messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the value at position (4, 4) of the inverse of matrix 1/96 * A where A =\n[[-7, 4, -8, 0],\n [-2, 4, -9, -2],\n [-1, 3, 3, -12],\n [-11, -10, -1, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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, 8, 3, -12],\n [0, -8, -5, 2],\n [0, 0, 9, 12],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\b... | 26 | MATH |
[
{
"content": "Find the inverse of 1/96 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, -4, -6],\n [-4, 2, 4, 9],\n [-4, 4, 10, 4],\n [-6, 9, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 248 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[6, -8, 1, -9],\n [11, -5, 7, -6],\n [-3, 2, -3, 11],\n [4, -4, -1, -8]]\nRound your answer to the nearest integer.\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 1/96 * A where A =\n[[-11, -10, 1, -3],\n [-10, -5, -2, -10],\n [1, -2, -10, -3],\n [-3, -10, -3, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -13 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[12, 0, -8, 7],\n [0, -10, -12, 12],\n [0, 0, 5, -4],\n [0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 114 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[12, 12, -9, 6],\n [6, 0, -12, -2],\n [6, 5, -6, 4],\n [2, -5, -10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | -42 | MATH |
[
{
"content": "Find the inverse of 1/96 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, 7, 2, -11],\n [3, -2, 1, 9],\n [12, 6, 7, -5],\n [-9, -9, -11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 307 | MATH |
[
{
"content": "Find the inverse of 1/96 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, 12, -9],\n [-9, -10, 5, -10],\n [11, -5, 0, -5],\n [2, -2, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{You... | -22 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-3, 6, 3, 9],\n [8, -11, 3, 3],\n [9, 10, -4, 2],\n [11, 3, 3, 8]]\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 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[-6, 12, -12, -9],\n [-1, 0, -12, 9],\n [8, 10, -7, 8],\n [-4, -9, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 18 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-7, 2, -6, -2],\n [3, -11, -4, 6],\n [9, 1, 8, -4],\n [-5, -5, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[7, -10, 3, -7],\n [-10, 6, 4, 2],\n [10, -12, 8, -9],\n [10, -12, 7, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -13 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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, -12, -7, -2],\n [0, -5, -2, 12],\n [0, 0, -2, 11],\n [0, 0, 0, 8]]\n\nPresent the answe... | 172 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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, 12, -11, 10],\n [-6, 5, -5, -10],\n [-5, 5, 10, -9],\n [-11, -5, -5, -2]]\n\nPresent t... | -12 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[6, 5, -2, -1],\n [5, -5, -2, 8],\n [-2, -2, 7, -6],\n [-1, 8, -6, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 169 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, -11, 12, 9],\n [7, -1, -11, 12],\n [11, -11, -3, -6],\n [1, -2, -4, -7]]\n\nPresent the answer in LaTex format: \\box... | -46 | MATH |
[
{
"content": "Find the inverse of 1/96 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, -3, 8, 6],\n [-10, -8, -8, -5],\n [12, 7, 12, 10],\n [-4, -10, 10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 411 | MATH |
[
{
"content": "Find the inverse of 1/96 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[[-11, 8, -1, 9],\n [12, -9, 12, 3],\n [12, 9, -4, -7],\n [-6, -6, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your ... | 11 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-6, 11, -4, 9],\n [0, -8, -5, -4],\n [0, 0, -2, 1],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-4, 6, -3, 8],\n [6, 8, 5, 8],\n [-3, 5, 7, -1],\n [8, 8, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 9, -2, -5],\n [0, -6, 2, 7],\n [0, 0, 11, 9],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 4 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[-11, 1, 2, -7],\n [1, 1, 2, 6],\n [2, 2, 4, 4],\n [-7, 6, 4, -10]]\n\nPresent the answer in LaTex forma... | 307 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[-8, 11, -4, 1],\n [-1, 1, -2, -9],\n [-6, 12, 5, 4],\n [-5, -10, 5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-1, -12, -5, -10],\n [10, -1, 7, -10],\n [-12, 7, -12, 6],\n [-4, -1, 12, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | -9 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[9, 6, -2, 2],\n [6, 8, 6, 1],\n [-2, 6, -9, 0],\n [2, 1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value of the entry with the largest absolute value rounded to the nearest integer?