messages listlengths 1 1 | ground_truth stringclasses 799 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the value at position (1, 1) of the inverse of matrix 1/60 * A where A =\n[[6, -3, -8],\n [-4, 0, -1],\n [3, -1, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-2, 0, 2],\n [0, -1, 3],\n [0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 133 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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, -7, 5],\n [-3, 0, 6],\n [-4, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | -16 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[1, 4, 0],\n [4, -1, 6],\n [0, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[5, -1, 7],\n [0, 1, -4],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 117 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, 2, -9],\n [0, 3, 10],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -213 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[7, 3, 1],\n [2, 9, -2],\n [6, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[-9, 4, -2],\n [4, 9, 2],\n [-2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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, 6, 6],\n [0, 4, -2],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 162 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[9, -2, 9],\n [0, -1, -5],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -60 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[10, 4, 8],\n [1, 9, -7],\n [-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": "For the inverse of 1/60 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[1, -6, 3],\n [-3, -3, -4],\n [1, 7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -28 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[-8, -8, 5],\n [-7, -1, -7],\n [7, -6, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -17 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-9, -6, 6],\n [-6, 7, 0],\n [6, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-9, -10, -3],\n [0, -3, 1],\n [0, 0, -4]]\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 1/60 times the matrix below, what is the value at position (3, 2) rounded to the nearest integer?\n[[1, 0, 7],\n [0, -9, -6],\n [7, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[7, 7, 9],\n [3, 4, 8],\n [-10, 10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[2, 4, 0],\n [4, 4, 5],\n [0, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 0, -10],\n [0, -6, 4],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 5 | MATH |
[
{
"content": "Find the inverse of 1/60 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, -1, -5],\n [-1, 0, 0],\n [-5, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 849 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-3, -6, -1],\n [0, 4, -3],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 172 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[7, 3, -5],\n [0, 10, 5],\n [0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[1, 4, -4],\n [4, 5, 0],\n [-4, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -13 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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, -4, 2],\n [-4, 10, -6],\n [2, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | -251 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[-3, 4, -10],\n [10, -4, -6],\n [-10, 5, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 156 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[6, -6, -2],\n [-6, -7, 6],\n [-2, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, 4, -2],\n [4, -8, 5],\n [-2, 5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[10, 8, -7],\n [8, -9, -7],\n [-7, -7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -24 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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, -7, 5],\n [10, -3, 2],\n [1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 60 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, -3, 2],\n [8, 8, 5],\n [-7, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 111 | MATH |
[
{
"content": "Find the inverse of 1/60 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, 3, -2],\n [3, 7, 6],\n [-2, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 214 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[6, 10, 5],\n [-2, -10, 10],\n [10, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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[[4, -4, 4],\n [-5, -7, -6],\n [-5, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 35 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-1, 8, -6],\n [-10, 3, -4],\n [-2, -7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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[[-1, -2, 1],\n [0, 5, -6],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 0 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-6, -2, -10],\n [0, 5, -10],\n [0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[5, -5, -8],\n [0, 1, 10],\n [-1, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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[[5, 2, 4],\n [-9, 9, -3],\n [1, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | -20 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-9, 0, 2],\n [0, 1, -10],\n [2, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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, -3, 4],\n [0, -7, 2],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 40 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value at position (3, 3) rounded to the nearest integer?\n[[-1, -1, 10],\n [0, -1, 3],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -15 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 times the following and determine the value at position (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, 6, -6],\n [0, 10, -2],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 0 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 times the following and determine the value at position (2, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, -7, 2],\n [0, 2, 4],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 30 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[10, -4, 7],\n [-4, 7, -7],\n [7, -7, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-4, 0, 2],\n [0, -8, 1],\n [2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 53 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, -6, 8],\n [0, -3, 8],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[-1, -4, -3],\n [-4, -1, -6],\n [-3, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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, -8, 9],\n [-7, -9, -9],\n [-4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 99 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value at position (1, 2) rounded to the nearest integer?