messages listlengths 1 1 | ground_truth stringlengths 1 6 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-12, -6, 9, 1],\n [0, 6, 8, -10],\n [0, 0, 10, 8],\n [0, 0, 0, -1]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -78 | MATH |
[
{
"content": "Find the inverse of 1/96 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, 11, 6, 3],\n [12, -3, -12, 11],\n [-4, 10, 5, 1],\n [9, -7, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 116 | 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, -9, -8, 5],\n [0, 2, -6, 1],\n [0, 0, 1, -10],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \... | 34 | 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[[-4, 2, -4, 8],\n [2, -2, 2, 0],\n [-4, 2, -5, 5],\n [8, 0, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 413 | 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[[7, -4, 0, 0],\n [-4, 4, 5, 9],\n [0, 5, -10, -1],\n [0, 9, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 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[[3, 7, -6, -8],\n [-12, -5, -10, 2],\n [-7, 11, 7, 7],\n [-7, -10, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -18 | 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, 0, 1, -2],\n [0, 10, 6, -9],\n [1, 6, 4, 2],\n [-2, -9, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 17 | 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[[-7, -1, -7, 1],\n [0, 1, 11, 5],\n [0, 0, -6, -8],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 430 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-5, 6, 6, 10],\n [9, 8, 3, -6],\n [4, -9, -9, 5],\n [9, 12, -9, 1]]\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 all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[7, -7, 2, -9],\n [3, 4, -2, -5],\n [-3, 2, -10, -3],\n [9, 10, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{You... | -34 | 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[[-12, 0, -3, 10],\n [-2, 9, -1, -2],\n [1, 12, 3, -1],\n [-10, 11, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | -34 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[11, -5, -5, -3],\n [-4, 5, 12, -12],\n [9, 6, -9, -11],\n [5, 9, -12, -8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -372 | 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[[-10, -2, 9, -8],\n [9, 10, 9, -1],\n [2, -1, -8, 1],\n [-10, 2, 12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -19 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-5, 1, -1, -3],\n [10, 9, -8, 7],\n [-9, 10, -7, 10],\n [10, 5, 11, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | 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, -2, -9, 5],\n [0, 12, 10, 5],\n [0, 0, 9, -2],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | 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[[0, 8, -3, 10],\n [4, 7, -4, -5],\n [-2, 12, 6, -3],\n [6, 11, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 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[[-6, 8, 6, 6],\n [0, -1, -3, 5],\n [0, 0, -4, -2],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | 0 | 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, 1, 0, -5],\n [1, 7, 5, -2],\n [0, 5, 3, -5],\n [-5, -2, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 1540 | MATH |
[
{
"content": "Find the value of the entry with the largest absolute value of the inverse of matrix 1/96 * A where A =\n[[0, -4, 0, -2],\n [-3, 12, -6, -4],\n [-5, -2, -8, -1],\n [-8, 12, 11, 6]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | -34 | MATH |
[
{
"content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[11, -4, -2, 2],\n [-4, -5, -3, -8],\n [-2, -3, -6, 6],\n [2, -8, 6, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "For the inverse of 1/96 times the matrix below, what is the trace (sum of diagonal elements) rounded to the nearest integer?\n[[9, -9, 10, 10],\n [0, -9, 8, -9],\n [0, 0, -8, 8],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -21 | 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[[-10, -8, -10, 9],\n [-5, 6, 6, 11],\n [3, 3, 10, 9],\n [-3, -2, -12, 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 1/96 * A where A =\n[[-8, 6, 9, -1],\n [0, -1, 11, 9],\n [0, 0, 7, 0],\n [0, 0, 0, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 288 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[8, 4, 2, 2],\n [4, -1, -4, -2],\n [2, -4, -7, 6],\n [2, -2, 6, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 166 | 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[[-8, 12, 3, 4],\n [0, 12, -6, 7],\n [0, 0, 7, -5],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 105 | 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, 4, 2, 4],\n [0, -12, -7, -3],\n [-1, 7, 3, -1],\n [-7, 1, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 182 | MATH |
