messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[-14, 6, 5, 2, -15],\n [0, -14, 15, 11, 6],\n [0, 0, 2, -5, 5],\n [0, 0, 0, 1, -2],\n [0, 0, 0, 0, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -2, 12, 4, 8],\n [-2, -9, -9, 7, -13],\n [12, -9, 1, -4, -10],\n [4, 7, -4, 5, -10],\n [8, -13, -10, -10, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 548 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -10, 2, -3, 13],\n [2, -10, -2, 10, 12],\n [-6, -6, 7, 4, -5],\n [-3, -4, 2, 7, 13],\n [-12, 8, -6, 9, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 780 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[14, 6, 8, 5, 9],\n [14, -11, 3, -7, 8],\n [5, 6, 7, -3, -10],\n [11, 6, 1, -4, 9],\n [-2, 11, 7, -10, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 396 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -4, -2, -1, -3],\n [-4, -12, -12, -8, 2],\n [-2, -12, -7, -1, 2],\n [-1, -8, -1, 3, 12],\n [-3, 2, 2, 12, 15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-13, 5, 4, 7, 11],\n [7, 6, -10, 3, -1],\n [6, -14, -12, 0, 4],\n [5, 6, 3, 9, -10],\n [4, -12, 10, 7, -14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 466 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 2, -1, -8, 10],\n [2, -10, -7, 7, -10],\n [-1, -7, -11, 4, -4],\n [-8, 7, 4, -2, 9],\n [10, -10, -4, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 999 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, 7, -13, 4, -11],\n [0, 15, 15, 8, -12],\n [0, 0, -11, 1, 8],\n [0, 0, 0, 8, -2],\n [0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 560 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 0, -11, 11, -3],\n [8, 11, 6, 1, -9],\n [9, 0, 7, 13, -15],\n [14, -13, -11, 7, -2],\n [11, -2, 0, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 317 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -15, -1, 15, 0],\n [-8, 1, -8, 10, -14],\n [-8, -11, 6, 15, -9],\n [-7, -3, 3, -2, 0],\n [13, 9, -10, -10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 103 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -2, -8, 4, -2],\n [-2, -5, -10, 4, 8],\n [-8, -10, -1, 4, -9],\n [4, 4, 4, -7, 7],\n [-2, 8, -9, 7, 14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 150 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, -12, 4, 11, 7],\n [0, 14, 7, -13, -2],\n [0, 0, -2, -12, 2],\n [0, 0, 0, 12, -14],\n [0, 0, 0, 0, -12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 128 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -1, 7, 8, 13],\n [0, -11, 6, 8, 10],\n [0, 0, 3, -2, -7],\n [0, 0, 0, -10, 12],\n [0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 620 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, 4, 15, -5, -10],\n [0, 1, 10, 14, -8],\n [0, 0, -6, -3, 3],\n [0, 0, 0, -11, 3],\n [0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 136 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -11, 10, 0, 0],\n [-11, 2, 6, -3, 0],\n [10, 6, 1, -4, 8],\n [0, -3, -4, 11, 4],\n [0, 0, 8, 4, 13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 600 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -2, 1, -12, -5],\n [0, -15, 4, -3, -10],\n [0, 0, -11, 7, 13],\n [0, 0, 0, -12, -10],\n [0, 0, 0, 0, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 120 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -9, 4, -4, -8],\n [-9, 3, 10, -10, -12],\n [4, 10, -4, 2, 0],\n [-4, -10, 2, -7, 0],\n [-8, -12, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 712 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, -5, -15, 15, -12],\n [0, 8, -8, -15, 0],\n [-9, 15, -2, -12, 12],\n [-2, 8, -12, 6, -11],\n [1, -10, 10, 13, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 291 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, -1, -2, -5, 3],\n [7, 6, -2, 8, -3],\n [4, 7, 13, -3, 8],\n [-12, -15, -9, -12, -3],\n [3, -8, 11, -12, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 106 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[14, 9, 6, 10, -4],\n [9, 1, -2, 5, -8],\n [6, -2, 10, -7, -13],\n [10, 5, -7, 6, 0],\n [-4, -8, -13, 0, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 318 