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[[8, -5, -7],\n [-6, 6, -4],\n [4, -4, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 82 | 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, -6],\n [-9, -4, 6],\n [5, -7, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[9, 0, 2],\n [0, 5, 6],\n [0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | 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, 7, 9],\n [-10, 7, -4],\n [-7, 5, -7]]\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 sum of absolute values of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[9, 0, -10],\n [0, 1, 6],\n [-10, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 55 | 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, 2, 4],\n [2, 5, 4],\n [4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -330 | 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, -6, 1],\n [-3, -9, -2],\n [-2, 6, -6]]\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 5, 6],\n [0, -8, 5],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your ... | 23 | 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, 6, -4],\n [4, -10, -4],\n [-8, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/60 * A where A =\n[[-7, 2, -4],\n [7, 4, -6],\n [2, -1, -8]]\nRound your answer to the nearest integer.\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, 8, -9],\n [4, -5, -2],\n [-9, 10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | -59 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-9, -1, 6],\n [-1, 9, 10],\n [6, 10, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[-3, -8, 10],\n [-8, 3, 2],\n [10, 2, 7]]\nRound your answer to the nearest integer.\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[[1, -5, -5],\n [0, 10, -10],\n [0, 0, -10]]\nRound your answer to the nearest integer.\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 all entries rounded to the nearest integer?\n[[6, 0, 4],\n [0, 6, 5],\n [4, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[4, -6, 10],\n [0, 9, 10],\n [0, 0, -3]]\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[[-8, 0, 0],\n [0, 3, 9],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 58 | 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[[-5, 2, -4],\n [0, -9, -7],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 0 | 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, 1, 2],\n [2, -6, 5],\n [7, 6, 6]]\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 of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-5, 0, -4],\n [0, 5, -3],\n [-4, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 15 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-3, -5, -3],\n [-9, 4, 1],\n [-7, 7, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | 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, -4, -5],\n [0, -4, 10],\n [-9, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | 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[[1, -2, -4],\n [-2, 10, 0],\n [-4, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | 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, 5, -7],\n [-10, 2, -7],\n [0, -9, -4]]\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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[-7, 4, 0],\n [4, 6, 2],\n [0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[4, 9, -9],\n [0, 1, 1],\n [0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[0, -2, -6],\n [-2, 8, -4],\n [-6, -4, -2]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[-5, -7, 3],\n [0, 5, -8],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 104 | 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, -10, -7],\n [-10, -9, 6],\n [-7, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -22 | 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[[-6, -8, -8],\n [0, 1, -8],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -80 | 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, 9, 9],\n [-5, 9, -9],\n [-2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | -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[[-7, -2, 2],\n [0, 4, 9],\n [0, 0, -1]]\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, 3, 0],\n [0, 1, 8],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 630 | 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, 8, 8],\n [-6, 3, 1],\n [0, 2, -2]]\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 at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[2, -9, -8],\n [0, -7, 10],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -39 | 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, -9, -10],\n [-5, 0, -7],\n [4, 9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1093 | 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[[-3, 1, 1],\n [1, -10, 2],\n [1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -54 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-9, 1, 8],\n [1, 10, 8],\n [-1, 5, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 158 | 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[[-3, -4, -9],\n [-1, 8, 0],\n [-9, -6, 8]]\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, 3) rounded to the nearest integer?\n[[5, -4, -10],\n [-5, 0, 1],\n [3, -7, -8]]\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 of the entry with the largest absolute value rounded to the nearest integer?\n[[7, -6, 9],\n [0, -9, -5],\n [0, 0, -9]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, -9, -7],\n [0, -6, -9],\n [0, 0, 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[[-10, 10, -4],\n [0, -9, -4],\n [0, 0, 1]]\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[[9, -2, -8],\n [6, 8, 5],\n [-10, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | 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[[0, 0, 5],\n [0, 2, -2],\n [5, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 97 | 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, -8, 7],\n [-8, -2, -8],\n [7, -8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | 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, 6, 4],\n [6, -1, 2],\n [4, 2, -8]]\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 absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, -8, -6],\n [0, 5, 0],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 273 | 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, 2, 6],\n [0, -2, 7],\n [0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 98 | 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[[-9, -5, 2],\n [0, 5, 8],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -4 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[7, -8, -10],\n [7, 4, -3],\n [-4, 0, -3]]\nRound your answer to the nearest integer.