\n[[4, 4, 2, 6],\n [4, -2, -4, 0],\n [2, -4, -11, -2],\n [6, 0, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 32 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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, -6, -12, -8],\n [0, -6, -7, -5],\n [0, 0, 3, 0],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex for... | 176 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-4, -2, 8, -4],\n [-2, -1, 2, -3],\n [8, 2, -11, -4],\n [-4, -3, -4, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 107 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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, -2, -8, 0],\n [-2, -12, 4, -2],\n [-8, 4, 8, -4],\n [0, -2, -4, -11]]\n\nPresent the answer in LaTex for... | -19 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, -9, -10, -2],\n [3, 2, 7, 5],\n [3, 1, 3, -6],\n [-6, -12, -5, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 783 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[2, -3, 7, -11],\n [0, -2, 10, 4],\n [0, 0, 12, 8],\n [0, 0, 0, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | -72 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, -7, -10, -8],\n [0, 12, -2, 12],\n [0, 0, -2, -4],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{You... | -23 | MATH |
[
{
"content": "Find the inverse of 1/96 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, 9, 7, -1],\n [0, -6, 1, -8],\n [0, 0, -7, -10],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 44 | MATH |
[
{
"content": "Find the inverse of 1/96 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[[11, 5, -8, 6],\n [5, 10, 1, 0],\n [-8, 1, -11, 2],\n [6, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | -49 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[12, -2, -4, 4],\n [-2, -4, -1, -10],\n [-4, -1, 6, 6],\n [4, -10, 6, -12]]\n\nPresent the ... | -31 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-8, 4, 11, 7],\n [0, 8, 7, 6],\n [0, 0, -1, 2],\n [0, 0, 0, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -96 | MATH |
[
{
"content": "Find the value at position (3, 2) of the inverse of matrix 1/96 * A where A =\n[[-7, 1, -12, -10],\n [0, 11, 4, -8],\n [0, 0, 10, 0],\n [0, 0, 0, 11]]\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 1/96 * A where A =\n[[0, 8, -6, -4],\n [8, 6, -6, -9],\n [-6, -6, -5, 5],\n [-4, -9, 5, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -46 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[-5, -7, -8, -2],\n [-12, 8, -4, -12],\n [4, -9, 10, 12],\n [1, 12, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the inverse of 1/96 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, 6, 6, 11],\n [0, -3, 9, -11],\n [0, 0, 4, -1],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | -288 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[3, 8, -2, -6],\n [8, 7, 6, 6],\n [-2, 6, -3, -2],\n [-6, 6, -2, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -69 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 1) rounded to the nearest integer?\n[[8, -2, -12, 11],\n [0, -2, 5, -6],\n [0, 0, 2, 8],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 1) of the inverse. Round your answer to the nearest integer:\n[[0, -5, -11, -3],\n [-5, -11, 8, -8],\n [-9, -6, 0, 3],\n [5, 7, 9, 6]]\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 1/96 * A where A =\n[[2, 9, 10, 7],\n [0, 1, -4, 2],\n [0, 0, 1, -9],\n [0, 0, 0, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 232 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-7, -1, -10, -11],\n [0, 2, -1, -9],\n [0, 0, -11, 6],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{You... | 59 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-10, 5, -8, -8],\n [0, -10, 8, 5],\n [0, 0, 7, 12],\n [0, 0, 0, -12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-2, -6, -9, 0],\n [-6, -11, 4, 4],\n [-9, 4, 11, 0],\n [0, 4, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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, 2, -4],\n [0, -11, 0, 0],\n [2, 0, -12, 3],\n [-4, 0, 3, -7]]\n\nPresent the answer in LaTex format: ... | -23 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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, -1, -4, -2],\n [0, 8, 6, 9],\n [0, 0, -12, -1],\n [0, 0, 0, 9]]\n\nPresent the answer ... | 12 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-1, -10, -3, 7],\n [0, 11, -10, 9],\n [0, 0, -8, 0],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -175 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[9, 11, 0, 2],\n [0, 1, 3, 1],\n [0, 0, -3, 8],\n [0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 919 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[2, -4, -10, 6],\n [-4, 3, -5, -5],\n [-10, -5, -3, -6],\n [6, -5, -6, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 11 | MATH |
