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 of the entry with the largest absolute value rounded to the nearest integer?\n[[-3, 1, 0],\n [1, -2, 6],\n [0, 6, 1]]\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 of the entry with the largest absolute value rounded to the nearest integer?\n[[1, -1, 0],\n [-7, 10, 0],\n [-4, 5, 5]]\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, -4, 0],\n [-4, -9, -2],\n [0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -148 | 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, 8, -4],\n [0, -4, -1],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | 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, 8, -1],\n [8, 8, 0],\n [-1, 0, -2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, -6, -5],\n [-6, 4, -6],\n [-5, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -16 | MATH |
[
{
"content": "Find the value at position (3, 2) of the inverse of matrix 1/60 * A where A =\n[[10, 1, -2],\n [1, 8, 6],\n [-2, 6, -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 value at position (2, 2) of the inverse of matrix 1/60 * A where A =\n[[-6, -4, 2],\n [-4, -5, -2],\n [2, -2, 2]]\nRound your answer to the nearest integer.\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 absolute values of all entries rounded to the nearest integer?\n[[-4, 2, -7],\n [5, -9, -10],\n [-1, 9, -1]]\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 value at position (3, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[1, 0, 5],\n [0, -4, 4],\n [5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -3 | 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[[7, 3, 8],\n [3, 7, 1],\n [8, 1, -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 absolute values of all entries rounded to the nearest integer?\n[[8, 5, -6],\n [5, -10, 6],\n [-6, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | 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, -1, 5],\n [0, -1, 8],\n [0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 148 | 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, -4],\n [0, 3, 0],\n [0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 49 | 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[[5, 4, 1],\n [-10, 0, -2],\n [-5, -10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | -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[[-5, 1, -6],\n [0, -1, 1],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 144 | MATH |
[
{
"content": "Find the value at position (2, 1) of the inverse of matrix 1/60 * A where A =\n[[-2, 8, -8],\n [8, -5, 2],\n [-8, 2, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | 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[[0, -3, 3],\n [-7, 7, 2],\n [3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | 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, -2, -5],\n [-1, 3, -6],\n [-1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 119 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value at position (3, 2) rounded to the nearest integer?\n[[-8, 6, -4],\n [6, -8, 0],\n [-4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Find the value at position (2, 1) of the inverse of matrix 1/60 * A where A =\n[[-8, -1, 3],\n [0, -2, 7],\n [0, 0, -2]]\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 (2, 1) rounded to the nearest integer?\n[[3, -3, 8],\n [0, -8, -9],\n [0, 0, 8]]\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[[6, 4, 3],\n [0, -1, -10],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -38 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-6, 8, 6],\n [0, 9, -9],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-5, 2, 4],\n [2, -10, -3],\n [4, -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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-5, -4, 8],\n [0, -8, -9],\n [0, 0, 7]]\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[[6, 9, 10],\n [-3, -7, 10],\n [-1, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[9, -8, 7],\n [0, -2, 7],\n [-5, 9, 10]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-10, 10, -9],\n [-8, 3, 6],\n [-4, -10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -4 | MATH |
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/60 * A where A =\n[[-5, -9, -9],\n [-9, 9, 8],\n [7, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[1, -2, -4],\n [-2, 7, -8],\n [-4, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 times the following and determine the trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[5, 4, -8],\n [-4, -9, -3],\n [-2, -5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 18 | 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, -1, 7],\n [-1, 9, 6],\n [-4, -5, -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 (2, 3) rounded to the nearest integer?\n[[-1, 4, 4],\n [4, 10, -5],\n [4, -5, -2]]\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, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, -8, -10],\n [0, -8, 9],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | -8 | 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, 6, -1],\n [0, 10, 4],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -12 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[9, 10, -9],\n [-9, -4, -10],\n [-10, -3, -6]]\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 value at position (1, 2) rounded to the nearest integer?\n[[9, 4, 0],\n [8, -6, 1],\n [1, -1, -8]]\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 at position (2, 1) of the inverse. Round your answer to the nearest integer:\n[[8, 3, -3],\n [-1, 8, 10],\n [-6, -7, 7]]\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 of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[-8, -9, -7],\n [2, 3, 2],\n [9, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -84 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[5, -4, -8],\n [7, 8, -9],\n [-6, 5, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | 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, 9, 7],\n [0, -3, 7],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 460 | 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, -10, 6],\n [-10, 10, -6],\n [6, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 261 | 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, 8, -7],\n [0, 5, 0],\n [0, 0, 8]]\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, -2, -5],\n [-2, 1, -2],\n [-5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 14 | 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[[-1, 2, 6],\n [2, 2, -6],\n [6, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 78 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/60 * A where A =\n[[10, -3, -7],\n [-8, -9, -3],\n [-5, 1, -9]]\nRound your answer to the nearest integer.\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 (3, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, -2, -6],\n [0, 10, 9],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 0 | 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, 0],\n [0, -3, 7],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 187 | MATH |
[
{
