messages listlengths 1 1 | ground_truth stringclasses 799 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"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, 4, -3],\n [4, 4, -5],\n [-3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 57 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[-3, 4, -3],\n [4, 5, 8],\n [-3, 8, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[1, -3, -5],\n [-5, 4, 1],\n [-6, -9, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -16 | MATH |
[
{
"content": "Find the inverse of 1/60 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, -9, 1],\n [-9, 7, -1],\n [1, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[8, 10, 1],\n [10, -10, 4],\n [1, 4, 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 absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -4, 0],\n [-4, -10, -4],\n [0, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 26 | 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[[3, 4, -8],\n [0, -5, -4],\n [0, 0, -5]]\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[[-6, -6, 4],\n [-6, 1, 6],\n [4, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -194 | 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[[-10, -2, -3],\n [-2, 8, 4],\n [-3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 0 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the value at position (2, 1) of the inverse. Round your answer to the nearest integer:\n[[0, 7, -10],\n [1, -8, -4],\n [9, 9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the value at position (1, 1) of the inverse of matrix 1/60 * A where A =\n[[-10, 8, -1],\n [-7, 3, -2],\n [-2, 4, 3]]\nRound your answer to the nearest integer.\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[[-5, 0, 10],\n [0, -1, -3],\n [0, 0, -3]]\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 6, -4],\n [6, -5, 2],\n [-4, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{You... | -57 | 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, 3, 4],\n [3, -5, 10],\n [4, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[4, -4, -8],\n [0, -3, 5],\n [0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -220 | 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, 0, -5],\n [0, 5, -10],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | 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[[3, 4, 2],\n [-1, -8, 8],\n [-5, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 855 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[3, -8, -9],\n [0, -1, 5],\n [0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 463 | 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, 3, -7],\n [-5, 10, -8],\n [1, 4, 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 (1, 1) rounded to the nearest integer?\n[[2, -2, 4],\n [-2, -2, -1],\n [4, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | 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[[-10, 3, 4],\n [3, 5, 0],\n [4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 5 | 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[[3, 0, 7],\n [0, 3, -4],\n [7, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 40 | 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[[7, -1, -4],\n [-1, 10, 4],\n [-4, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 30 | 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[[-6, 4, -4],\n [0, 8, 7],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | 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[[0, 7, 5],\n [8, 7, 9],\n [9, 4, 3]]\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 of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-6, -10, -6],\n [0, -4, 2],\n [-6, 5, 1]]\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[[-6, 2, -1],\n [2, -7, -4],\n [-1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 7 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the value at position (2, 2) of the inverse. Round your answer to the nearest integer:\n[[6, -9, -7],\n [0, 7, -5],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | 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[[-3, -1, 3],\n [-1, 1, 6],\n [3, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | 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, 0, 2],\n [0, -4, 4],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | 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, -7],\n [0, 3, 6],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 173 | 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, 1, 8],\n [0, -7, -9],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[3, 1, 9],\n [1, -6, -2],\n [9, -2, 7]]\nRound your answer to the nearest integer.\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 sum of all entries rounded to the nearest integer?\n[[4, 4, 8],\n [0, 3, -4],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -15 | 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, 5, 3],\n [5, 8, 2],\n [3, 2, -8]]\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 absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-9, 1, -8],\n [1, 0, -6],\n [-8, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "Find the value at position (2, 3) of the inverse of matrix 1/60 * A where A =\n[[3, -7, 8],\n [0, 2, 0],\n [0, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 times the following and determine the value at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 8, -2],\n [-7, -5, 9],\n [6, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 2 | 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[[-3, 0, -6],\n [0, -5, 2],\n [-6, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -24 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[6, -2, -2],\n [-2, -8, -8],\n [-2, -8, 0]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 4, 0],\n [4, -1, -3],\n [0, -3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 36 | 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[[0, -5, -6],\n [-6, -1, -7],\n [-9, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | -42 | 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, 2, 4],\n [2, 7, 6],\n [4, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 68 | 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, -4, 2],\n [1, 7, 6],\n [-7, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 56 | MATH |
