6, -4, -2, -4],\n [-1, 9, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 8 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-9, -5, 12, 6],\n [3, 1, -1, -1],\n [-4, -7, -12, 5],\n [-9, -1, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 58 | 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, -7, -6, -12],\n [0, 8, -2, 9],\n [0, 0, -6, -5],\n [0, 0, 0, -9]]\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[[-10, 2, 6, 4],\n [2, -3, -1, 6],\n [6, -1, -3, -4],\n [4, 6, -4, -1]]\n\nPresent the answe... | 174 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[10, -8, 6, 8],\n [-8, -4, -6, 2],\n [6, -6, 9, -1],\n [8, 2, -1, -5]]\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[[-11, 7, -10, -1],\n [-9, 12, -6, 5],\n [3, -5, -6, -1],\n [8, -11, -12, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 30 | 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, 4, 4, 4],\n [4, -9, -8, -3],\n [4, -8, 1, -2],\n [4, -3, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | -2 | 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[[4, 0, 4, 2],\n [0, 10, -4, -4],\n [4, -4, -3, -11],\n [2, -4, -11, -7]]\n\nPresent the answer in LaTex format: \\boxed{You... | 32 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 2, 1, -1],\n [-7, -5, -9, 12],\n [-8, 8, -1, -1],\n [-2, 4, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your... | 55 | 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, 10, 0, -4],\n [10, -1, -7, -8],\n [7, -2, -12, -12],\n [5, -12, -1, -4]]\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[[-5, 0, 1, 8],\n [0, 0, -8, 2],\n [1, -8, 1, -2],\n [8, 2, -2, -12]]\n\nPresent the answer in LaTex form... | 1218 | 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[[-9, -2, 2, 0],\n [-2, -6, 0, -8],\n [2, 0, -9, -3],\n [0, -8, -3, -4]]\n\nPresent the answer in LaTex format: \\boxe... | 12 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, 7, -9, -4],\n [1, -7, -3, 10],\n [3, -3, -9, -5],\n [10, -3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 80 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-8, 6, -3, 12],\n [0, -10, 9, -3],\n [0, 0, -12, 12],\n [0, 0, 0, -4]]\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[[-9, -5, -5, -4],\n [-5, -7, -5, 10],\n [-5, -5, -6, -3],\n [-4, 10, -3, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -47 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[7, 2, 11, -7],\n [-3, -8, 3, 7],\n [-10, -12, -5, -7],\n [-3, 2, 4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 90 | 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[[4, 9, 8, 2],\n [0, 9, 7, 9],\n [0, 0, 4, 1],\n [0, 0, 0, 12]]\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[[3, -1, -4, -2],\n [-1, -2, -6, -3],\n [-4, -6, -2, -2],\n [-2, -3, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 158 | 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, -4, 2, -12],\n [0, -2, -11, 1],\n [0, 0, -5, 0],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 106 | 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[[-8, 8, -8, -2],\n [8, 2, 3, 8],\n [-8, 3, 6, -6],\n [-2, 8, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | 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, -11, -11, 12],\n [-2, -5, 4, -10],\n [4, -1, 11, 6],\n [-8, 1, 7, -1]]\n\nPresent the answer in LaTex fo... | -2 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-4, 0, -7, -6],\n [0, -4, -10, 9],\n [0, 0, -2, -12],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1896 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[4, -6, 9, 4],\n [6, -5, 3, 9],\n [-9, 8, -1, -5],\n [-4, -12, -5, 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 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, -3, 8],\n [0, -8, 1, -11],\n [0, 0, 6, -1],\n [0, 0, 0, 1]]\n\nPresent the answer ... | -130 | 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[[7, -2, 3, 10],\n [0, 12, 2, -7],\n [0, 0, 3, 2],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, -4, -3, 4],\n [0, -9, 5, 5],\n [0, 0, -10, 3],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[1, -12, 4, 9],\n [-10, 7, -10, -2],\n [6, -4, -1, 1],\n [3, -8, 10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -31 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, 2, 2, 0],\n [2, -2, 2, -4],\n [2, 2, -6, -1],\n [0, -4, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -246 | 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, 1, -12, -7],\n [6, 10, -7, 9],\n [-6, 5, 2, 3],\n [-5, -8, 10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-5, -6, 3, -10],\n [-1, 3, 11, 12],\n [4, -9, -5, 10],\n [1, -6, 3, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -248 | 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, -3, 6, -4],\n [-8, 3, 11, -2],\n [-12, -5, -11, -12],\n [5, 6, -1, -11]]\n\nPresent the answer in LaTex f... | 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[[-9, 2, 2, -3],\n [2, 1, 4, 2],\n [2, 4, 4, -6],\n [-3, 2, -6, 8]]\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[[-10, 9, -1, 2],\n [9, -12, -6, -6],\n [-1, -6, -11, 10],\n [2, -6, 10, -4]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, -12, -12, -5],\n [1, 8, 6, 3],\n [-5, -3, 8, 0],\n [10, 6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -99 | 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, -7, -2, -10],\n [0, 12, -7, -11],\n [0, 0, -3, 9],\n [0, 0, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -32 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[1, -2, 2, 1],\n [-2, -3, 6, 9],\n [2, 6, 0, 1],\n [1, 9, 1, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-5, -4, -3, 9],\n [-4, 7, 2, -6],\n [-3, 2, 1, 8],\n [9, -6, 8, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | 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, -1, 4, 1],\n [-1, 0, 1, 0],\n [4, 1, -8, -5],\n [1, 0, -5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | 10 | MATH |
[
{
"content": "Find the value at position (3, 1) of the inverse of matrix 1/96 * A where A =\n[[11, 3, 3, 4],\n [3, 1, 8, 5],\n [3, 8, 12, -2],\n [4, 5, -2, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[9, -1, -7, -11],\n [0, -12, 9, -8],\n [0, 0, 1, 8],\n [0, 0, 0, -12]]\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[[12, 12, -10, -2],\n [-4, 4, 5, -5],\n [-1, -8, 11, -6],\n [0, -6, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[6, -3, -7, 12],\n [10, -9, 5, -2],\n [-11, 1, 12, 8],\n [-7, -1, 2, -5]]\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 value at position (2, 3) rounded to the nearest integer?\n[[-11, -4, 2, 4],\n [-4, 6, 0, -5],\n [2, 0, 1, 9],\n [4, -5, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[9, -6, 0, -2],\n [-5, -2, 7, 9],\n [-9, 5, -3, 4],\n [-10, 4, 1, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 217 | 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, 6, 2, 5],\n [-9, -2, 11, -10],\n [-12, 0, 7, -3],\n [-5, 3, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[-2, 6, 0, -9],\n [-10, -4, 0, -3],\n [10, 10, -9, 12],\n [-3, -3, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[7, -2, -6, 3],\n [-7, -9, -7, -1],\n [-11, -1, -11, 11],\n [1, -2, 12, 9]]\nRound your answer to the nearest integer.\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -4, -10, -2],\n [-4, -10, 5, 4],\n [-10, 5, -3, 0],\n [-2, 4, 0, 12]]\n\nPresent the a... | -9 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[5, 0, 4, 6],\n [1, -9, -10, 11],\n [8, 6, 11, 9],\n [-8, -1, 7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | 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[[4, 0, 1, 0],\n [0, 6, -11, -10],\n [0, 0, 2, 1],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-5, 12, -3, -8],\n [9, -5, -3, 1],\n [-1, 3, 3, 8],\n [-9, -7, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 83 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[1, 1, 6, 0],\n [1, 6, 3, 4],\n [6, 3, -4, 10],\n [0, 4, 10, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 67 | 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, -5, 0],\n [6, -1, -1, -4],\n [-5, -1, -2, 7],\n [0, -4, 7, -7]]\n\nPresent the answer in LaTex f... | 273 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-8, 10, 12, 5],\n [-7, -5, -10, 9],\n [-12, 12, 11, -6],\n [0, 5, 11, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 67 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[10, -3, 7, -1],\n [0, 1, -5, -3],\n [0, 0, -12, 11],\n [0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 86 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, -8, 6, -6],\n [1, -8, -4, 8],\n [9, -12, 9, -12],\n [-7, -9, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 2) rounded to the nearest integer?\n[[-8, 4, 4, 10],\n [0, -6, 8, 12],\n [0, 0, -9, 5],\n [0, 0, 0, -10]]\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 value at position (3, 4) rounded to the nearest integer?\n[[6, -9, 5, 0],\n [-7, 9, -5, -6],\n [0, -5, 2, -8],\n [4, -4, 7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[6, -2, -4, 6],\n [-2, 1, 2, -1],\n [-4, 2, 8, -5],\n [6, -1, -5, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 548 | 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, 9, 4, -9],\n [-3, -2, -11, 4],\n [7, -12, 7, 12],\n [-5, -4, -6, -10]]\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, 7, 1, -6],\n [7, -5, 12, 2],\n [1, 12, -6, -3],\n [-6, 2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 12 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -1, 9, -11],\n [5, 1, -8, -11],\n [1, -3, 9, 11],\n [8, 1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxe... | -1 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-5, -11, 5, 12],\n [0, -9, 6, -7],\n [0, 0, -5, -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"
}
