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[[6, 12, -1, -2],\n [0, -10, 2, -5],\n [0, 0, 11, 9],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -73 | 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, 6, 11, 5],\n [12, -6, 8, -6],\n [-12, -3, -7, 5],\n [3, 0, -3, 6]]\n\nPresent the answer in LaTex format... | 2 | 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, 2, 10, -7],\n [0, 12, 9, -3],\n [0, 0, -11, -9],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 47 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-4, 2, -4, -4],\n [2, -11, 3, -9],\n [-4, 3, 0, -4],\n [-4, -9, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your an... | -25 | 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, -2, -2, -7],\n [-8, 1, -2, -8],\n [-1, 1, 6, -11],\n [-12, 2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-5, -5, 8, 3],\n [-9, 5, -4, -9],\n [8, -12, 8, -9],\n [8, 3, 11, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[1, -9, -3, 4],\n [-6, -8, 7, 1],\n [6, -1, 6, 4],\n [-1, -10, 1, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, -3, 4, 1],\n [-3, -6, -5, 8],\n [4, -5, 10, 6],\n [1, 8, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 53 | 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[[6, -2, -4, 2],\n [-2, -3, -2, -4],\n [-4, -2, -2, -2],\n [2, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1062 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[10, -10, -6, -5],\n [-10, 12, 0, -6],\n [-6, 0, -1, 10],\n [-5, -6, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | -23 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[4, -12, -11, 10],\n [0, 3, -12, -1],\n [0, 0, 5, -2],\n [0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 86 | 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, 12, -11, 12],\n [0, 12, -12, 10],\n [0, 0, -9, 5],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -65 | 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, 2, 4, 0],\n [2, 5, 1, 3],\n [4, 1, -7, -2],\n [0, 3, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[11, -10, -8, 4],\n [-10, 2, -10, -6],\n [-8, -10, -6, 2],\n [4, -6, 2, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | 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, 0, 4, 4],\n [0, 12, -8, 6],\n [4, -8, -11, 10],\n [4, 6, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 63 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 2) of the inverse. Round your answer to the nearest integer:\n[[-11, -2, 1, 1],\n [0, 1, 12, -8],\n [0, 0, 4, 9],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 96 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[3, 0, 6, -2],\n [0, 2, 1, -2],\n [6, 1, 10, 6],\n [-2, -2, 6, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 42 | 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[[2, 8, 4, 10],\n [0, 6, 5, -11],\n [0, 0, 4, 8],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: ... | 433 | 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, 3, 1],\n [3, 8, -9, 12],\n [-4, -2, 12, 9],\n [-11, 6, -8, -9]]\n\nPresent the answer in LaTex format:... | 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[[11, 8, 12, 9],\n [-11, 4, -10, 6],\n [5, 11, 3, -2],\n [3, 8, 3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the value at position (4, 4) of the inverse of matrix 1/96 * A where A =\n[[-12, 2, -7, 3],\n [0, 8, -7, 9],\n [0, 0, 7, -8],\n [0, 0, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[6, 0, 6, 2],\n [4, -5, -9, 1],\n [10, 11, -5, -8],\n [4, 6, -10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | -16 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[11, -4, 8, -4],\n [2, -10, 5, -11],\n [3, -11, -3, 1],\n [10, 4, -2, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Find the value at position (4, 2) of the inverse of matrix 1/96 * A where A =\n[[11, -9, 2, -2],\n [4, 12, 3, -7],\n [-12, 11, 5, 2],\n [3, 3, -1, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 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[[2, -5, -2, -12],\n [0, -11, -8, 7],\n [0, 0, -3, 4],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 57 | 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[[-10, -6, -4, -7],\n [-6, -3, -7, -6],\n [-4, -7, -1, 0],\n [-7, -6, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 231 | 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[[-10, 4, -5, 8],\n [4, 8, 8, 0],\n [-5, 8, 9, -2],\n [8, 0, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 9 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[4, 6, 12, -8],\n [0, -7, -11, 4],\n [0, 0, 5, -12],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answe... | -30 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[8, -8, 2, 2],\n [-8, 0, 7, 8],\n [2, 7, -4, 7],\n [2, 8, 7, -2]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -6, -3, 3],\n [-6, 9, 4, -5],\n [-3, 4, 4, -2],\n [3, -5, -2, 4]]\n\nPresent the answer in LaTex for... | 411 | 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, 7, 4],\n [-8, 11, 12, -8],\n [8, 11, -11, -10],\n [11, -3, 6, -12]]\n\nPresent the... | -1532 | 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[[-2, 2, 11, -10],\n [2, -7, -7, -4],\n [11, -7, 4, 2],\n [-10, -4, 2, 3]]\n\nPresent the answer in LaTex... | 61 | 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, 3, -2, 3],\n [3, -2, 2, 4],\n [-2, 2, -9, 3],\n [3, 4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2101 | 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, 12, 2, 0],\n [-6, -6, 7, -8],\n [-4, 12, 1, 8],\n [7, -7, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 590 | 