messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1
value |
|---|---|---|
[
{
"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[[-12, 11, -3, -9],\n [0, -9, -8, 2],\n [0, 0, 4, -5],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: ... | 16 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[12, 5, 3, -3],\n [0, -5, 8, -7],\n [0, 0, -8, 9],\n [0, 0, 0, 1]]\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 sum of all entries of the inverse. Round your answer to the nearest integer:\n[[2, -3, -4, -2],\n [-3, 1, 4, -4],\n [-4, 4, -7, -2],\n [-2, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | -20 | 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[[2, 1, 0, -1],\n [0, 4, -9, 6],\n [0, 0, 5, 1],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[11, 2, 2, -7],\n [2, 3, -1, 2],\n [2, -1, -2, 1],\n [-7, 2, 1, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1223 | 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, 2, 2, 4],\n [2, 12, 0, 5],\n [2, 0, 10, -5],\n [4, 5, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 22 | 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[[12, -4, -3, 7],\n [0, -4, 11, 11],\n [0, 0, 4, -1],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 66 | MATH |
[
{
"content": "Find the value at position (3, 4) of the inverse of matrix 1/96 * A where A =\n[[11, 11, -12, 0],\n [5, -5, 4, 11],\n [4, 7, -11, 9],\n [12, 2, 3, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[5, 12, 12, -7],\n [-5, -6, 2, -8],\n [0, 11, -6, 0],\n [-5, -9, -10, -11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | -23 | 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[[10, 12, 9, 0],\n [0, -8, 0, 0],\n [0, 0, 12, -10],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 19 | 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[[10, -4, 9, 8],\n [0, 11, -1, -8],\n [-5, 5, 11, 11],\n [12, 3, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | 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, 8, 4],\n [12, 1, -7, -7],\n [7, 2, 6, -9],\n [5, 4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 658 | 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[[2, -4, -1, 6],\n [-4, 4, 1, -6],\n [-1, 1, -7, -1],\n [6, -6, -1, 7]]\n\nPresent the answer in LaTex format:... | -243 | 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[[5, -9, -3, 0],\n [6, -8, 0, 0],\n [7, 12, -8, 11],\n [-10, -6, -12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | -198 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 1) rounded to the nearest integer?\n[[3, 1, 4, -3],\n [1, 4, 4, -4],\n [4, 4, 7, -4],\n [-3, -4, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23 | 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, 6, -4, 3],\n [6, -11, 3, -1],\n [-4, 3, 0, -2],\n [3, -1, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 183 | 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, 7, -3, -7],\n [0, -10, 12, -11],\n [0, 0, 4, -9],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex f... | 573 | 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[[-12, 12, -6, 1],\n [0, 10, -8, -6],\n [0, 0, -7, 3],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -79 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[8, -5, 12, 5],\n [10, -5, 12, 4],\n [3, -3, -1, -4],\n [6, -9, -2, 9]]\n\nPresent the answer in LaTex format: \\boxe... | -3 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-9, -8, -2, -10],\n [-7, -12, -11, 6],\n [-2, 8, 2, -7],\n [8, -2, -7, 5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-8, -8, 2, -1],\n [-3, -6, 6, 1],\n [9, 4, 5, -6],\n [5, -8, -6, 11]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 122 | 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[[-12, -12, 2, 4],\n [0, -12, 11, -7],\n [0, 0, -7, -8],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{You... | -24 | 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[[-6, -2, 2, 2],\n [-2, -9, -2, -11],\n [2, -2, 3, 2],\n [2, -11, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | -7 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[9, -3, -2, -4],\n [-3, -1, -2, 0],\n [-2, -2, 10, -8],\n [-4, 0, -8, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -71 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 4) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, -2, 6, 6],\n [-2, 3, -3, 7],\n [6, -3, 11, 2],\n [6, 7, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{... | 8 | 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, -8, 10],\n [0, -5, 12, 1],\n [0, 0, 10, 9],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 161 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (3, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-9, -1, -3, -6],\n [0, 6, -5, -5],\n [0, 0, 12, -8],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed... | 0 | 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[[-6, 4, 0, 8],\n [4, -11, -2, -2],\n [0, -2, -12, -2],\n [8, -2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -20 | 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[[10, -5, -8, 8],\n [0, 1, 6, -2],\n [0, 0, -5, -3],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | -179 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[0, -5, 0, 12],\n [12, 5, 6, 7],\n [3, -6, -1, -9],\n [5, 9, -9, -11]]\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 of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-9, -10, -2, -10],\n [0, 11, 6, -1],\n [0, 0, 6, -10],\n [0, 0, 0, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | -20 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[3, -10, 1, 3],\n [0, 11, -10, -12],\n [0, 0, -8, -10],\n [0, 0, 0, -3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 40 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[6, -4, -4, -1],\n [-4, 6, 1, 5],\n [-4, 1, -5, 0],\n [-1, 5, 0, -7]]\nRound your answer to the nearest integer.\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 1/96 * A where A =\n[[-3, -4, -2, 8],\n [-3, -3, -2, 5],\n [-7, 7, 11, -1],\n [9, 9, 10, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 996 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[-7, -10, -2, -6],\n [0, -4, -7, -12],\n [0, 0, 1, -5],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -24 | MATH |
[
{
"content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[-5, -12, -11, -1],\n [-9, -3, -11, -8],\n [-2, 10, -10, 3],\n [-9, -10, 10, -12]]\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 trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[-4, -10, 2, 0],\n [-10, 0, -9, 3],\n [2, -9, -8, 1],\n [0, 3, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 3 | 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[[4, 8, -12, -9],\n [0, 10, -10, -10],\n [0, 0, -9, 6],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 24 | 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[[-9, 3, -6, -3],\n [0, 4, -3, 6],\n [0, 0, -12, 1],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your an... | 30 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-1, -7, 2, -10],\n [0, 9, 8, 5],\n [0, 0, -3, 0],\n [0, 0, 0, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 587 | 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, 4, -10, -11],\n [3, 2, -1, 3],\n [4, -3, 3, 7],\n [-8, 4, -1, -2]]\n\nPresent the answer in LaTex format... | 3 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-6, 8, -4, 7],\n [0, 9, 3, 12],\n [0, 0, 1, -5],\n [0, 0, 0, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -84 | 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[[2, 12, -10, -6],\n [0, 1, -12, 11],\n [0, 0, 11, -3],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex forma... | 145 | 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, 1, 0],\n [-6, 0, -6, 2],\n [1, -6, 1, 6],\n [0, 2, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 54 | 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[[-9, 3, 2, 6],\n [10, -7, -3, 6],\n [2, -8, -8, 6],\n [4, -3, -3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 30 | 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[[8, -8, 9, 1],\n [0, 9, 7, -8],\n [0, 0, 8, -6],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-1, 9, -4, 0],\n [0, 5, -12, -9],\n [0, 0, -6, -7],\n [0, 0, 0, 1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[9, -2, 7, 4],\n [-6, -9, 3, 9],\n [-2, 0, -5, -4],\n [-9, -6, -12, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -60 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[8, -2, 4, -9],\n [-2, -9, 6, 0],\n [4, 6, 6, 8],\n [-9, 0, 8, 3]]\nRound your answer to the nearest integer.\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, 11, 11, -5],\n [-4, 12, -12, -1],\n [11, -7, 5, 3],\n [1, 8, -11, -12]]\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 (4, 2) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 4, 5, -8],\n [8, -1, 4, -4],\n [-10, -1, -12, 3],\n [12, 10, 5, -10]]\n\nPresent the answer in LaTex format: \\b... | -15 | 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[[-12, 2, -2, -6],\n [2, 12, 10, -9],\n [-2, 10, -11, 10],\n [-6, -9, 10, 11]]\n\nPresent the answer in LaTex format: ... | -7 | 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[[3, 0, -2, -6],\n [0, 2, -2, 0],\n [-2, -2, -11, -7],\n [-6, 0, -7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-10, -4, -3, -9],\n [-4, 7, 8, -8],\n [-3, 8, -2, 2],\n [-9, -8, 2, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 8 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-2, -7, 5, -8],\n [8, 6, 1, -9],\n [-7, 5, 9, -4],\n [-9, -4, -4, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -19 | MATH |