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 4, 14, -6, -10],\n [-10, 2, -2, 15, -5],\n [1, 8, -13, 2, 6],\n [14, -12, 14, -5, 7],\n [14, 11, 13, 9, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 436 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -4, -14, -3, -12],\n [0, -5, 5, 15, -5],\n [0, 0, -4, -5, -11],\n [0, 0, 0, -1, -15],\n [0, 0, 0, 0, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 880 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -4, -4, 14, -12],\n [-7, 0, -15, 6, -10],\n [6, 9, -5, -8, -14],\n [-10, 1, -12, -14, 12],\n [-13, -1, 3, -6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 648 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, -8, -2, -10, 14],\n [0, -11, -8, -14, -2],\n [0, 0, -8, 3, -2],\n [0, 0, 0, -10, 6],\n [0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 600 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 8, -14, 5, -3],\n [0, 8, -4, -2, 6],\n [0, 0, -6, -6, -8],\n [0, 0, 0, 15, -10],\n [0, 0, 0, 0, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 680 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, 13, 11, -11, 15],\n [-6, -1, -15, 15, 0],\n [-6, 15, -10, 4, 0],\n [4, 1, -15, 8, -10],\n [-11, -7, 7, 7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 985 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -15, -9, 10, -12],\n [10, -6, 8, 5, 10],\n [-7, -1, -13, -15, -15],\n [-10, -13, -9, 6, 3],\n [-6, 8, -6, -12, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 742 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 8, -6, -1, -12],\n [0, -13, -6, 13, -11],\n [0, 0, -1, 4, 11],\n [0, 0, 0, -6, 5],\n [0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 64 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, 12, -2, -14, -14],\n [0, -2, 6, 11, -15],\n [0, 0, 2, -1, 13],\n [0, 0, 0, -3, 0],\n [0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 380 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[14, -12, -7, -13, 7],\n [0, -5, 14, 12, 15],\n [0, 0, 12, 15, -2],\n [0, 0, 0, 12, -3],\n [0, 0, 0, 0, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 640 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 2, 11, -8, 6],\n [0, 5, 6, -13, 9],\n [0, 0, 4, -5, 15],\n [0, 0, 0, -2, 7],\n [0, 0, 0, 0, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 680 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -12, -3, 7, 8],\n [-12, 9, -8, -10, -12],\n [-3, -8, -5, 10, 10],\n [7, -10, 10, -3, -8],\n [8, -12, 10, -8, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 644 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 10, 5, -3, -6],\n [4, 0, 2, -10, 8],\n [-8, 10, 3, -1, 12],\n [12, 14, 3, 1, -1],\n [11, 10, 11, -12, 6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 392 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 8, -9, -4, 14],\n [5, -3, 5, -7, -10],\n [7, 4, 3, -12, 5],\n [-9, -12, 6, 8, -6],\n [14, 13, -1, 9, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 224 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 8, -1, 1, -2],\n [8, -6, -3, 1, 5],\n [-1, -3, -5, -8, 3],\n [1, 1, -8, -13, 4],\n [-2, 5, 3, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 228 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-13, -5, -13, 0, 8],\n [0, 4, -6, -9, -12],\n [0, 0, 15, 10, 9],\n [0, 0, 0, -13, 0],\n [0, 0, 0, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -1, 13, 1, -15],\n [-2, 12, 3, 2, 1],\n [6, -8, 9, 11, -14],\n [4, 5, -3, -11, -1],\n [-11, 9, 15, 11, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 256 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 7, 7, -8, -13],\n [4, -5, 10, 13, 9],\n [0, 2, 6, 8, -4],\n [5, 1, 9, 7, 8],\n [-1, -5, -13, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 124 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 9, -7, 5, -10],\n [-12, -13, 5, -7, 2],\n [-6, 12, -11, -6, -13],\n [0, -10, 7, -5, 1],\n [7, 0, -9, -15, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 308 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 10, -5, -14, -8],\n [14, 9, 6, -11, 14],\n [-6, -1, -5, -10, -6],\n [4, -7, -7, 4, -4],\n [14, 13, -9, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 84 