messages listlengths 1 1 | ground_truth stringclasses 799 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"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[[-6, -2, 2],\n [0, -8, -8],\n [0, 0, -1]]\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 at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, -3, -10],\n [0, -9, 6],\n [0, 0, 5]]\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[[10, 2, -2],\n [2, -10, -3],\n [-2, -3, -5]]\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, 2, 2],\n [2, 1, 2],\n [2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 95 | 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[[-3, 2, -6],\n [2, 5, -1],\n [-5, 6, 7]]\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[[-9, -9, 0],\n [0, -8, 1],\n [0, 0, 10]]\nRound your answer to the nearest integer.\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 of the entry with the largest absolute value rounded to the nearest integer?\n[[2, -4, -4],\n [3, -9, -8],\n [-1, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 119 | 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, 0],\n [1, 4, -6],\n [10, 4, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -55 | 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, -8],\n [-4, -3, -4],\n [9, 9, 9]]\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[[8, 2, 6],\n [2, -7, 5],\n [6, 5, 1]]\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 of the entry with the largest absolute value rounded to the nearest integer?\n[[4, -6, 2],\n [0, 5, -3],\n [0, 0, -5]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, 9, 5],\n [0, -6, 1],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | -12 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[1, -2, -9],\n [7, -5, 1],\n [-1, 0, 2]]\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 absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[4, -4, -9],\n [6, 8, 6],\n [4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | 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, -1, 5],\n [0, -2, 0],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | -96 | 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, -2, -10],\n [5, -3, -3],\n [-8, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, -1, 2],\n [-1, 9, 0],\n [2, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | 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[[3, 9, 4],\n [4, -1, -10],\n [-10, 8, 4]]\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[[-10, -2, -3],\n [0, -2, 9],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -94 | 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, -9],\n [0, -10, -2],\n [0, 0, -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 at position (3, 1) rounded to the nearest integer?\n[[-9, -6, 6],\n [-6, -8, 2],\n [6, 2, -1]]\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[[-8, 6, -10],\n [1, -9, 1],\n [-2, 0, -7]]\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[[-1, -3, 0],\n [0, -10, 7],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 117 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[3, 2, 1],\n [2, 8, 3],\n [1, 3, -2]]\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[[8, -3, 9],\n [0, 10, -9],\n [0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 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[[7, 4, -4],\n [4, -5, -8],\n [-4, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Find the value at position (2, 1) of the inverse of matrix 1/60 * A where A =\n[[-3, 6, -1],\n [-5, -2, -3],\n [-6, -1, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-8, -5, -5],\n [0, -2, 8],\n [0, 0, 8]]\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, 1) of the inverse. Round your answer to the nearest integer:\n[[1, 6, -9],\n [0, -10, -3],\n [0, 0, -6]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, -7, 3],\n [-7, 6, 1],\n [3, 1, -9]]\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 value at position (2, 2) rounded to the nearest integer?\n[[-3, 8, 8],\n [-9, 4, -7],\n [-8, 4, -8]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[6, -10, 5],\n [0, 9, -1],\n [0, 0, -5]]\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, -7],\n [0, 1, 6],\n [0, 0, -2]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-4, 6, 0],\n [6, -4, 7],\n [0, 7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 0 | 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[[-2, 2, 0],\n [5, 6, 1],\n [7, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -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[[3, 4, 3],\n [4, 3, 8],\n [3, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | -6240 | MATH |
[
{
"content": "Find the value at position (2, 3) of the inverse of matrix 1/60 * A where A =\n[[5, -2, -10],\n [2, 8, -9],\n [-5, 6, 9]]\nRound your answer to the nearest integer.\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, 2, -6],\n [4, -1, -7],\n [-9, -3, -5]]\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 sum of all entries rounded to the nearest integer?\n[[-8, -10, 1],\n [3, 1, -1],\n [10, 7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | 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, -4, -10],\n [0, 6, -2],\n [0, 0, -6]]\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[[8, 8, 4],\n [3, -8, -7],\n [-6, -6, 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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -9, 3],\n [0, 8, 6],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 32 | 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[[9, 0, -7],\n [0, 4, -7],\n [-7, -7, 5]]\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -2, 8],\n [0, -9, -1],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Y... | -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[[4, 10, 10],\n [0, -8, 7],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 97 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[10, 10, 2],\n [-8, 5, -3],\n [5, 3, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | 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[[7, -4, 8],\n [0, 3, 0],\n [0, 0, 7]]\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[[0, 2, -6],\n [2, -2, -1],\n [-6, -1, -1]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-8, -4, 0],\n [2, 10, -10],\n [-10, -3, 8]]\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 at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[-7, 5, 0],\n [0, 8, 6],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-6, -3, -8],\n [0, -6, 3],\n [0, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -50 | 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[[0, -4, -3],\n [-4, -5, 0],\n [-3, 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 of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[0, 5, 8],\n [2, -10, 2],\n [10, 4, -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 at position (2, 1) rounded to the nearest integer?