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/96 * A where A =\n[[1, -2, -8, 3],\n [-2, 8, -2, 2],\n [-8, -2, -3, -1],\n [3, 2, -1, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-4, -8, -5, -3],\n [0, -11, 8, -5],\n [0, 0, -5, -5],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 184 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[2, 1, -6, -7],\n [-11, -9, -11, -8],\n [6, 10, -1, -4],\n [-3, 8, 12, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 4) of the inverse. Round your answer to the nearest integer:\n[[-2, -7, 5, -3],\n [0, -6, -4, 6],\n [0, 0, -10, -9],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 9 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-4, 9, -4, -2],\n [3, 11, -7, -3],\n [-4, 4, -5, 1],\n [8, -1, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -136 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[2, 5, -7, 10],\n [0, 9, 11, -3],\n [0, 0, -1, 8],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -57 | MATH |
[
{
"content": "Find the inverse of 1/96 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, 4, -3],\n [0, 7, 4, -8],\n [0, 0, -10, 0],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 553 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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, 4, 5],\n [6, -5, 3, -1],\n [-3, -8, -11, 7],\n [-12, 2, 5, 5]]\n\nPresent the answer in LaTex for... | 78 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[0, 4, -6, 0],\n [4, -1, -4, 7],\n [-6, -4, 7, -1],\n [0, 7, -1, 9]]\n\nPresent the answer in LaTex format: \... | -33 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[-12, 0, 12, 9],\n [0, 12, 6, 2],\n [0, 0, -11, -3],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex for... | 209 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (1, 2) rounded to the nearest integer?\n[[-7, -2, 2, 2],\n [-2, -8, -6, 0],\n [2, -6, -12, -2],\n [2, 0, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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, 11, -10],\n [0, 2, 5, 7],\n [0, 0, -9, 3],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\... | 56 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-12, -8, 7, 8],\n [-8, 5, 0, 1],\n [7, 0, 10, 8],\n [8, 1, 8, 8]]\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 1/96 times the following and determine the value at position (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, -12, -9, -7],\n [-10, -6, -9, 1],\n [-12, 2, 8, 12],\n [-2, -7, 2, -8]]\n\nPresent the answer in LaTex format: \\... | -3 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[11, -7, -11, -12],\n [0, 10, 3, 11],\n [0, 0, -7, 0],\n [0, 0, 0, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -21 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-11, 4, 3, -2],\n [4, 6, 4, 0],\n [3, 4, 2, -2],\n [-2, 0, -2, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -98 | MATH |
[
{
"content": "Find the value at position (1, 3) of the inverse of matrix 1/96 * A where A =\n[[9, 1, -3, -4],\n [0, 3, -1, -4],\n [0, 0, 3, 2],\n [0, 0, 0, -9]]\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 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[2, -2, 4, 0],\n [-8, -10, 11, -12],\n [2, -5, 5, 1],\n [5, 7, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Find the value at position (4, 4) of the inverse of matrix 1/96 * A where A =\n[[-6, -4, 4, 2],\n [-1, -10, 10, 12],\n [-3, 8, -12, -2],\n [5, 8, 12, -10]]\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 1/96 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, -4, 7, 6],\n [-5, 10, -12, 1],\n [2, 12, 1, 7],\n [1, -3, -9, -12]]\n\nPresent the answer in LaTex... | 176 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-1, 4, -2, 5],\n [12, -11, -1, -5],\n [6, 9, 7, -8],\n [4, -8, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-5, 3, -11, 4],\n [-6, -3, -11, -10],\n [6, -11, 0, 5],\n [3, 1, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 265 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (4, 2) of the inverse. Round your answer to the nearest integer:\n[[5, 10, 8, 0],\n [3, 12, -9, 8],\n [-9, -9, -1, -10],\n [5, 5, 9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 19 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, -5, 0, -4],\n [-5, 0, -2, 2],\n [0, -2, 5, -4],\n [-4, 2, -4, -2]]\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 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[5, -9, -10, -1],\n [0, 7, 1, 7],\n [0, 0, -12, 5],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 57 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of absolute values of all entries rounded to the nearest integer?