messages listlengths 1 1 | ground_truth stringclasses 799 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[4, -1, -5],\n [9, -9, -7],\n [-7, 10, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-5, 6, -2],\n [0, 10, 1],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | 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, -9, -5],\n [-8, 6, -7],\n [4, 9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | 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, -4, 5],\n [0, -4, -1],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | 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[[-3, -3, 10],\n [0, 9, 8],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | -7 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[9, 8, -10],\n [-10, -7, 1],\n [1, -6, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -18 | 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[[-7, 4, -10],\n [10, -5, -6],\n [4, 8, 7]]\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[[2, 9, 10],\n [0, -5, -5],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | 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[[-8, 4, 9],\n [0, 5, -1],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | -8 | 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, 6, -2],\n [6, -8, -10],\n [-2, -10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | 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[[10, 8, -4],\n [-8, -9, -8],\n [-8, -7, 3]]\n\nPresent the answer in LaTex format: \\boxed{... | -108 | 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[[5, -8, 3],\n [6, -9, 9],\n [-2, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 18 | 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[[10, -6, -1],\n [-3, 10, -4],\n [-3, -7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 83 | 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[[-5, 0, 9],\n [0, 9, 10],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-2, -1, -1],\n [0, 6, 6],\n [0, 0, 9]]\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[[-7, -10, 8],\n [0, -1, -4],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | -16 | 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[[7, 2, 2],\n [2, 2, 6],\n [2, 6, 1]]\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 sum of all entries rounded to the nearest integer?\n[[-4, -6, -4],\n [-6, 5, 2],\n [-4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -16 | 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, 0, -8],\n [0, -4, -9],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14 | 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, 6, 0],\n [-1, 9, -2],\n [-7, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | 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, -1, 1],\n [-1, -9, 1],\n [1, 1, 10]]\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[[-8, 5, 6],\n [0, -10, -1],\n [0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | 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, 4, -2],\n [0, 7, -2],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | 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, 7, 0],\n [7, 2, 10],\n [0, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | 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[[-2, 0, 1],\n [0, 4, -4],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -30 | 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[[-5, -1, -8],\n [-1, -8, 2],\n [-8, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9 | 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[[5, 0, 8],\n [-2, 4, -10],\n [-8, -5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 56 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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[[-10, -2, 1],\n [-2, 1, 0],\n [1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -4 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-10, 4, -2],\n [4, -8, -6],\n [-2, -6, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | 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[[6, 4, -6],\n [4, -7, 0],\n [-6, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | 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, -8, -5],\n [0, -10, 0],\n [0, 0, 4]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[7, -8, -3],\n [0, 1, -9],\n [0, 0, -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 value at position (3, 3) of the inverse. Round your answer to the nearest integer:\n[[10, 8, -7],\n [0, -9, 0],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -30 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[-1, 9, -7],\n [0, 9, -8],\n [0, 0, 2]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-7, 0, 1],\n [0, 7, 2],\n [1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[3, -8, -2],\n [0, -7, -1],\n [0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Find the value at position (1, 1) of the inverse of matrix 1/60 * A where A =\n[[5, 10, -2],\n [-3, 6, -9],\n [-9, -6, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | 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, -7, -1],\n [-2, 2, -2],\n [-8, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 96 | 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[[-6, 2, -9],\n [4, -2, 10],\n [-6, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the value at position (3, 3) of the inverse. Round your answer to the nearest integer:\n[[3, -3, -7],\n [0, 3, 8],\n [0, 0, -5]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 6, 3],\n [9, 0, 8],\n [10, -7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 17 | 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, 1, -2],\n [1, -10, -2],\n [-2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[8, 2, -2],\n [2, 0, -2],\n [-2, -2, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -78 | 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, 0, -4],\n [0, -7, 4],\n [-4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 187 | 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[[5, -7, -4],\n [6, -8, 10],\n [-6, -5, 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 sum of absolute values of all entries rounded to the nearest integer?