[
{
"content": "Find the value at position (3, 1) of the inverse of matrix 1/96 * A where A =\n[[-3, 4, -3, 4],\n [4, 10, 6, 2],\n [-3, 6, -6, 7],\n [4, 2, 7, -2]]\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 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-7, -4, -2, -10],\n [-4, 12, 1, -2],\n [-2, 1, 0, -2],\n [-10, -2, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 178 | 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[[-10, -3, -2, 4],\n [-3, -1, -4, -5],\n [-2, -4, 5, -6],\n [4, -5, -6, -1]]\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 sum of absolute values of all entries rounded to the nearest integer?\n[[-9, 7, 10, -9],\n [10, -6, -12, 12],\n [-4, 11, 3, -2],\n [-6, 9, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2939 | 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[[4, 10, 1, -8],\n [10, 6, 12, -2],\n [1, 12, -10, -10],\n [-8, -2, -10, 0]]\n\nPresent the answer in LaTex format: \\... | -26 | 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, -8, -6, -2],\n [-2, 3, 4, 4],\n [-3, -1, -1, 12],\n [4, 3, -5, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 38 | 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[[8, 2, -4, -8],\n [2, 5, 9, -4],\n [-4, 9, 5, 6],\n [-8, -4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Y... | -9 | 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[[-10, 6, -2, -8],\n [6, 3, -4, 8],\n [-2, -4, 2, 5],\n [-8, 8, 5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 105 | 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, 1, -8, -5],\n [1, 8, 8, -8],\n [-8, 8, -2, 2],\n [-5, -8, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answe... | -8 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[8, 7, 1, 11],\n [0, 7, -5, 1],\n [0, 0, 4, 9],\n [0, 0, 0, 8]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 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[[2, 0, -6, -6],\n [0, 1, 0, -10],\n [0, 0, 7, -7],\n [0, 0, 0, -1]]\n\nPresent the answer i... | -960 | 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[[-9, -11, -12, 11],\n [0, 12, -10, 8],\n [0, 0, -12, -12],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex fo... | -24 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[6, 10, -2, 10],\n [10, 11, 6, 3],\n [-2, 6, 12, 0],\n [10, 3, 0, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21 | 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[[0, -6, -11, 0],\n [5, -5, -7, -9],\n [4, -5, -8, -11],\n [-5, 10, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{... | 104 | 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, 10, 10, 6],\n [0, 8, 1, 3],\n [0, 0, 8, -8],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | 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, 2, -10, -6],\n [0, 4, -1, -4],\n [0, 0, -4, -10],\n [0, 0, 0, 2]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | -120 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[3, 12, -3, 3],\n [6, 4, 0, 9],\n [12, -11, -10, 0],\n [-12, 2, 6, 10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the sum of all entries of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-6, -8, -9, 2],\n [-8, 12, -2, -1],\n [-9, -2, -6, 6],\n [2, -1, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Y... | -28 | 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[[-12, -7, 10, 3],\n [3, -1, 3, -10],\n [10, -8, 12, -4],\n [1, -7, -2, -7]]\n\nPresent the answer in LaTex fo... | 5 | 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[[5, 11, 7, 1],\n [-2, 11, 6, 1],\n [8, -10, -1, 11],\n [0, -6, -4, 12]]\n\nPresent the answer in LaTex f... | 212 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[3, -9, 5, -12],\n [1, 5, 9, -4],\n [1, 7, -3, -12],\n [-9, 5, 1, -5]]\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 absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[4, -2, 8, 0],\n [-2, -8, 6, -7],\n [8, 6, -6, 2],\n [0, -7, 2, -4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 178 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-4, -6, -3, 1],\n [0, 8, -6, -11],\n [0, 0, 5, -3],\n [0, 0, 0, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[9, -5, 8, 10],\n [0, 6, -2, 11],\n [0, 0, 11, 0],\n [0, 0, 0, -12]]\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 1/96 times the matrix below, what is the value at position (4, 1) rounded to the nearest integer?