] | 175 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, -6, 7, 9],\n [0, 1, 2, 5],\n [0, 0, -10, 2],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\b... | 98 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[8, 1, -4, 3],\n [0, 11, -2, -7],\n [0, 0, -12, 10],\n [0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87 | 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[[-3, -1, 7, -5],\n [0, 11, 1, -9],\n [0, 0, -1, 7],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 688 | 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[[-12, -4, 6, -1],\n [-4, -11, 2, -3],\n [6, 2, 11, 0],\n [-1, -3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[12, 4, 5, -10],\n [-5, 9, 10, 7],\n [9, -11, 3, -4],\n [3, -5, -6, 7]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[5, -11, -5, 5],\n [-11, -1, -6, 4],\n [-5, -6, -6, 0],\n [5, 4, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 186 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-9, 9, -2, -11],\n [0, -10, 7, 4],\n [0, 0, 7, -10],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -39 | 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, -5, -6, -10],\n [-5, -4, 3, -2],\n [-6, 3, -5, -2],\n [-10, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 22 | 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, 8, 5],\n [0, -11, 7, -12],\n [0, 0, 10, 3],\n [0, 0, 0, -4]]\n\nPresent the answer... | 61 | 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[[-8, 5, 11, 5],\n [0, 12, 8, 0],\n [0, 0, 2, -8],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{You... | 0 | 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, 7, 0, -5],\n [-11, 5, -10, 2],\n [9, -8, 6, 0],\n [0, -12, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 288 | 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, -5, -12, -6],\n [7, -8, 1, 6],\n [-2, 10, 4, 2],\n [0, 3, 12, -8]]\n\nPresent the answ... | 75 | 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, -9, 3, -3],\n [-11, -2, 6, 7],\n [-10, -9, -12, 6],\n [-3, 5, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -80 | 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, -1, -4],\n [3, 5, -2, 8],\n [-1, -2, 0, -1],\n [-4, 8, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 471 | MATH |
[
{
"content": "Find the value at position (3, 2) of the inverse of matrix 1/96 * A where A =\n[[-11, -3, -1, 4],\n [0, 0, -12, 0],\n [5, 9, 8, -10],\n [-6, 7, 5, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-11, 1, -2, -8],\n [1, -6, 2, -4],\n [-2, 2, -7, -2],\n [-8, -4, -2, 7]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[9, 4, -10, 2],\n [4, -1, -4, 7],\n [-10, -4, 12, 4],\n [2, 7, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 393 | 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[[6, -12, 10, 1],\n [11, -2, 12, 12],\n [9, 3, -2, -7],\n [-6, -3, -7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -6 | 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, -9, 11, -2],\n [-3, 5, 12, 1],\n [-5, -4, -11, 1],\n [-6, -1, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your ... | -11 | 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, 3, 5, -10],\n [0, 10, 0, 9],\n [0, 0, -12, -11],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -415 | 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, -3, -4, -10],\n [-3, -11, -2, -2],\n [-4, -2, 2, 9],\n [-10, -2, 9, -12]]\n\nPresent the answer in LaTex... | -35 | 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, -4, 0, 2],\n [-4, -1, 0, 3],\n [0, 0, 1, -2],\n [2, 3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 207 | 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[[3, 11, -1, -11],\n [0, -12, 0, -8],\n [0, 0, -12, -11],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | -80 | 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, 2, -8, -4],\n [2, 7, 9, 8],\n [-8, 9, -3, -11],\n [-4, 8, -11, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your ... | 27 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[11, 4, -10, 10],\n [-7, -8, -8, 3],\n [-4, 3, 9, -2],\n [11, -11, 9, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | 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[[-3, 3, -8, -5],\n [0, 12, -2, -10],\n [0, 0, -7, 3],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxe... | 0 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[1, -12, 0, 5],\n [0, 2, -8, 0],\n [0, 0, -1, -9],\n [0, 0, 0, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-4, -9, -7, -11],\n [-4, 3, 2, 7],\n [10, 7, 1, 3],\n [7, -3, -4, -6]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -9, 8, -7],\n [0, -11, 8, -2],\n [0, 0, 4, 10],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex for... | 156 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -8, 4, 10],\n [0, -6, -11, -11],\n [0, 0, -3, 4],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your a... | -700 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[-5, -7, 10, 10],\n [0, 3, -7, -11],\n [0, 0, 9, 3],\n [0, 0, 0, -12]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[-12, 10, 3, 3],\n [-7, -1, 1, 8],\n [10, 10, 3, 2],\n [-4, -2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 149 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[3, 1, 10, -1],\n [0, 7, -11, -8],\n [0, 0, -3, 3],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | MATH |
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