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-13, 1, 11, -8, 15],\n [0, -2, -3, 1, -7],\n [10, 9, 3, -1, 14],\n [6, -4, -7, 6, -9],\n [10, -13, -10, -2, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 347 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -9, 14, -8, -14],\n [3, -10, -11, -9, 10],\n [13, 8, 2, -9, -8],\n [8, -5, -1, 6, 7],\n [-1, 14, 8, 15, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 675 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, 2, -12, 1, 0],\n [2, 7, 12, -4, -6],\n [-12, 12, -6, -8, -6],\n [1, -4, -8, 13, 4],\n [0, -6, -6, 4, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 994 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -5, -12, -14, -3],\n [0, -12, 1, -6, -4],\n [0, 0, -3, -12, 1],\n [0, 0, 0, 12, -8],\n [0, 0, 0, 0, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 264 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -5, -7, -4, -9],\n [-10, -14, -15, 6, 12],\n [1, 0, -2, 9, -7],\n [-7, 13, -12, 5, -4],\n [1, -4, 4, 0, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 764 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 1, 14, -13, 6],\n [0, -4, 3, -8, 3],\n [0, 0, -5, 13, -10],\n [0, 0, 0, 12, 9],\n [0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-14, 8, 0, -8, 8],\n [8, -11, -5, -4, 2],\n [0, -5, -3, 2, 7],\n [-8, -4, 2, -8, -2],\n [8, 2, 7, -2, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 992 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, -3, -6, 6, -4],\n [-3, -11, 8, 12, 0],\n [-6, 8, -15, -6, 2],\n [6, 12, -6, -9, -14],\n [-4, 0, 2, -14, 14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 726 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, 6, -10, 0, 7],\n [6, -6, -2, 4, 11],\n [-10, -2, 13, -2, 7],\n [0, 4, -2, -4, 6],\n [7, 11, 7, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 360 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, 6, 0, 1, -8],\n [6, 15, 4, -10, -10],\n [0, 4, 15, -2, -4],\n [1, -10, -2, -15, 0],\n [-8, -10, -4, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 932 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -8, 9, 4, 14],\n [-14, 14, 7, 9, -5],\n [14, -6, 15, -6, 15],\n [3, -11, -12, 9, 8],\n [-14, 8, 13, -15, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 478 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 15, -11, 8, -2],\n [7, -4, -5, 15, 4],\n [2, 14, 14, 13, 5],\n [0, -1, -10, -13, 6],\n [3, 9, -11, 6, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 206 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, -13, -10, -1, -6],\n [-13, 9, 1, -1, 10],\n [-10, 1, -7, 6, -9],\n [-1, -1, 6, 4, 4],\n [-6, 10, -9, 4, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 623 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -7, -2, -11, -2],\n [-7, -8, -2, -3, 2],\n [-2, -2, 5, 10, -8],\n [-11, -3, 10, 4, 6],\n [-2, 2, -8, 6, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 188 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, 10, 0, 6],\n [-2, -2, 0, 0, 3],\n [10, 0, 2, -8, -8],\n [0, 0, -8, 1, 1],\n [6, 3, -8, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 146 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -8, 0, 11, -10],\n [-2, 5, -11, -15, 2],\n [5, 7, -8, 6, 10],\n [-4, -5, 12, -1, -5],\n [-6, 11, 14, 11, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 813 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, -2, -4, -4, 4],\n [-2, 9, 8, -10, -1],\n [-4, 8, -3, -8, 0],\n [-4, -10, -8, 14, 0],\n [4, -1, 0, 0, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 2, -7, -14, -13],\n [-13, 1, -15, 3, 5],\n [-1, -13, 5, 6, 10],\n [7, -8, 9, -4, -4],\n [2, -14, 6, 8, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 730 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 2, -2, 3, 10],\n [2, 9, -1, 4, -8],\n [-2, -1, 11, 13, 2],\n [3, 4, 13, 13, -6],\n [10, -8, 2, -6, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 400 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 7, -10, 1, 14],\n [4, -1, 2, 0, 4],\n [7, -4, -9, -2, -15],\n [-2, -8, 13, -1, 5],\n [-15, 6, -1, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 743 