[
{
"content": "Find the inverse of 1/96 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[[9, 1, -10, -3],\n [0, 9, 0, 0],\n [-1, 6, -5, 8],\n [4, -10, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 31 | 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, 8, 12, 12],\n [0, -4, 10, -6],\n [0, 0, -5, 12],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 1098 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[10, 9, 2, -5],\n [9, -12, -3, -1],\n [2, -3, -3, -4],\n [-5, -1, -4, -9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | -106 | MATH |
[
{
"content": "Find the value at position (1, 1) of the inverse of matrix 1/96 * A where A =\n[[9, 6, -10, -4],\n [0, 9, 2, 12],\n [0, 0, -5, -2],\n [0, 0, 0, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the trace (sum of diagonal elements) of the inverse. Round your answer to the nearest integer:\n[[10, 1, -11, 0],\n [10, -12, -6, 6],\n [-4, -5, -2, 8],\n [4, 2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 11 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (1, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[2, -3, 5, -4],\n [0, 10, 10, 10],\n [0, 0, 4, 9],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | -96 | 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[[3, -4, -8, 2],\n [10, 6, -8, 1],\n [9, -12, 1, 6],\n [-4, 8, 5, 12]]\n\nPresent the answer in LaTex format: \\boxed{... | -2 | 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[[6, 3, 7, -4],\n [7, -3, 5, -11],\n [-2, 8, -1, -9],\n [-8, 6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | -115 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (4, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-5, -6, -6, 10],\n [-6, -7, 4, -6],\n [-6, 4, -6, 2],\n [10, -6, 2, 9]]\n\nPresent the answer in LaTex format: \\box... | 2521 | 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, 0, -6, -9],\n [-1, 4, -9, 11],\n [7, -9, 7, 9],\n [5, -2, 5, 12]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 22 | 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[[10, 2, 11, -11],\n [2, 11, -8, -1],\n [11, -8, 1, 6],\n [-11, -1, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 115 | 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[[12, 4, 6, 0],\n [4, -5, 8, 2],\n [6, 8, 8, -2],\n [0, 2, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 93 | 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[[8, -10, -10, -6],\n [0, -12, -3, 9],\n [0, 0, -2, 6],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -30 | 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[[0, -10, 3, -8],\n [7, -4, 2, -6],\n [5, 3, 3, -2],\n [-7, 10, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (2, 3) rounded to the nearest integer?\n[[-4, -7, 1, 8],\n [0, 4, 0, -10],\n [0, 0, 6, -7],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | 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[[-4, 9, -10, -2],\n [7, 0, 10, -6],\n [-11, -9, -12, 1],\n [4, 5, 3, 8]]\n\nPresent the ans... | 204 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-11, 7, -3, 3],\n [-8, -3, 9, 3],\n [3, -8, 7, -10],\n [0, 4, 1, -1]]\nRound your answer to the nearest integer.\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 value at position (2, 1) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[11, 1, -2, 3],\n [0, 12, 11, -10],\n [0, 0, 4, 11],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 0 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 1) rounded to the nearest integer?