\n[[-7, -1, 4],\n [-1, 7, 1],\n [4, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[9, 2, 6],\n [2, 4, 4],\n [6, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Find the inverse of 1/60 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, 1, 0],\n [0, 1, -2],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 times the following and determine the value at position (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -4, 1],\n [-9, -8, -1],\n [5, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -10 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-10, 9, 6],\n [-8, -9, 0],\n [0, 10, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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, 10, -10],\n [0, 8, 4],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 92 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the value at position (3, 2) of the inverse. Round your answer to the nearest integer:\n[[-7, -4, 6],\n [-4, -5, 0],\n [6, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-4, 8, 7],\n [0, -6, 5],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the value at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[-8, 2, 3],\n [9, -5, 1],\n [1, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[5, -1, 1],\n [6, 0, 1],\n [5, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 174 | MATH |
[
{
"content": "Find the inverse of 1/60 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, 5, 3],\n [0, 6, 9],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-9, 1, 0],\n [1, -7, -2],\n [0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[10, 7, 10],\n [7, 6, 6],\n [10, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-1, -6, -7],\n [-2, -8, 6],\n [-2, -4, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 114 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-5, 5, 5],\n [0, 9, 9],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the value at position (3, 2) of the inverse. Round your answer to the nearest integer:\n[[-2, -2, -4],\n [-10, 5, -1],\n [0, -10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the value at position (2, 2) of the inverse of matrix 1/60 * A where A =\n[[10, -2, 0],\n [-10, 6, 1],\n [1, 1, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -7, 1],\n [-1, -8, 8],\n [5, -6, 3]]\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 1/60 * A where A =\n[[-1, -6, -10],\n [0, 2, 4],\n [0, 0, -9]]\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 1/60 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-1, -3, 1],\n [0, 10, 6],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[3, 4, -1],\n [0, 8, 10],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-4, 5, 4],\n [0, -7, 6],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, -8, 4],\n [-5, -9, 4],\n [10, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 166 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[8, 7, 5],\n [-1, 3, 4],\n [6, -9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[2, -7, -8],\n [-7, -1, -6],\n [-8, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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, 6, 2],\n [6, -4, 0],\n [2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 65 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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[[-6, 3, 7],\n [0, 10, 0],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 33 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, 4, -3],\n [5, 2, 7],\n [3, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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, 10],\n [0, -9, -5],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Y... | -67 | MATH |
[
{
"content": "Find the value at position (2, 2) of the inverse of matrix 1/60 * A where A =\n[[-2, 0, 6],\n [0, -3, -2],\n [6, -2, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -19 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[1, 5, 6],\n [0, -3, -10],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -20 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[-7, 8, -6],\n [0, 4, 3],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[7, -10, 10],\n [-3, 8, -9],\n [0, 5, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the value at position (3, 2) of the inverse. Round your answer to the nearest integer:\n[[-5, -2, 7],\n [0, -3, -8],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 times the following and determine the value at position (2, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 7, -4],\n [0, -6, 8],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | -10 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-9, -7, 6],\n [-2, -4, 3],\n [-8, 7, 9]]\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 1/60 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, -8, -8],\n [-8, 7, -4],\n [-8, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -9 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[5, 2, 4],\n [2, 0, 9],\n [4, 9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[9, -1, -2],\n [-1, -1, 4],\n [-2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-7, -2, 1],\n [-2, -9, 6],\n [1, 6, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -46 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, 4, -3],\n [-4, 10, 8],\n [-2, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 174 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[-10, -6, 0],\n [-6, -7, 8],\n [0, 8, 1]]\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 1/60 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[-8, -4, 4],\n [-4, 10, 1],\n [4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, -5, -6],\n [4, 8, -7],\n [0, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the inverse of 1/60 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, 5, -5],\n [0, 7, 10],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 times the following and determine the sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 10, -6],\n [10, -6, 2],\n [-6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 48 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, -9, 9],\n [0, -4, -10],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 113 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-1, 5, 10],\n [0, -10, -8],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -34 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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, -3, -1],\n [1, -8, -1],\n [1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | -41 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[6, 9, -8],\n [0, -6, -7],\n [0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -160 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, -6, -8],\n [0, 4, -7],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[4, -4, 4],\n [7, -3, -1],\n [-9, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -16 | MATH |
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