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 11, -3, 14, -6],\n [-11, -2, 1, -8, 1],\n [10, 7, 7, -7, -15],\n [-10, 10, -2, -10, -15],\n [-10, -6, 7, 7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 449 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 4, -9, 8, -8],\n [4, -5, 0, 2, 1],\n [-9, 0, 13, 1, 4],\n [8, 2, 1, 1, -3],\n [-8, 1, 4, -3, 10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 368 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -4, -14, -1, 15],\n [12, -12, -8, 13, 4],\n [-10, 8, 8, 10, -9],\n [-9, -13, -6, -6, -13],\n [10, 3, -9, -4, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 443 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 0, 2, -12, 2],\n [0, -14, -3, 8, -2],\n [0, 0, 2, 4, 12],\n [0, 0, 0, 12, -9],\n [0, 0, 0, 0, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 984 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, -10, -14, 13, 5],\n [0, 10, 14, -11, 13],\n [0, 0, 15, -6, 5],\n [0, 0, 0, 7, -13],\n [0, 0, 0, 0, -7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 950 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, 6, 4, -10, -8],\n [0, 2, -7, 7, -5],\n [0, 0, 6, 6, -4],\n [0, 0, 0, 12, -12],\n [0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 840 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[14, 8, -4, 1, -10],\n [8, -8, 2, -8, -4],\n [-4, 2, -15, 5, 6],\n [1, -8, 5, -4, -2],\n [-10, -4, 6, -2, 15]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 396 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -13, 0, 11, -8],\n [-1, -3, -13, -4, -4],\n [-5, 10, -1, 8, -5],\n [-9, 14, -11, 13, 10],\n [-5, 1, -6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 654 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, -14, 6, -15, 4],\n [10, 3, 0, -14, -5],\n [14, 10, -5, 14, -15],\n [11, -2, -13, 0, -7],\n [-13, 12, 14, -7, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 814 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 12, 9, -11, -7],\n [-15, -7, 7, 6, 14],\n [-4, -11, -5, -4, -6],\n [-3, 13, 5, -3, -15],\n [11, -3, -14, 7, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 422 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, -8, -5, 11, 7],\n [0, 14, 3, 6, 6],\n [0, 0, 8, -15, 14],\n [0, 0, 0, 10, -13],\n [0, 0, 0, 0, -15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 400 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, -1, 7, 13, 8],\n [15, -2, -3, -7, 12],\n [-7, -14, -8, -3, -10],\n [5, -9, 3, -12, -3],\n [4, 3, 12, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 718 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 11, 0, 0, -12],\n [0, -7, -6, 10, 14],\n [0, 0, -8, 10, -8],\n [0, 0, 0, 8, 1],\n [0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 624 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -10, 15, -8, -6],\n [0, 10, 14, 13, 1],\n [0, 0, 14, 5, 7],\n [0, 0, 0, -8, 9],\n [0, 0, 0, 0, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 200 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -13, 0, 10, -1],\n [0, 6, 9, -13, -3],\n [0, 0, 3, 2, 13],\n [0, 0, 0, 10, 5],\n [0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 880 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, 6, -9, 10, -10],\n [0, -12, 12, 5, -2],\n [0, 0, 8, 15, 1],\n [0, 0, 0, 1, -10],\n [0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 376 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-14, -15, -2, 7, 2],\n [-6, 7, -2, -2, 4],\n [12, -14, -5, 11, 3],\n [8, -9, 4, 5, 2],\n [-2, -13, -11, 9, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 820 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 6, -6, -2, -13],\n [0, -4, 12, -4, -3],\n [0, 0, 4, 15, 10],\n [0, 0, 0, -12, 5],\n [0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 848 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -7, 5, -6, 6],\n [2, 13, -4, -12, -5],\n [-13, -2, -15, 5, -9],\n [-8, 1, 6, -4, 7],\n [-10, -2, 12, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 482 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -2, -13, -6, 3],\n [0, -1, -2, -15, -3],\n [0, 0, 1, 8, 14],\n [0, 0, 0, 1, -1],\n [0, 0, 0, 0, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 