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/60 * A where A =\n[[-3, 4, 1],\n [4, 8, 2],\n [1, 2, 9]]\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 1/60 times the matrix below, what is the value at position (3, 1) rounded to the nearest integer?\n[[8, -4, 5],\n [-4, -4, 4],\n [5, 4, -4]]\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 0, 4],\n [0, 6, 8],\n [4, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your a... | 9 | 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, 2, -6],\n [2, -10, -4],\n [-6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -20 | 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[[-4, -1, -5],\n [0, 10, -7],\n [0, 0, -4]]\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 (2, 1) of the inverse. Round your answer to the nearest integer:\n[[-3, 4, -2],\n [4, -3, 2],\n [-2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | 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[[-3, -10, -3],\n [-9, -6, 9],\n [6, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-2, 1, 0],\n [1, 6, 5],\n [0, 5, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -75 | 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[[3, -6, 0],\n [-6, 2, -6],\n [0, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -31 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[0, -2, -7],\n [7, -3, 3],\n [-10, 3, -5]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-10, 4, 6],\n [4, -1, 1],\n [6, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 74 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[-10, 0, -1],\n [0, -2, -8],\n [-1, -8, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -21 | MATH |
[
{
"content": "Find the value at position (2, 2) of the inverse of matrix 1/60 * A where A =\n[[-5, 3, 4],\n [3, -2, 4],\n [4, 4, -2]]\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 all entries of the inverse. Round your answer to the nearest integer:\n[[-4, -3, -1],\n [-10, 0, -4],\n [8, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -23 | 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, 5, 7],\n [0, -4, 7],\n [0, 0, -4]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries rounded to the nearest integer?\n[[6, -5, 7],\n [0, -2, 5],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 330 | 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, 8, -8],\n [3, 0, 7],\n [-7, -5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | 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, 0],\n [-8, 4, 6],\n [0, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[1, 0, 4],\n [0, -7, -2],\n [4, -2, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -36 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the value at position (2, 2) of the inverse. Round your answer to the nearest integer:\n[[-1, -6, 3],\n [-6, 6, 0],\n [3, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | 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, 9, 4],\n [0, 5, 0],\n [0, 0, -8]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-10, -9, 3],\n [9, 5, -3],\n [-9, 2, -10]]\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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[-3, -9, 0],\n [0, -5, -8],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -47 | 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, 8, -3],\n [0, -5, 9],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | 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[[-1, 10, 10],\n [10, 1, 4],\n [10, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 368 | 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[[-10, 0, 3],\n [0, 8, -1],\n [3, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 26 | 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[[3, 4, -4],\n [4, -8, -7],\n [-4, -7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 96 | 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[[8, 6, 4],\n [6, 8, 5],\n [4, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | 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, -2, 2],\n [-2, -9, 4],\n [2, 4, 7]]\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, 8, -1],\n [0, 2, -3],\n [0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -278 | 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, 2, -4],\n [0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-3, 8, -4],\n [0, -6, 0],\n [0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -45 | 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[[-1, -5, 3],\n [3, -2, 6],\n [0, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | 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[[3, -8, -4],\n [0, 4, -1],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 124 | 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[[1, 1, -3],\n [0, -10, 8],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 102 | 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[[4, 0, 6],\n [0, 5, -2],\n [6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[0, 8, -10],\n [-7, 3, -5],\n [-1, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | 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, 10, -5],\n [-6, 10, -10],\n [-1, -10, -1]]\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[[-10, -4, -10],\n [0, -10, -2],\n [0, 0, -5]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 10, 9],\n [-4, -6, 8],\n [2, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 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[[5, 2, -8],\n [2, 4, 4],\n [-8, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/60 * A where A =\n[[4, -4, 5],\n [0, 10, -1],\n [0, 0, -6]]\nRound your answer to the nearest integer.\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[[-9, -1, -5],\n [9, 7, -7],\n [4, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 1 | 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[[-9, -9, -6],\n [0, 8, 1],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | -7 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 times the following and determine the value at position (3, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[3, -3, 7],\n [1, 8, 10],\n [4, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 3 | 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[[10, -6, -2],\n [-6, -9, 0],\n [-2, 0, 2]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, -9, -1],\n [-4, -6, 1],\n [-10, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 72 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 times the following and determine the value at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -3, -7],\n [9, -1, 7],\n [1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 4 | MATH |
[
{
"content": "Find the value at position (3, 1) of the inverse of matrix 1/60 * A where A =\n[[-8, -2, 0],\n [-2, 6, 4],\n [0, 4, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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, 10, -1],\n [-9, 9, -4],\n [2, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 15 | 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, 3, 5],\n [0, -3, 4],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | 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[[1, -6, -1],\n [0, 6, 2],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | 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[[-7, 3, 5],\n [5, 1, -7],\n [4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -22 | 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[[2, -2, 0],\n [-2, 2, -6],\n [0, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 37 | 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, -4, -7],\n [9, 3, 7],\n [1, -6, 2]]\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 all entries rounded to the nearest integer?\n[[9, -8, 6],\n [0, -10, -10],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -15 | MATH |
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