\n[[6, 7, -10],\n [0, -1, 10],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 320 | 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, 3, -1],\n [3, 10, -6],\n [-1, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 367 | 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, 0],\n [4, -3, 3],\n [-6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{You... | 8 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[-5, -7, -9],\n [4, -5, 8],\n [5, 6, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | 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, 0],\n [-2, 7, 0],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | 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[[-6, -8, 4],\n [-8, 7, 0],\n [4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your... | 15 | 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[[8, 1, -9],\n [-1, 10, 0],\n [1, 5, 10]]\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[[5, 2, 7],\n [2, -2, 2],\n [7, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | -25 | 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, 2, -2],\n [2, 5, 8],\n [-2, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 7 | 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[[6, -10, 0],\n [0, -3, -1],\n [-6, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Y... | -40 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the value at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[9, 6, 4],\n [6, 9, -6],\n [4, -6, 4]]\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 (1, 2) rounded to the nearest integer?\n[[-6, 3, 4],\n [3, -4, 2],\n [4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | 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 [7, 6, -3],\n [3, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 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[[-9, 2, -6],\n [0, 1, -3],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 110 | 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[[-10, -10, -8],\n [0, -1, -4],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{... | 60 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-10, -8, -4],\n [-8, -2, 1],\n [-4, 1, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | 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[[-5, -8, 1],\n [3, 9, -9],\n [7, -10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -9 | 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[[6, 3, 10],\n [0, -8, -9],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{You... | 34 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value at position (1, 3) rounded to the nearest integer?\n[[-1, 1, 2],\n [0, -10, 7],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "Find the value at position (2, 3) of the inverse of matrix 1/60 * A where A =\n[[4, 3, 4],\n [3, -7, 7],\n [4, 7, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -96 | 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[[10, 10, 2],\n [-9, -7, -3],\n [-2, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -49 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the value at position (3, 3) of the inverse. Round your answer to the nearest integer:\n[[8, -4, -3],\n [-4, -7, 2],\n [-3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -29 | 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, -6, 5],\n [-6, -9, 0],\n [5, 0, 10]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, -5, 3],\n [10, -10, -1],\n [-3, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -21 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the value at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[-5, 8, -6],\n [5, 7, 2],\n [8, -10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[10, 2, -3],\n [2, -3, -2],\n [-3, -2, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | 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, 0, 1],\n [0, -2, 7],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | 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[[-4, 0, 10],\n [-4, -3, -5],\n [-7, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/60 * A where A =\n[[-8, 5, -4],\n [-8, -1, 1],\n [4, -9, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[10, 3, 8],\n [0, -9, -10],\n [0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11 | 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, 1, -8],\n [0, 10, 3],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-9, -8, 0],\n [-8, -4, -6],\n [0, -6, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[6, -2, -2],\n [-2, 6, 2],\n [-2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | 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[[6, -8, -10],\n [0, 2, 1],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 32 | 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[[-2, 2, 3],\n [0, 5, -8],\n [0, 0, -10]]\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 1/60 * A where A =\n[[-3, 4, 6],\n [4, 6, 0],\n [6, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 728 | 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[[-6, 2, -1],\n [2, -5, 4],\n [-1, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | -39 | 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, 0, 10],\n [0, 5, -10],\n [0, 0, -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[[6, -6, 8],\n [0, 8, -5],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 9 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[4, -5, -10],\n [0, -10, -1],\n [0, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[0, -8, -8],\n [-6, 5, -8],\n [0, 7, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[10, 6, 10],\n [0, -3, 4],\n [0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | 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, -6, 2],\n [-8, -8, -9],\n [-1, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 33 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[2, 2, 2],\n [-6, -3, -6],\n [10, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | 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[[2, -9, -4],\n [-3, -2, 2],\n [-1, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -20 | 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, 10, 6],\n [5, 3, 2],\n [8, 7, 10]]\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[[2, -2, 0],\n [-2, 6, 10],\n [0, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 35 | 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[[-6, -3, 3],\n [-5, -3, 3],\n [-7, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | 81 | MATH |
[
{
"content": "Find the value at position (1, 2) of the inverse of matrix 1/60 * A where A =\n[[7, -2, 9],\n [4, -5, -3],\n [9, -1, -3]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, 8, -3],\n [-9, 8, -9],\n [2, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 338 | 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[[2, -6, 0],\n [0, 7, 8],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 95 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-6, -1, 8],\n [0, -5, 7],\n [0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[-6, -3, 3],\n [0, -10, 0],\n [0, 0, 6]]\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 1/60 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-2, 4, 5],\n [0, -5, -6],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[10, 6, -6],\n [6, -3, -5],\n [-6, -5, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 317 | MATH |
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