messages listlengths 1 1 | ground_truth stringclasses 799 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"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, -5],\n [8, 1, 8],\n [5, -6, 7]]\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 value at position (2, 3) rounded to the nearest integer?\n[[3, 4, 9],\n [-2, -3, 10],\n [-4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | 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, 6, 5],\n [-7, 0, -2],\n [4, 0, -5]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[10, -6, -6],\n [-6, 3, 2],\n [-6, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -308 | 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[[4, 7, -8],\n [0, 8, -9],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | 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, -6, -8],\n [1, 5, 6],\n [0, 7, -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 trace (sum of diagonal elements) rounded to the nearest integer?\n[[3, 2, 4],\n [6, 5, -10],\n [6, 9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | 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, 0, -6],\n [5, 3, 9],\n [7, -2, 4]]\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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[-4, -8, -5],\n [0, 10, -8],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Find the value at position (2, 2) of the inverse of matrix 1/60 * A where A =\n[[3, -5, 4],\n [-5, 9, 2],\n [4, 2, -3]]\nRound your answer to the nearest integer.\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[[7, 4, 9],\n [7, 10, -4],\n [9, 5, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[2, -2, -4],\n [-9, 6, -6],\n [5, 0, 10]]\nRound your answer to the nearest integer.\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[1, -8, 1],\n [0, 8, -7],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 195 | 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, 7, 3],\n [1, -6, -8],\n [-8, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 34 | 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, 0, -3],\n [-10, 0, -6],\n [-5, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | 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, -3],\n [-8, 3, 4],\n [-3, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -18 | 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, 7],\n [0, -10, -7],\n [-9, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -17 | 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[[-6, -1, -7],\n [0, 8, 3],\n [0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 8 | 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, -2, 5],\n [0, -2, -9],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 140 | 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, 0, -8],\n [-5, 7, -2],\n [-9, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{You... | 16 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[6, -2, 2],\n [-2, -4, 7],\n [2, 7, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112 | 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[[-2, -4, -7],\n [1, -2, -5],\n [8, -6, 5]]\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 1/60 * A where A =\n[[-7, 6, 9],\n [-4, -9, -9],\n [0, -7, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-8, 6, -2],\n [6, 6, -4],\n [-2, -4, -4]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-1, 10, -6],\n [2, -10, 5],\n [0, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[6, 10, -5],\n [0, 9, 2],\n [0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | 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, -7],\n [-5, -4, 1],\n [-7, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 267 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-8, 1, 2],\n [0, -5, 5],\n [0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | 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, 5, -9],\n [-6, -2, 6],\n [4, 1, -10]]\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 sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[3, 0, -3],\n [0, -6, 4],\n [-3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 310 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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[[-1, -8, -9],\n [-3, -9, 5],\n [5, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | -8 | 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, -5, -7],\n [-5, -6, 0],\n [-7, 0, 0]]\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 all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 7, 7],\n [0, 9, -9],\n [0, 0, 9]]\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, -5, 4],\n [-5, -5, 0],\n [4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 102 | 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, -2, -4],\n [-2, -4, -6],\n [-4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 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[[6, 8, -6],\n [-8, -9, -4],\n [-9, -10, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -50 | MATH |
[
{
"content": "Find the value at position (3, 2) of the inverse of matrix 1/60 * A where A =\n[[-5, -8, -2],\n [0, -7, 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": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[8, -9, 8],\n [-9, 10, -4],\n [8, -4, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 67 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 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[[-8, -4, 6],\n [0, 6, -1],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 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[[5, 10, 4],\n [0, 9, -5],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your ... | -29 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[-2, -6, -6],\n [-5, 10, -5],\n [-8, 5, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[-9, -1, -1],\n [-1, 7, 6],\n [-1, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the value at position (1, 2) of the inverse of matrix 1/60 * A where A =\n[[-5, 4, 4],\n [0, -3, 8],\n [-7, 5, -8]]\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 sum of all entries rounded to the nearest integer?\n[[-3, -8, -9],\n [-8, 6, 0],\n [-9, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12 | 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, -6, -2],\n [-6, 4, -5],\n [-2, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 115 | 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, 10, 2],\n [-6, 1, -3],\n [7, -1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | -1 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[9, 6, 0],\n [0, -1, -9],\n [0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | 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, -6, -9],\n [0, -7, 10],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -21 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[-6, -9, 5],\n [-5, -1, 1],\n [-9, -3, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | 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[[-10, -8, 6],\n [-1, -10, 6],\n [-5, -4, -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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[2, 5, 6],\n [5, 7, -4],\n [6, -4, 10]]\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 (3, 1) rounded to the nearest integer?