\n[[-7, 3, 2, -4],\n [3, -1, 5, -10],\n [2, 5, 5, 0],\n [-4, -10, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | 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[[10, 2, 2, 0],\n [2, -4, 0, 2],\n [2, 0, 2, 2],\n [0, 2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your a... | -288 | 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[[-8, 1, -6, 10],\n [-9, -1, 2, 11],\n [-3, -1, -7, 3],\n [2, 11, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | -102 | 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, 8, -7, -6],\n [0, 12, 4, 6],\n [0, 0, -9, 11],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \... | 15 | 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, -8, -8, 4],\n [-8, -5, 0, -8],\n [-8, 0, 12, 8],\n [4, -8, 8, -1]]\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 of the entry with the largest absolute value of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[6, 1, 4, 2],\n [0, -10, 6, 4],\n [0, 0, 1, 4],\n [0, 0, 0, 11]]\n\nPresent the answer in L... | 96 | 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, -5, 8, 0],\n [-5, -5, 2, 1],\n [8, 2, 4, 4],\n [0, 1, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 36 | 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[[-1, 10, 2, 2],\n [10, -7, 4, 0],\n [2, 4, -4, -1],\n [2, 0, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -38 | 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, 8, 3, 0],\n [8, 8, 1, -9],\n [3, 1, 12, -2],\n [0, -9, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 71 | 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[[-5, 4, -4, 9],\n [7, 1, -3, -6],\n [-10, -9, 11, -10],\n [-2, 1, 9, -10]]\n\nPresent the answer in LaTe... | 151 | 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, 0, -4, -3],\n [0, -1, 1, 2],\n [-4, 1, -8, 10],\n [-3, 2, 10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 194 | 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[[10, -11, 8, 5],\n [-4, -9, 5, 9],\n [-3, -8, -12, -1],\n [-7, -10, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | -1 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[-2, -5, -11, -6],\n [0, 5, 3, 0],\n [0, 0, 12, -6],\n [0, 0, 0, 4]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -197 | MATH |
[
{
"content": "Find the sum of all entries of the inverse of matrix 1/96 * A where A =\n[[7, 0, -5, -2],\n [0, 1, -2, 5],\n [0, 0, -6, -1],\n [0, 0, 0, 6]]\nRound your answer to the nearest integer.\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[[-9, -7, 7, -4],\n [0, -12, 7, -10],\n [0, 0, -8, -6],\n [0, 0, 0, -12]]\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 1/96 times the matrix below, what is the sum of all entries rounded to the nearest integer?\n[[-4, 3, 6, -7],\n [0, -5, 9, 6],\n [0, 0, 4, 0],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | 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, 0, 4],\n [-10, -12, 8, 0],\n [0, 8, -11, 2],\n [4, 0, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | 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[[-12, -11, -11, -8],\n [-10, -6, 4, -8],\n [-12, 3, -1, -12],\n [-9, 1, 4, -3]]\n\nPresent the answer in LaTex format... | 4 | 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[[-9, 7, 11, -5],\n [0, 2, -5, 1],\n [0, 0, -8, 6],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\b... | 73 | 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[[-8, 4, -9, 10],\n [-1, -8, 10, -9],\n [-8, 9, 1, 1],\n [6, 4, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 12 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[12, 9, 10, -8],\n [-7, 2, -1, -6],\n [-5, -4, -4, -6],\n [3, -7, -10, 9]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 132 | 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, -1, 7, -4],\n [0, -9, 1, -5],\n [0, 0, 6, 10],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: ... | 4 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-1, 7, 6, -12],\n [12, -1, -3, 6],\n [12, 9, -2, 9],\n [-5, -7, 7, -5]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 95 | 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[[4, -8, 10, -6],\n [-8, 1, 8, -1],\n [10, 8, -12, -4],\n [-6, -1, -4, -4]]\n\nPresent the answer in LaTex format: \\b... | -3 | MATH |
[
{