0, 13, 8, -7],\n [-15, 10, 4, 15, 6],\n [-3, 4, 4, -5, 6],\n [-6, 13, -13, 1, -1],\n [6, 6, -1, -11, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 138 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -15, 11, 4, -7],\n [3, -4, -7, -13, 8],\n [3, -7, -3, -8, 14],\n [6, 3, 10, -3, 6],\n [9, 3, 11, 0, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 368 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 14, 9, -7, -12],\n [0, 4, 15, -2, -1],\n [0, 0, -10, 0, 8],\n [0, 0, 0, 6, 8],\n [0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 560 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -2, -1, -2, -8],\n [-2, -14, -6, 6, -6],\n [-1, -6, -13, -2, 0],\n [-2, 6, -2, -15, 0],\n [-8, -6, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 12 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, 5, -12, -11, -11],\n [0, -8, 5, 14, -14],\n [0, 0, -9, 15, 13],\n [0, 0, 0, 4, 1],\n [0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 304 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 0, -9, -5, 0],\n [0, -8, 13, -14, -6],\n [0, 0, -2, 13, 11],\n [0, 0, 0, 5, 14],\n [0, 0, 0, 0, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 760 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -6, 11, -5, 7],\n [-9, 13, 3, 12, 11],\n [-1, -13, -15, -2, 4],\n [-5, -5, -4, 5, 0],\n [-11, -15, 6, 10, -11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 60 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 1, 2, -1, -1],\n [1, 8, 8, -8, -4],\n [2, 8, 10, 2, -10],\n [-1, -8, 2, 1, 4],\n [-1, -4, -10, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 396 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -6, 0, -2, 9],\n [-6, -4, 8, 2, 8],\n [0, 8, 0, 0, 10],\n [-2, 2, 0, 0, -14],\n [9, 8, 10, -14, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 696 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 8, 14, -8, -14],\n [0, -5, -6, 0, 14],\n [0, 0, 10, 8, -3],\n [0, 0, 0, -7, 1],\n [0, 0, 0, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 3, -8, -8, 1],\n [-1, -11, 3, -6, 3],\n [15, 10, -15, -8, 5],\n [-4, -12, 2, -14, 4],\n [4, -3, 15, 6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 832 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 14, -14, -11, 1],\n [7, 14, -15, -14, -13],\n [1, -5, 8, -4, 2],\n [-6, -2, -10, 1, 13],\n [-4, 12, -11, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 113 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -5, -8, 6, -12],\n [0, -11, 11, -8, 12],\n [0, 0, -3, -9, 6],\n [0, 0, 0, 2, 2],\n [0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 660 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 0, -2, 4, 8],\n [0, 15, -3, 12, 4],\n [-2, -3, 7, 6, -2],\n [4, 12, 6, -13, 6],\n [8, 4, -2, 6, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 572 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, -10, 15, -8, 0],\n [-8, 10, 5, -8, 0],\n [6, -1, -8, 2, 2],\n [14, -5, 7, -11, -13],\n [-10, 3, 4, -7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 694 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, 13, -15, -8, -14],\n [7, 3, -12, 7, 11],\n [14, -2, -4, 15, 2],\n [-7, -11, 5, -14, -11],\n [4, -6, 2, 15, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 497 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -1, 0, 0, 2],\n [-1, 9, -7, 1, -4],\n [0, -7, 7, -4, 2],\n [0, 1, -4, -8, 2],\n [2, -4, 2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 771 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -4, 6, -6, -12],\n [-4, -11, -12, 4, 7],\n [6, -12, -1, -3, 2],\n [-6, 4, -3, 1, 6],\n [-12, 7, 2, 6, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 458 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 0, 10, -2, -6],\n [2, 12, 8, 7, -15],\n [6, -15, -11, -10, 5],\n [-11, 0, 12, 0, 8],\n [-1, -2, 7, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 892 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -2, 2, -6, -6],\n [-2, -2, 0, -10, 1],\n [2, 0, -1, -8, -6],\n [-6, -10, -8, -5, -5],\n [-6, 1, -6, -5, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 50 | MATH |
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