messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 5, 0, -11, -6],\n [7, 14, 11, 3, 13],\n [-6, -4, -4, 3, -9],\n [10, 3, 9, 0, 3],\n [6, 4, 11, -9, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 684 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 1, 9, 2, 8],\n [-13, 6, 5, 9, -5],\n [9, -6, 0, -9, -3],\n [2, 0, 4, -10, 4],\n [14, -3, -2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 106 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 6, 0, -8, 2],\n [6, 10, 8, 4, 2],\n [0, 8, -9, 4, -6],\n [-8, 4, 4, -14, 3],\n [2, 2, -6, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 518 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 4, 12, -4, 0],\n [4, -5, 2, -10, 0],\n [12, 2, 8, 8, 12],\n [-4, -10, 8, 15, -7],\n [0, 0, 12, -7, 3]]\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -4, -8, -2, -10],\n [-4, 13, 8, -8, -3],\n [-8, 8, 15, -10, 4],\n [-2, -8, -10, -1, -2],\n [-10, -3, 4, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 188 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, 14, -4, 13, 4],\n [0, 14, 0, -2, -10],\n [0, 0, -11, -4, -5],\n [0, 0, 0, -4, 5],\n [0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 136 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -15, -1, 11, 13],\n [1, -12, 7, 9, -6],\n [-4, 0, -12, -15, 4],\n [3, -1, 14, -5, 3],\n [-1, -14, -1, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 420 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 0, 6, -4, 2],\n [0, 7, -6, -6, -4],\n [6, -6, 12, -4, 4],\n [-4, -6, -4, -9, 1],\n [2, -4, 4, 1, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 424 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 12, -10, 0, 0],\n [-7, -4, 13, 2, 2],\n [-8, -11, -14, -9, 4],\n [-2, -11, -14, -14, -4],\n [-7, -1, -11, 2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 968 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -1, 9, -9, 11],\n [0, 4, -4, 10, -14],\n [0, 0, 1, 10, 7],\n [0, 0, 0, 1, 15],\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"
}
] | 72 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 5, -12, 10, 13],\n [5, 13, 2, 5, -1],\n [-12, 2, -1, 2, -8],\n [10, 5, 2, 3, 4],\n [13, -1, -8, 4, -15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 823 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 11, 3, 11, -6],\n [0, 1, -12, -11, -12],\n [0, 0, -7, -13, 9],\n [0, 0, 0, 13, -15],\n [0, 0, 0, 0, 11]]? 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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 11, 5, -9, 7],\n [0, 12, 13, -4, 12],\n [0, 0, -6, 2, 6],\n [0, 0, 0, 12, 5],\n [0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 192 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 9, 0, -3, 10],\n [0, 11, -2, 5, 9],\n [4, -9, -12, -15, -12],\n [-4, 6, 5, 11, 7],\n [-12, -3, 13, 0, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 32 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 10, 0, -2, 10],\n [10, -15, -2, -3, -2],\n [0, -2, 12, 6, -5],\n [-2, -3, 6, -3, 0],\n [10, -2, -5, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 928 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, 3, -5, -5, 10],\n [0, 4, 12, -2, -10],\n [0, 0, -7, 15, 14],\n [0, 0, 0, -7, 3],\n [0, 0, 0, 0, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 372 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, 10, -8, -2, -10],\n [0, -8, 2, -7, 11],\n [0, 0, -14, -13, -5],\n [0, 0, 0, 7, 13],\n [0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 344 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 7, 4, 2, 5],\n [7, -5, 13, -2, 2],\n [4, 13, 5, 4, 6],\n [2, -2, 4, 13, 14],\n [5, 2, 6, 14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 88 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, 14, -9, -12, 0],\n [0, 11, 2, 11, -8],\n [0, 0, -12, -2, -4],\n [0, 0, 0, -4, -5],\n [0, 0, 0, 0, 14]]\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": "Determine the value of det(A) where A =\n[[-11, -13, -5, 14, 0],\n [0, -13, -13, 0, 14],\n [0, 0, -6, -1, -9],\n [0, 0, 0, 4, -10],\n [0, 0, 0, 0, -2]]\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":... | 864 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, -7, -1, 14, -12],\n [0, -15, 10, -4, -13],\n [0, 0, 11, 4, -6],\n [0, 0, 0, -2, 15],\n [0, 0, 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"
}