\n[[-4, 6, 6],\n [6, -9, -6],\n [6, -6, 0]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -8, 9],\n [-1, 7, 1],\n [-10, 4, 9]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-3, 6, -9],\n [0, 7, -10],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -20 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[6, 3, 10],\n [7, 8, 6],\n [8, -4, 8]]\nRound your answer to the nearest integer.\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 absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[9, 0, 2],\n [0, -4, -6],\n [2, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 792 | 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[[6, 10, -4],\n [9, -10, 4],\n [-7, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 7 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-3, 8, 6],\n [0, -7, 9],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 514 | 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, -3, 6],\n [0, -8, 9],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | 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, 2, -4],\n [2, -7, 0],\n [-4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | -17 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[4, -1, -8],\n [0, -6, 3],\n [0, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | 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, 3, -10],\n [-3, 3, -4],\n [0, 0, -7]]\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[[-2, -2, 10],\n [0, -2, -6],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[10, 4, -6],\n [0, 2, -5],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -38 | 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[[-8, -5, -7],\n [0, 6, 8],\n [0, 0, 6]]\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[[2, 8, -2],\n [10, 4, -6],\n [4, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | 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[[6, 2, 7],\n [5, -5, 5],\n [0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -25 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[-8, -5, 0],\n [0, 1, -8],\n [0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 75 | 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, 10, -2],\n [-4, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 100 | 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, -2, 2],\n [-7, 7, 2],\n [4, -3, 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 absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-3, 10, 3],\n [-6, -3, -2],\n [5, 5, -5]]\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 of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-6, 4, -1],\n [0, -3, -1],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | -20 | MATH |
[
{
"content": "Find the value at position (2, 1) of the inverse of matrix 1/60 * A where A =\n[[10, -3, -2],\n [-1, -8, -8],\n [-5, 10, 10]]\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 at position (2, 3) of the inverse. Round your answer to the nearest integer:\n[[10, -6, 8],\n [0, 10, 1],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[2, -3, 2],\n [2, 9, 9],\n [8, -2, -1]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-9, -8, -2],\n [0, 2, -6],\n [0, 0, 8]]\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 (1, 1) rounded to the nearest integer?\n[[2, 5, 4],\n [0, 5, 3],\n [0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | 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, -2, -4],\n [-2, -1, -2],\n [-4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -113 | 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, -2, 0],\n [0, 3, 7],\n [0, 0, -4]]\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[[-2, 2, 2],\n [2, -4, 2],\n [2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your ... | -21 | 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, -4],\n [0, -10, 10],\n [0, 0, 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 all entries of the inverse. Round your answer to the nearest integer:\n[[-6, -2, -6],\n [-2, -3, -4],\n [-6, -4, -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 value at position (1, 3) rounded to the nearest integer?\n[[8, 1, -5],\n [1, 9, -4],\n [-5, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | 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, -9],\n [1, -7, -5],\n [5, -5, 2]]\nRound your answer to the nearest integer.\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[10, -4, 6],\n [-4, 2, 3],\n [6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[-9, 4, -7],\n [-1, 5, 0],\n [7, 4, 4]]\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[4, -2, 4],\n [-2, 6, -8],\n [4, -8, 0]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-9, -6, 5],\n [-6, -1, -6],\n [5, -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 (3, 3) rounded to the nearest integer?\n[[-4, 6, 1],\n [-7, 2, -10],\n [-5, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the value at position (1, 1) of the inverse. Round your answer to the nearest integer:\n[[5, -9, 9],\n [-1, -5, -8],\n [7, -2, -10]]\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[[-4, -4, -8],\n [-4, 8, 0],\n [-8, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 795 | 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, -6, 8],\n [0, -8, 2],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the value at position (1, 1) of the inverse of matrix 1/60 * A where A =\n[[-7, -2, 0],\n [-2, 2, -4],\n [0, -4, 3]]\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 all entries of the inverse. Round your answer to the nearest integer:\n[[5, 0, -1],\n [0, 9, 9],\n [0, 0, -2]]\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[[5, -8, -6],\n [-6, -6, -7],\n [-5, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | -10 | 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, 8, 0],\n [8, -3, 2],\n [0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -94 | 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, 10, -4],\n [-3, -6, -7],\n [0, -5, 4]]\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 value of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-6, -3, -4],\n [-3, 8, 0],\n [-4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 244 | MATH |
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