"content": "Find the value at position (4, 4) of the inverse of matrix 1/96 * A where A =\n[[-8, 2, -12, 12],\n [0, 9, 11, 4],\n [0, 0, 9, 7],\n [0, 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": "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, 3, -1, -4],\n [3, -6, 0, 6],\n [-1, 0, 3, 1],\n [-4, 6, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 31 | 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[[-1, 5, 10, 8],\n [10, -9, -8, 4],\n [-6, 7, -3, 5],\n [3, -7, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed... | 5 | 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[[12, 12, 4, 7],\n [0, 1, -8, -1],\n [0, 0, 7, 12],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{You... | -55 | 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, 1, 12, -3],\n [0, 2, -10, -8],\n [0, 0, 2, 10],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 108 | 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[[4, 4, -5, -1],\n [0, -4, 11, 2],\n [0, 0, 4, -2],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -36 | 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[[-5, -5, 4, 9],\n [-5, -5, -1, 7],\n [4, -1, 8, 4],\n [9, 7, 4, 11]]\n\nPresent the answer in LaTex format: \... | -60 | 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, 12, -6, -4],\n [10, 7, -1, -5],\n [11, -12, 8, -10],\n [3, -11, 6, -11]]\n\nPresent the answer in LaTex... | 115 | 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[[-11, -2, -1, 8],\n [-9, 3, 11, -10],\n [-6, 8, -10, 9],\n [-7, -3, 3, 5]]\n\nPresent the answer in LaTex format: \\b... | -4 | MATH |
[
{
"content": "Find the inverse of 1/96 times the matrix and calculate the value at position (1, 3) of the inverse. Round your answer to the nearest integer:\n[[-12, 4, -6, 6],\n [4, 11, 0, 2],\n [-6, 0, -3, -1],\n [6, 2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | -32 | 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, 10, -9, 5],\n [-5, -9, 12, -5],\n [-12, 1, -10, 11],\n [-6, 2, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{You... | -14 | 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[[-1, 7, -3, -11],\n [-2, -7, -1, -6],\n [9, 7, 10, -6],\n [4, -3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 21 | 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[[-7, 0, 3, 6],\n [0, 10, 5, 12],\n [0, 0, 10, -12],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 115 | MATH |
[
{
"content": "Find the value at position (1, 4) of the inverse of matrix 1/96 * A where A =\n[[-8, -4, 4, -5],\n [-4, -1, -6, 3],\n [4, -6, -10, -10],\n [-5, 3, -10, 3]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "Calculate the inverse matrix of 1/96 times the following and determine the value at position (2, 3) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-2, 12, -7, 11],\n [-1, -4, 7, 7],\n [11, -7, -11, -12],\n [2, 7, 2, 0]]\n\nPresent the answer in LaTex format: \\bo... | -2 | MATH |
[
{
"content": "Find the value at position (3, 3) of the inverse of matrix 1/96 * A where A =\n[[9, -11, -7, -5],\n [8, -8, 7, 3],\n [11, 11, -7, 12],\n [-2, 0, -4, -11]]\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 1/96 times the matrix below, what is the value at position (2, 2) rounded to the nearest integer?\n[[-4, 3, 7, -2],\n [3, 1, 4, -6],\n [7, 4, -8, -2],\n [-2, -6, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "Find the value at position (4, 3) of the inverse of matrix 1/96 * A where A =\n[[-1, 4, 11, -3],\n [0, -10, -1, -12],\n [0, 0, 6, 0],\n [0, 0, 0, 4]]\nRound your answer to the nearest integer.\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 of the entry with the largest absolute value of the inverse. Round your answer to the nearest integer:\n[[2, 6, 3, 4],\n [6, 11, -6, 1],\n [12, 3, -8, 1],\n [-7, -3, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answe... | -26 | MATH |
[
{
"content": "Find the trace (sum of diagonal elements) of the inverse of matrix 1/96 * A where A =\n[[-11, 2, 2, -10],\n [2, -3, -1, 0],\n [2, -1, -2, 8],\n [-10, 0, 8, -7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -45 | 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[[-12, 4, 11, 8],\n [-12, -2, -6, 4],\n [-6, 4, 0, -11],\n [4, -5, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | -6 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the inverse of matrix 1/96 * A where A =\n[[-4, -2, 8, 12],\n [8, -7, -12, 0],\n [-8, -3, 2, -11],\n [12, 9, 4, -10]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | 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[[8, -6, 6, 1],\n [0, 7, 0, 0],\n [0, 0, 5, 1],\n [0, 0, 0, 11]]\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 trace (sum of diagonal elements) of the resulting matrix. Your answer should be rounded to the nearest integer:\n[[-11, 3, -5, 5],\n [0, -12, 12, -9],\n [-11, 3, -1, -1],\n [-11, 2, -11, -6]]\n\nPresent the answer in LaTex ... | -5 | 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, -4, -2, -6],\n [-4, 3, -4, 5],\n [-2, -4, 5, -6],\n [-6, 5, -6, 0]]\n\nPresent the answer in LaTex ... | 228 | MATH |
[
{
"content": "Find the value at position (4, 2) of the inverse of matrix 1/96 * A where A =\n[[-4, 4, 4, 12],\n [-10, 8, -10, -8],\n [2, -12, 8, 9],\n [-12, 4, 3, 7]]\nRound your answer to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
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