] | 50 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[15, -11, 14, -2, -10],\n [8, 7, 6, -7, -6],\n [-11, 6, -8, 3, 2],\n [-1, -15, -4, -3, 5],\n [15, -15, -6, -13, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 580 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 4, 0, -4, 10],\n [4, -11, 0, 4, 0],\n [0, 0, -8, 0, -2],\n [-4, 4, 0, -4, 0],\n [10, 0, -2, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 520 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -12, 4, -11, -6],\n [7, -5, -8, -3, -6],\n [11, -3, 14, -9, 5],\n [-10, -4, -13, 13, -10],\n [3, 15, 8, 15, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 374 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -1, 4, 3, 14],\n [2, -10, -15, 1, -2],\n [10, 10, 9, 3, 5],\n [12, -5, -8, 13, 2],\n [-12, 9, 9, 9, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 3, -2, 0, 8],\n [3, 10, 0, 3, 1],\n [-2, 0, 11, 2, 6],\n [0, 3, 2, 5, 8],\n [8, 1, 6, 8, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 14, -14, -3, 5],\n [13, -9, 9, 14, 14],\n [-12, 6, 1, 7, 5],\n [12, -12, -8, -14, -5],\n [-14, -11, 7, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 971 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -12, 10, -14, 2],\n [0, 11, 7, -3, -8],\n [0, 0, 11, 12, 5],\n [0, 0, 0, -13, -11],\n [0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 992 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 0, 2, 13, -6],\n [0, 4, 8, 8, -12],\n [0, 0, -15, -15, 5],\n [0, 0, 0, -2, -9],\n [0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 680 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 9, -2, 10, -1],\n [15, -6, 1, -14, -10],\n [5, -5, 9, 8, 7],\n [8, -4, 8, 15, 9],\n [4, -10, -12, -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}",
"role"... | 480 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -6, 6, -3, -9],\n [-6, 4, -12, 10, -2],\n [6, -12, -11, 2, 0],\n [-3, 10, 2, 10, -6],\n [-9, -2, 0, -6, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 852 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 4, 0, 1, 3],\n [4, -7, 6, -2, -8],\n [0, 6, -3, -2, -7],\n [1, -2, -2, -10, 9],\n [3, -8, -7, 9, -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": "us... | 884 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 12, -11, 2, -4],\n [-8, -5, 6, -3, 13],\n [-8, 11, 3, 2, 8],\n [-2, 8, 15, -4, -14],\n [-5, 15, 14, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 810 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 14, -10, -6, 4],\n [-9, 12, 5, 8, 11],\n [12, -4, 5, -12, -15],\n [3, -2, 10, -2, 1],\n [1, -11, -1, -9, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 4 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-13, -10, 5, -10, -6],\n [-4, -5, 6, -4, -7],\n [10, 15, 8, -1, 8],\n [-11, 9, 15, -6, 8],\n [3, 2, 10, 9, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 843 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 4, 5, 6, -6],\n [4, -3, 4, -1, 4],\n [5, 4, 4, 0, -12],\n [6, -1, 0, -3, -6],\n [-6, 4, -12, -6, -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": "... | 828 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 0, -5, 0, 12],\n [-15, 6, -13, -15, 11],\n [10, -15, 13, -3, 2],\n [-2, 6, -8, -5, -6],\n [-7, 1, -1, -9, 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}",
"... | 644 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-15, 0, 2, -4, 8],\n [0, 6, 0, -2, 1],\n [2, 0, 1, -6, -6],\n [-4, -2, -6, -13, 7],\n [8, 1, -6, 7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 731 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 9, -5, -5, 7],\n [0, -1, 9, -6, 0],\n [0, 0, -7, 4, -12],\n [0, 0, 0, 3, 5],\n [0, 0, 0, 0, -13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 908 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -4, 1, 0, -4],\n [-4, 2, 0, 6, -12],\n [1, 0, -12, 1, -4],\n [0, 6, 1, 6, -2],\n [-4, -12, -4, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 840 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 0, -10, -1, -10],\n [0, 5, -15, -8, 13],\n [0, 0, 5, -5, -11],\n [0, 0, 0, -1, 6],\n [0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 100 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 8, -12, 1, 13],\n [0, -6, -7, -12, 7],\n [0, 0, 9, -15, -6],\n [0, 0, 0, 5, 6],\n [0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 240 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 2, -1, 1, -9],\n [-1, 3, 15, 8, 2],\n [-7, 5, -4, 5, 5],\n [8, -1, -6, 9, -12],\n [-2, -13, 5, -5, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 959 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-14, 13, 1, 6, 6],\n [0, 11, -2, -1, -1],\n [0, 0, 4, 15, -4],\n [0, 0, 0, 15, -9],\n [0, 0, 0, 0, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 720 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-15, 1, -11, -8, 12],\n [1, 14, 10, -13, -6],\n [6, 8, -2, -11, -5],\n [10, 14, 8, -3, -6],\n [7, 4, -15, 1, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 183 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, -1, -3, 8, -8],\n [-10, 11, -2, -6, 0],\n [8, -7, -4, 0, 2],\n [14, -13, 15, 14, -6],\n [-5, 0, 13, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 320 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 14, 13, -15, -11],\n [-12, -12, -11, 2, 6],\n [2, -3, -10, -11, -6],\n [-7, -12, -6, -7, -2],\n [-12, -2, 0, -3, -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}"... | 176 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -13, -8, -15, 7],\n [-8, -3, 8, 13, 10],\n [2, -9, -4, -4, -14],\n [5, -6, -5, -4, 7],\n [1, -5, 0, 11, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 499 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 15, -4, 4, 10],\n [0, 14, -11, 5, -5],\n [0, 0, -15, 12, -15],\n [0, 0, 0, 7, 2],\n [0, 0, 0, 0, 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}",