\n[[-8, 10, -9, -6],\n [9, -3, -5, -12],\n [-1, 1, -11, -1],\n [-5, -6, -10, -12]]\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[[9, -5, 0, -1],\n [-5, 4, -5, -6],\n [0, -5, 9, -2],\n [-1, -6, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 103 | 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, 4, 0, 2],\n [4, 11, -4, 8],\n [0, -4, 9, 4],\n [2, 8, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 23 | 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[[-4, 6, -4, -4],\n [6, 10, 1, -1],\n [-4, 1, -2, 8],\n [-4, -1, 8, -11]]\n\nPresent the answer in LaTex format: \\boxed{You... | 21 | 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[[-10, -9, 8, -2],\n [0, 9, -12, -5],\n [0, 0, 2, -3],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -62 | 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, -1, -1, 0],\n [2, 4, -8, -5],\n [-9, -1, -12, -5],\n [-6, -8, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 174 | 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[[6, 7, 7, 11],\n [4, -5, 2, -8],\n [-9, 7, -4, 2],\n [3, -7, -1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 710 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (4, 1) of the inverse. Round your answer to the nearest integer:\n[[4, -2, 12, -5],\n [11, 7, 11, -1],\n [2, -3, 10, 1],\n [-5, 5, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -16 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-9, 0, 6, -8],\n [0, 11, 8, 0],\n [6, 8, -3, -2],\n [-8, 0, -2, 1]]\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 absolute values of all entries rounded to the nearest integer?\n[[1, 12, -4, -3],\n [6, -8, 11, -6],\n [-2, -1, -5, 8],\n [0, 6, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 126 | 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, -9, 9, 2],\n [9, -2, 1, 7],\n [12, -3, 3, -1],\n [-10, 7, -11, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -25 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-2, -8, -8, 8],\n [-8, 2, 10, 0],\n [-8, 10, 2, -2],\n [8, 0, -2, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1375 | 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[[11, -9, -4, 0],\n [1, 7, 10, -10],\n [-1, -3, 7, 5],\n [6, 2, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 106 | 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[[-2, 0, 6, -6],\n [0, 10, -4, 0],\n [6, -4, 6, 6],\n [-6, 0, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your a... | 66 | 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[[9, 12, 8, -2],\n [-12, -4, -3, -11],\n [6, 4, -3, 3],\n [0, -4, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | -11 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[0, 2, 6, 2],\n [2, -12, -6, 2],\n [6, -6, 12, -11],\n [2, 2, -11, 6]]\n\nPresent the answer in LaTex format: \\boxed... | -8 | 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[[9, 1, -10, 7],\n [1, -6, 7, 5],\n [-2, 12, 6, 11],\n [-6, 7, -8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -19 | MATH |
[
{
"content": "Find the value at position (4, 4) of the inverse of matrix 1/96 * A where A =\n[[3, -2, 0, 0],\n [-2, 2, -2, -4],\n [0, -2, -11, -8],\n [0, -4, -8, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[-7, -4, 2, -10],\n [-4, 6, -2, -4],\n [2, -2, 12, 0],\n [-10, -4, 0, 0]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 13 | 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, 9, 7, 12],\n [0, 10, 9, 6],\n [12, -2, 1, 3],\n [6, 10, -8, -6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 16 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (3, 1) of the inverse. Round your answer to the nearest integer:\n[[-9, 0, 7, 4],\n [3, 10, 10, 2],\n [10, -6, 0, -3],\n [-1, 7, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 8 | 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[[-6, 6, 0, -10],\n [7, 5, 6, -3],\n [7, -8, 4, -11],\n [-2, 4, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 73 | 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[[-9, 2, -4, 0],\n [2, 4, -2, -2],\n [-4, -2, -10, 0],\n [0, -2, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | 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[[5, 12, 3, 4],\n [0, -6, -9, -2],\n [0, 0, 8, -5],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | -60 | 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, -12, -7, 1],\n [-6, 12, 5, -6],\n [9, -9, 10, -2],\n [-6, 8, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 162 | 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, -6, -11, 10],\n [11, -4, 7, 6],\n [4, 3, -2, -7],\n [6, 1, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 468 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the value at position (3, 2) rounded to the nearest integer?\n[[-9, 7, -6, -4],\n [-7, 8, -7, -8],\n [12, 1, 1, 6],\n [-7, 12, -5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -18 | MATH |
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