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, -2, -6],\n [-4, 6, 8, -4],\n [-2, 8, 12, -9],\n [-6, -4, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -686 | 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, 8, -5, -12],\n [-6, -12, -7, 10],\n [4, -2, -5, -3],\n [-4, 12, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | -13 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 11, -12, 4],\n [0, -2, 1, 5],\n [0, 0, -8, -7],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your a... | -838 | 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, 6, 4, 10],\n [6, -6, -3, -8],\n [4, -3, 8, 0],\n [10, -8, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answ... | -24 | 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[[8, 3, 7, -10],\n [9, 10, 11, -9],\n [-5, -1, -12, 7],\n [-4, -3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | -2 | 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, 8, -10, -2],\n [1, -9, 7, 10],\n [-8, -11, -8, -7],\n [8, 8, 9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -24 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, -11, 5, -9],\n [0, 9, 7, 2],\n [0, 0, -1, -8],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{You... | 0 | 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[[4, -4, -6, -10],\n [-4, 8, -4, 6],\n [-6, -4, 7, 8],\n [-10, 6, 8, -6]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, -3, 0, 3],\n [-3, 0, 2, 0],\n [0, 2, 11, -2],\n [3, 0, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 104 | 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[[-4, -6, -4, -2],\n [-6, -2, 0, -2],\n [-4, 0, -2, 4],\n [-2, -2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | 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, -6, 2, 10],\n [11, 8, 11, 3],\n [12, 0, 7, 10],\n [-10, -7, -9, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -44 | 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, 6, 2],\n [5, -1, 10, 0],\n [12, -1, 2, -8],\n [3, 1, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your an... | 60 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-3, 0, -1, 4],\n [0, 3, 4, 0],\n [-1, 4, 10, -2],\n [4, 0, -2, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1238 | 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, -10, 12, -4],\n [12, 12, -1, -12],\n [6, 1, -10, 4],\n [6, -5, 9, -5]]\n\nPresent the ... | -16 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 2) of the inverse. Round your answer to the nearest integer:\n[[-12, 1, -11, -2],\n [7, 6, -7, -8],\n [4, -9, 10, -12],\n [10, -12, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 3 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[-11, 4, -2, 1],\n [0, -9, -9, -11],\n [0, 0, -1, -3],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-12, -4, -9, -10],\n [0, -12, 8, 3],\n [0, 0, -8, 1],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 80 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 1) of the inverse. Round your answer to the nearest integer:\n[[-2, 6, 4, -2],\n [6, 11, -7, -11],\n [4, -7, -10, -2],\n [-2, -11, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | -28 | 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[[-10, -10, -5, -3],\n [0, 7, 7, -11],\n [0, 0, -10, -2],\n [0, 0, 0, -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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 4, -12, -10],\n [-4, 4, 11, 9],\n [-2, 3, 6, -5],\n [2, -2, -4, 11]]\n\nPresent the an... | 121 | 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, 8, 10],\n [0, -7, -8, -2],\n [0, 0, 8, -12],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 3) rounded to the nearest integer?\n[[-2, -4, 8, 11],\n [-4, 9, 3, -4],\n [8, 3, -6, -2],\n [11, -4, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[11, -2, 9, -9],\n [0, 11, -8, -1],\n [0, 0, 10, -10],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 71 | 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, 8, -3],\n [0, -12, -4, -5],\n [0, 0, 4, -1],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | -72 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 12, 1, -1],\n [-2, -11, 4, 4],\n [-5, 0, -2, -11],\n [1, 4, 5, 1]]\n\nPresent the answer in LaTex f... | 81 | 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, 1, -4, -7],\n [0, -2, 2, -11],\n [0, 0, 11, -3],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 33 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[1, -7, -4, 1],\n [0, 2, -4, -4],\n [0, 0, -7, 7],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1376 | 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[[10, -3, -5, -3],\n [0, -6, 2, 3],\n [0, 0, -5, -10],\n [0, 0, 0, -1]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, 2, -2, -5],\n [-9, 8, 1, -12],\n [-8, 12, 6, 11],\n [5, 12, 11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 11 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-4, -2, -2, 9],\n [-2, 12, -2, 8],\n [-2, -2, 10, -2],\n [9, 8, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | 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, -1, 6, 4],\n [-1, -11, -2, 2],\n [6, -2, -10, -7],\n [4, 2, -7, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 19 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[12, 8, -3, 3],\n [9, -5, -9, 0],\n [-2, 7, -5, 5],\n [9, -11, -6, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -30 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[6, 3, -8, 4],\n [3, 5, -4, 0],\n [-8, -4, 8, 6],\n [4, 0, 6, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 116 | MATH |
[
{