"role": "use... | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, -10, 12, -1, -12],\n [0, -11, 2, 5, -12],\n [0, 0, 12, -7, 6],\n [0, 0, 0, -10, 6],\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"
}
] | 0 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, -12, 8, -9, -15],\n [6, -2, 9, -8, 3],\n [-10, 0, -9, -10, 0],\n [-13, 6, -12, 14, 9],\n [-1, 8, -3, 15, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 890 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, -5, -7, 12, -2],\n [-5, 3, 0, 0, 6],\n [-7, 0, 2, -2, -3],\n [12, 0, -2, 0, 6],\n [-2, 6, -3, 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"
}
] | 124 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -3, 3, 7, 0],\n [-3, 12, 2, -4, -8],\n [3, 2, -1, 4, 2],\n [7, -4, 4, 9, 2],\n [0, -8, 2, 2, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 122 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-15, 6, -4, 3, 12],\n [6, 10, 8, -3, 13],\n [-4, 8, -13, 10, 1],\n [3, -3, 10, -12, 13],\n [12, 13, 1, 13, 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... | 819 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 12, -15, 13, 5],\n [6, 2, 7, 9, 8],\n [-3, -2, 3, 7, -8],\n [0, -4, -1, -15, 14],\n [-1, 5, -10, 15, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 678 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 12, -8, -4, 5],\n [0, -13, 9, -11, 8],\n [0, 0, 13, -11, 15],\n [0, 0, 0, -3, 13],\n [0, 0, 0, 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"
}
] | 294 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, 0, 12, -7, 9],\n [15, 6, 11, 9, 7],\n [3, -11, 2, 6, 5],\n [2, -7, 6, 6, -8],\n [-13, -13, -6, -7, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 189 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 5, -7, -4, -5],\n [0, -2, -11, -10, -7],\n [0, 0, -3, -13, 15],\n [0, 0, 0, -13, 5],\n [0, 0, 0, 0, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 994 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -5, 9, -6, -4],\n [0, -1, 6, -15, -13],\n [0, 0, -9, 12, -11],\n [0, 0, 0, 3, -13],\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"
}
] | 216 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -5, 7, -11, 0],\n [-3, -4, -7, -11, 2],\n [6, -2, -5, -14, -7],\n [-9, 12, 3, 5, -7],\n [-15, -7, 8, 10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 138 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, -1, 7, 2, -12],\n [-13, 14, -3, -14, 1],\n [3, 15, 6, 1, 6],\n [-10, -5, -8, 11, -4],\n [-15, -6, 13, 2, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 460 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -8, 5, 7, -7],\n [-11, 5, -8, 9, 12],\n [-3, -6, 5, 2, -4],\n [-6, -2, 3, -2, -10],\n [5, -1, 6, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 551 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 11, -8, -8, 4],\n [0, -1, 10, -4, 15],\n [0, 0, 9, -2, -3],\n [0, 0, 0, 11, -13],\n [0, 0, 0, 0, -14]]? 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": "What is the determinant of the matrix:\n[[9, 3, 8, -4, 5],\n [3, 4, 8, -6, -5],\n [8, 8, -10, 7, 0],\n [-4, -6, 7, 1, 4],\n [5, -5, 0, 4, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 398 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -2, 14, 14, 1],\n [0, 1, -7, 11, 11],\n [0, 0, -14, -15, -6],\n [0, 0, 0, -9, 14],\n [0, 0, 0, 0, -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": "... | 134 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-15, -8, 4, 0, 5],\n [-8, 1, -6, 4, -1],\n [4, -6, 5, -4, -9],\n [0, 4, -4, 8, 13],\n [5, -1, -9, 13, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 575 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, 4, -8, -5, 12],\n [0, -10, -11, 0, -14],\n [0, 0, -10, 7, 12],\n [0, 0, 0, -1, 0],\n [0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 0 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 0, 10, 1, -9],\n [0, -3, 4, 2, -4],\n [10, 4, -4, -6, -8],\n [1, 2, -6, 14, 7],\n [-9, -4, -8, 7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 436 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -5, -7, 2, -6],\n [0, -1, 3, 10, 5],\n [0, 0, -1, 2, -7],\n [0, 0, 0, -13, -14],\n [0, 0, 0, 0, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 455 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 5, -3, -9, -12],\n [0, -2, -4, -3, -10],\n [0, 0, 11, -2, -11],\n [0, 0, 0, -7, 1],\n [0, 0, 0, 0, -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": "... | 842 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 10, 3, -3, -5],\n [0, -7, 6, -15, 7],\n [0, 0, 5, -1, -3],\n [0, 0, 0, -8, 11],\n [0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 880 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 7, -6, 6, 6],\n [1, -10, -12, -14, -5],\n [1, 10, -15, 0, -12],\n [-5, 1, 6, -10, -9],\n [-1, 9, -13, -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"