"content": "Find the value at position (3, 2) of the inverse of matrix 1/60 * A where A =\n[[-4, 6, -10],\n [-8, 5, -7],\n [0, 10, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "For the inverse of 1/60 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-3, 1, 0],\n [1, 7, 0],\n [0, 0, 10]]\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 all entries of the inverse. Round your answer to the nearest integer:\n[[2, 1, 0],\n [1, 7, 0],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | 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[[-4, 10, -4],\n [0, 8, -5],\n [0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 60 | 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, 9, -6],\n [-5, 1, 2],\n [6, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | 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, 0, 4],\n [0, -10, 3],\n [4, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 10 | 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, -4, 1],\n [6, 8, -10],\n [-2, 10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | 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, -6, 0],\n [-6, -9, -1],\n [0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 86 | 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, 2, -2],\n [2, -5, -4],\n [-2, -4, 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[[-8, -9, -2],\n [0, -1, -7],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 229 | 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, -7],\n [-7, -10, -2],\n [-7, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 59 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[0, -6, 2],\n [-6, 10, -1],\n [2, -1, -8]]\nRound your answer to the nearest integer.\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[[10, -1, -4],\n [-1, 2, -6],\n [-4, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed... | 10 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/60 * A where A =\n[[5, -3, 1],\n [-3, 7, 9],\n [-5, 6, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 51 | MATH |
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/60 * A where A =\n[[5, 2, 9],\n [0, 9, -7],\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 sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, 9, -1],\n [-5, -3, 3],\n [-10, -5, -6]]\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[[-6, -5, -10],\n [0, 6, 10],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 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[[8, 3, 2],\n [3, 7, -4],\n [2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | -17 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-6, 9, 5],\n [7, 6, -10],\n [0, -4, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 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[[8, 4, -9],\n [4, -4, 2],\n [-9, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 228 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[5, 10, -7],\n [0, 10, 3],\n [0, 0, 3]]\nRound your answer to the nearest integer.\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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[8, 1, 4],\n [6, 9, 1],\n [3, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 420 | MATH |
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/60 * A where A =\n[[5, 9, 8],\n [6, -2, 4],\n [-10, -4, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 390 | 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, -6, 8],\n [0, -10, -6],\n [0, 0, -10]]\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[[-7, 7, -4],\n [-6, -3, -3],\n [-4, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 213 | 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, -4, 4],\n [-4, 7, 2],\n [4, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 73 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[3, 3, 5],\n [0, -8, -1],\n [0, 0, 3]]\nRound your answer to the nearest integer.\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[[10, 3, 8],\n [0, 5, 8],\n [0, 0, 3]]\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, 9],\n [-9, 0, -2],\n [-9, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[-2, 1, 6],\n [1, 1, 0],\n [6, 0, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 480 | MATH |
[
{
"content": "Find the value at position (3, 1) of the inverse of matrix 1/60 * A where A =\n[[-1, 4, 10],\n [4, 1, -5],\n [9, 3, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/60 * A where A =\n[[-9, 0, -1],\n [0, -7, 0],\n [0, 0, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -27 | 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, 9, -5],\n [0, 10, 8],\n [0, 0, 8]]\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[[2, -5, 4],\n [-5, 0, -2],\n [4, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Find the inverse of 1/60 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, 10, -1],\n [0, 1, 8],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 696 | 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[[-10, 6, -9],\n [-4, 2, 2],\n [0, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 9 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-3, 9, -6],\n [0, 9, 9],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | -27 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/60 * A where A =\n[[1, -5, 4],\n [6, -9, -3],\n [10, 1, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/60 * A where A =\n[[-1, 3, 8],\n [0, -9, 5],\n [0, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | 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[[8, 1, -8],\n [1, 2, -3],\n [-10, 8, 5]]\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 value of the entry with the largest absolute value rounded to the nearest integer?\n[[-5, 9, -6],\n [0, 2, 1],\n [0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/60 times the following and determine the value at position (1, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -4, 1],\n [2, -2, -10],\n [-7, 9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 1 | 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, -9, -9],\n [0, 1, -8],\n [0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -108 | 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, 4, -9],\n [0, -8, -5],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 274 | MATH |
[
{
"content": "Find the value at position (2, 3) of the inverse of matrix 1/60 * A where A =\n[[9, 0, 5],\n [0, 9, 4],\n [0, 0, 10]]\nRound your answer to the nearest integer.\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[[5, -4, 9],\n [2, -1, 9],\n [0, 5, -9]]\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 value of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-8, -8, -4],\n [2, 4, -5],\n [-8, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Y... | -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[[-10, -4, 1],\n [0, 2, -9],\n [0, 0, 6]]\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 value at position (3, 3) of the inverse. Round your answer to the nearest integer:\n[[1, -6, -4],\n [-6, -3, -6],\n [-4, -6, 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[[8, -10, 3],\n [0, -1, 8],\n [0, 0, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -314 | 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, 6, 1],\n [6, 10, -8],\n [1, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
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