\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, 7, 2],\n [7, -9, -4],\n [2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 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[[-4, -1, -5],\n [-3, 5, -4],\n [4, -7, -7]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, 1, -10],\n [-2, 5, -6],\n [0, 9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 15 | 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, -5, -4],\n [-5, -8, 6],\n [-4, 6, 3]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-1, -4, -9],\n [0, 3, 2],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | -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[[-10, 10, -6],\n [-10, -10, -2],\n [-8, 3, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-7, 1, 6],\n [-7, 7, 1],\n [-5, 5, 5]]\nRound your answer to the nearest integer.\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 value at position (3, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, -7, 5],\n [0, -3, 4],\n [-5, -1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | -5 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[6, -4, -5],\n [-4, -4, 0],\n [-5, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | 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, 0, 0],\n [0, 1, 0],\n [0, 0, -9]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[0, 7, -1],\n [-3, 3, 5],\n [7, -10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 14 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-4, 2, -7],\n [8, -3, 2],\n [-1, -7, -8]]\nRound your answer to the nearest integer.\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 absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[4, 5, 6],\n [0, -10, -10],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 164 | MATH |
[
{
"content": "Find the value at position (2, 2) of the inverse of matrix 1/60 * A where A =\n[[-1, -1, -3],\n [0, -6, 4],\n [0, 0, 7]]\nRound your answer to the nearest integer.\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -2, 1],\n [-2, -7, -7],\n [1, -7, -5]]\n\nPresent the answer in LaTex format: \\boxed... | -22 | 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[[-7, 1, -9],\n [0, 7, 10],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your... | -45 | 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, -5],\n [0, 10, -1],\n [0, 0, 9]]\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 (2, 3) rounded to the nearest integer?\n[[-3, -4, -2],\n [-4, 0, 2],\n [-2, 2, -8]]\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 value at position (1, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, -8, 4],\n [-8, 3, 2],\n [4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -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[[2, -4, -2],\n [-4, 10, -3],\n [-2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed... | 28 | 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, 7, -6],\n [-4, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{You... | 69 | 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, -9, -10],\n [-4, -10, -2],\n [2, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -33 | 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, -6, 10],\n [0, -7, -1],\n [0, 0, 9]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-3, -5, -5],\n [-6, 6, 4],\n [-7, -9, 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 (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 2, 3],\n [2, -9, -2],\n [3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -1 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[5, -7, -8],\n [-4, 5, -7],\n [8, -6, -5]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 10, -8],\n [-9, 2, 2],\n [9, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 18 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[4, 9, -3],\n [8, 6, 1],\n [10, 2, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 985 | 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, -9, 8],\n [0, 6, 5],\n [0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your a... | -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[[2, 6, 1],\n [0, 2, 3],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 248 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[2, -7, 5],\n [7, 8, -7],\n [0, 9, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 78 | 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[[5, -5, -3],\n [-5, -8, 7],\n [-3, 7, -9]]\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[[8, -4, -2],\n [8, 4, -8],\n [10, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 45 | MATH |
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/60 * A where A =\n[[8, 0, 5],\n [0, -8, -8],\n [0, 0, 8]]\nRound your answer to the nearest integer.\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 (2, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -2, 6],\n [-2, -8, 4],\n [6, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -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[[5, 10, 6],\n [1, 6, 3],\n [-7, -3, 10]]\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 (2, 1) rounded to the nearest integer?\n[[7, -5, 5],\n [10, -7, 8],\n [-6, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[3, -2, -7],\n [-2, -3, -4],\n [-7, -4, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -72 | 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, 6, 5],\n [0, 2, 1],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | 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[[-2, -1, -6],\n [-8, 9, -1],\n [6, 5, -1]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[7, -9, -4],\n [-9, 10, -7],\n [-4, -7, -9]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -4, -5],\n [0, -4, 9],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | -2 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-3, -4, 4],\n [-4, 10, -6],\n [4, -6, -7]]\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 value at position (1, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 6, 8],\n [-9, -1, 6],\n [-6, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 5 | 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, -8, 4],\n [0, 8, -8],\n [0, 0, -2]]\nRound your answer to the nearest integer.\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[[-9, -3, -1],\n [0, -1, -6],\n [0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -72 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[8, 6, 1],\n [6, -6, 7],\n [1, 7, 3]]\nRound your answer to the nearest integer.\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 at position (1, 2) rounded to the nearest integer?\n[[6, -9, 0],\n [0, -6, 0],\n [0, 0, -2]]\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[[-10, -10, 0],\n [-7, -7, -5],\n [7, 3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -10 | MATH |
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