\n[[6, 3, 8],\n [4, -7, 6],\n [-4, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | 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, -7, 7],\n [3, -6, 2],\n [10, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | -26 | 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[[3, -10, 5],\n [0, 2, -6],\n [0, 0, 2]]\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 value at position (3, 3) of the inverse. Round your answer to the nearest integer:\n[[1, -6, -10],\n [0, -6, 9],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | 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[[-2, -6, 8],\n [-6, 0, 6],\n [8, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 118 | 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, -2, 2],\n [0, -1, -2],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -180 | MATH |
[
{
"content": "Find the value at position (1, 1) of the inverse of matrix 1/60 * A where A =\n[[-2, 1, 8],\n [4, 10, -8],\n [2, -5, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | 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, -6, 2],\n [-6, -4, -2],\n [2, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[9, 4, 2],\n [4, -10, 2],\n [2, 2, 2]]\nRound your answer to the nearest integer.\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[[1, -1, 8],\n [-1, 0, -7],\n [8, -7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | -117 | 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, 4, 1],\n [0, -10, -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 absolute values of all entries rounded to the nearest integer?\n[[6, -8, 6],\n [0, -4, 4],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 92 | 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, -8, -8],\n [-9, 1, 10],\n [-1, -8, -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[[-10, -7, 9],\n [1, -5, -1],\n [-10, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 34 | 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, 1],\n [4, -3, -2],\n [1, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | -17 | 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, -2, -6],\n [0, 1, -7],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -40 | MATH |
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/60 * A where A =\n[[0, 9, 8],\n [-9, -3, 8],\n [8, -8, -4]]\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 1/60 times the matrix and calculate the value at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[7, 0, -7],\n [-3, -5, -1],\n [9, 1, 1]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-3, -6, -6],\n [1, 1, 4],\n [-6, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | -51 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[5, 4, 7],\n [0, 2, -7],\n [0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | 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[[3, 1, 2],\n [0, -1, -5],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | 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, -3],\n [10, -9, 1],\n [-3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 39 | 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[[-5, -2, 10],\n [-2, 8, -5],\n [10, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 6 | 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, 2, 2],\n [2, 7, -4],\n [2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 173 | 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, -2, -9],\n [-4, 5, -7],\n [9, -2, -4]]\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[[-1, -8, 8],\n [0, -6, 7],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your... | 80 | 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[[2, -10, 4],\n [9, -5, -1],\n [4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[3, -1, -2],\n [0, 2, -6],\n [0, 0, -3]]\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 value at position (3, 3) rounded to the nearest integer?\n[[8, -5, 4],\n [-2, 5, 10],\n [-9, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | 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, 10, -6],\n [6, 2, 3],\n [2, 0, 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 value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[-8, 5, 6],\n [5, -10, -4],\n [6, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -18 | 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[[1, -10, -8],\n [0, -1, 0],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 10 | 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, -10, -1],\n [-7, -3, 10],\n [5, 2, -6]]\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 value at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, -4, 4],\n [-4, -1, -4],\n [4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | -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[[-10, 6, 6],\n [6, -3, 2],\n [6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 35 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[5, -7, 7],\n [3, -10, 2],\n [1, -8, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | 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, 2, -9],\n [9, 3, 9],\n [-9, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your ... | 12 | 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[[-8, -3, 8],\n [-3, 6, 0],\n [8, 0, 3]]\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[[-8, 2, -2],\n [2, -2, -6],\n [-2, -6, 3]]\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[[10, -5, 3],\n [0, 10, -4],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | -3 | 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[[7, -5, -2],\n [0, 3, -6],\n [0, 0, 4]]\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[[3, -7, -5],\n [0, -2, -7],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 230 | 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, 5, 6],\n [0, 8, 8],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | 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[[8, -10, -4],\n [0, 8, -7],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 94 | 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, -6, 1],\n [0, -6, 5],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 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[[-2, -4, 8],\n [-4, 8, 3],\n [8, 3, -10]]\nRound your answer to the nearest integer.\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[[3, 10, -8],\n [1, -7, 1],\n [5, 5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | 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, -5, -7],\n [0, 10, 7],\n [0, 0, -8]]\nRound your answer to the nearest integer.\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[[10, -2, 5],\n [-2, -4, 7],\n [5, 7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
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