"content": "Find the value at position (2, 4) of the inverse of matrix 1/96 * A where A =\n[[-7, 11, -4, 5],\n [0, 11, 12, -11],\n [0, 0, 4, -8],\n [0, 0, 0, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, 5, -2, -4],\n [5, -1, -4, 4],\n [-2, -4, -4, 10],\n [-4, 4, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your... | 29 | 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, 8, -1],\n [-4, -4, 3, -1],\n [8, 3, -5, 2],\n [-1, -1, 2, 2]]\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[[4, 12, -1, -1],\n [9, -1, -8, -8],\n [9, 7, 10, 1],\n [11, -4, 10, 11]]\n\nPresent the answer in LaTex forma... | 17 | 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, -1, -6, -4],\n [-1, 9, 6, -4],\n [-6, 6, 2, 2],\n [-4, -4, 2, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -14 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[9, 6, -10, -2],\n [0, -7, 12, -6],\n [0, 0, -5, -8],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 58 | 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, 7, -11, 1],\n [7, 9, 1, 2],\n [-11, 1, 11, -6],\n [1, 2, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the value at position (1, 2) of the inverse of matrix 1/96 * A where A =\n[[3, 0, 2, 2],\n [0, -5, 2, -8],\n [2, 2, -11, -4],\n [2, -8, -4, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-2, 1, 12, -9],\n [0, 7, -4, -3],\n [0, 0, 9, 2],\n [0, 0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -40 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-9, 2, 1, 0],\n [2, -10, -2, -3],\n [1, -2, 3, 0],\n [0, -3, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 109 | 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[[2, 5, -4, 2],\n [5, 1, -1, 2],\n [-4, -1, 9, 4],\n [2, 2, 4, -11]]\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-12, -4, 7, 11],\n [0, 12, 10, 6],\n [0, 0, 6, -2],\n [0, 0, 0, -1]]\n\nPresent the answer... | -132 | 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, -12, 4, -2],\n [0, 8, 0, 7],\n [0, 0, 8, 1],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 348 | 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[[6, 12, -8, 0],\n [12, -2, -2, 6],\n [-8, -2, 1, 6],\n [0, 6, 6, -2]]\n\nPresent the answer... | 11 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-8, 0, -5, -4],\n [0, -10, -7, -2],\n [-5, -7, -7, -1],\n [-4, -2, -1, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6936 | 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, 0, -1, -2],\n [0, 5, 9, -11],\n [-1, 9, -1, 0],\n [-2, -11, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -161 | 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, 2, 8, -11],\n [-6, -12, 1, 5],\n [-4, 10, -4, -3],\n [-7, 12, -5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -22 | 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, 6, 4, -2],\n [6, 11, 2, 2],\n [4, 2, -1, -7],\n [-2, 2, -7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -607 | MATH |
[
{
"content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[3, -1, -5, -8],\n [0, 8, 9, -4],\n [0, 0, -2, -5],\n [0, 0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | 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[[8, 0, -7, 9],\n [0, -5, 1, 3],\n [11, 3, 12, -7],\n [-11, -10, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | -4 | 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, -4, -3, -6],\n [0, -1, -3, -2],\n [0, 0, 1, 1],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | 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, -6, 4, 4],\n [-6, 7, 8, -5],\n [4, 8, 7, -4],\n [4, -5, -4, -7]]\n\nPresent the answer in LaTex for... | 96 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-3, -8, -2, 4],\n [-8, -11, 1, -2],\n [-2, 1, -6, 4],\n [4, -2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -588 | 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, -1, 8],\n [5, 12, -9, 12],\n [6, -11, 6, -4],\n [12, -3, -9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 50 | 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, 1, -10, 1],\n [8, -3, 10, -1],\n [5, 6, -4, -10],\n [11, -9, 3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 8 | MATH |
[
{
"content": "Find the value at position (2, 1) of the inverse of matrix 1/96 * A where A =\n[[12, 7, -1, -11],\n [0, 6, -7, 0],\n [0, 0, -7, 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"
}
] | 0 | 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[[10, 2, -2, -6],\n [11, 3, 10, -7],\n [-3, -5, -3, 4],\n [2, -3, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -25 | 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, 7, 0, -4],\n [0, -6, 4, 0],\n [0, 0, -5, -10],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[10, 9, -4, 4],\n [10, 10, -8, 11],\n [5, 6, -5, 7],\n [-8, 4, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 751 | MATH |
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/96 * A where A =\n[[-2, 6, -2, -9],\n [0, -12, 11, 5],\n [0, 0, 6, 0],\n [0, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | 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, 12, -4, -7],\n [1, 9, -2, -8],\n [6, -10, 3, -8],\n [-8, -1, -4, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | -28 | 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, -8, 4, -1],\n [4, -7, 4, -9],\n [-6, 12, -8, 0],\n [7, 7, 10, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | -45 | MATH |
[
{
"content": "Find the value at position (3, 2) of the inverse of matrix 1/96 * A where A =\n[[2, -10, 3, -3],\n [0, 7, 7, -1],\n [0, 0, -8, 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"
}
] | 0 | MATH |
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