\n[[-2, -6, -10, 1],\n [7, 8, -11, 0],\n [12, -4, -11, 7],\n [-6, -7, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 69 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -2, 11, 5],\n [0, 12, 5, 11],\n [0, 0, -10, 2],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed... | -2 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -10, 3, -1],\n [-10, -9, 0, -5],\n [3, 0, 1, -4],\n [-1, -5, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | 0 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[1, -2, -11, 11],\n [11, 2, -8, -3],\n [-11, 5, 1, 8],\n [2, -6, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65 | MATH |
[
{
"content": "Find the inverse of 1/96 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, 0, 10, -6],\n [0, -4, 2, 3],\n [10, 2, 0, 5],\n [-6, 3, 5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | -18 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-11, -10, -2, -7],\n [-4, -8, 11, 7],\n [-7, -12, 8, 11],\n [-11, -3, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | -2 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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, -2, 2, 3],\n [-2, -10, 2, 0],\n [2, 2, 4, -1],\n [3, 0, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 18 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (1, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[10, 6, -8, -4],\n [-4, -8, -1, 9],\n [12, 1, 7, -3],\n [-9, 7, -2, -7]]\n\nPresent the answer in LaTex format: \\box... | -7 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-11, 1, 12, -1],\n [-12, 11, 10, -4],\n [9, 4, 12, 2],\n [2, 6, 7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[7, 6, 6, 11],\n [0, -4, -12, -7],\n [0, 0, -8, -3],\n [0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 159 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[12, -12, 7, -6],\n [0, 3, -12, -11],\n [0, 0, 4, 2],\n [0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 454 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 4) of the inverse. Round your answer to the nearest integer:\n[[8, -1, -11, 1],\n [7, 2, -8, 8],\n [-7, -12, -7, -7],\n [8, 11, -9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | -8 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-10, 7, 4, 10],\n [0, -8, -9, 2],\n [0, 0, 7, 10],\n [0, 0, 0, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -17 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-1, 2, 12, 9],\n [6, 8, -9, 4],\n [7, 12, 7, 9],\n [-1, 2, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (2, 2) of the inverse. Round your answer to the nearest integer:\n[[5, -2, 4, 5],\n [-12, -2, -4, 12],\n [7, -7, 8, 5],\n [-8, 11, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | -1 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[9, 11, 1, 3],\n [3, 8, -5, -4],\n [1, -8, 1, -4],\n [-3, -10, 10, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 14 | MATH |
[
{
"content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[-11, -1, -4, 0],\n [-1, 10, -10, -6],\n [-4, -10, 12, -6],\n [0, -6, -6, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 2) of the inverse. Round your answer to the nearest integer:\n[[-12, 0, 12, 2],\n [5, -3, -12, 6],\n [-9, 11, 1, 9],\n [10, 7, 11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | -1 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the sum of absolute values of all entries of the inverse. Round your answer to the nearest integer:\n[[3, 8, 5, 0],\n [0, 3, -11, 9],\n [0, 0, 2, -5],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 1338 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[8, 10, -3, 12],\n [4, 9, 11, -10],\n [5, 11, 4, 5],\n [-1, -10, 8, 0]]\n\nPresent the answer in LaTex format: \\boxe... | 12 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-1, 9, 10, 6],\n [9, 1, 3, -7],\n [10, 3, -10, -4],\n [6, -7, -4, -4]]\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 1/96 times the matrix and calculate the sum of all entries of the inverse. Round your answer to the nearest integer:\n[[-5, 0, 11, -4],\n [0, -11, -9, 1],\n [0, 0, -8, -3],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -51 | MATH |
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