}... | 34 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[14, 1, -9, -11, 8],\n [-11, 8, -2, 10, 1],\n [3, 9, 0, 11, -12],\n [-8, 0, 2, -14, 3],\n [7, -6, 7, 9, -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":... | 595 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 5, 6, -12, -2],\n [0, 3, -12, -8, 8],\n [0, 0, -4, -1, 0],\n [0, 0, 0, 11, 5],\n [0, 0, 0, 0, 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": "use... | 592 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, 14, -11, 15, 8],\n [-5, 6, -6, 1, 0],\n [15, -10, 14, 8, 12],\n [-1, 5, -9, 7, -2],\n [10, 4, 9, -9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 669 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -13, 15, 10, -14],\n [11, -10, -1, 1, 14],\n [7, 6, -10, 10, -1],\n [4, 10, -13, -2, 3],\n [-1, 2, -5, -7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 762 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -4, 1, -2, -6],\n [-4, -5, 8, 6, 2],\n [1, 8, 9, -3, -2],\n [-2, 6, -3, 4, 8],\n [-6, 2, -2, 8, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 999 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -2, 4, 4, 8],\n [-2, 8, 14, -12, 2],\n [4, 14, 3, -10, 10],\n [4, -12, -10, 10, -2],\n [8, 2, 10, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 336 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -12, -3, -10, -4],\n [10, 6, -3, 4, 11],\n [-1, 15, 3, 8, 5],\n [15, 5, -11, -2, -4],\n [11, 8, 4, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 40 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -10, -14, 12, -4],\n [0, 9, 14, -7, 0],\n [0, 0, 10, -9, -6],\n [0, 0, 0, -15, 11],\n [0, 0, 0, 0, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -6, -4, 5, 9],\n [-6, -13, -14, -6, 2],\n [-4, -14, -8, 6, 4],\n [5, -6, 6, -4, -2],\n [9, 2, 4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 588 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -1, 1, 2, -11],\n [-1, -10, 10, 2, -6],\n [1, 10, -14, 6, 8],\n [2, 2, 6, 1, 0],\n [-11, -6, 8, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 772 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 14, 4, 8, 13],\n [0, -1, -15, -7, -1],\n [0, 0, -3, -9, -8],\n [0, 0, 0, 2, 6],\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"
}
] | 84 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, 7, -4, -2],\n [-4, -13, 0, 4, -1],\n [7, 0, 11, -4, 6],\n [-4, 4, -4, -6, -6],\n [-2, -1, 6, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 296 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 6, 9, -12, -14],\n [-3, 13, -5, 2, -5],\n [4, -2, 1, -6, -7],\n [14, -12, 1, -8, -1],\n [-5, 9, -13, 9, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 876 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -1, 0, 0, 8],\n [-1, 12, 12, -4, 0],\n [0, 12, 6, -9, 3],\n [0, -4, -9, 6, 4],\n [8, 0, 3, 4, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 714 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 4, 10, -2, -8],\n [-3, -5, 9, -2, 3],\n [-9, 8, 6, -10, -13],\n [9, 11, 8, 7, -5],\n [-14, 12, 4, -15, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 607 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 12, 0, 0, 4],\n [12, 14, -2, -2, 0],\n [0, -2, -3, 9, 0],\n [0, -2, 9, -14, 6],\n [4, 0, 0, 6, -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}",
"role": "use... | 960 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -7, 8, 12, -10],\n [-7, -4, -4, 1, -4],\n [8, -4, -2, -1, 4],\n [12, 1, -1, -13, 7],\n [-10, -4, 4, 7, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 657 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -3, 0, 3, 11],\n [0, 10, -2, -5, -6],\n [0, 0, 4, 11, 3],\n [0, 0, 0, 12, -5],\n [0, 0, 0, 0, -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": "user... | 800 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 9, -10, -3, -5],\n [0, 9, -1, 4, -14],\n [0, 0, -13, 11, 0],\n [0, 0, 0, 8, -3],\n [0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 792 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -9, 6, 7, -9],\n [0, 6, 5, -1, 8],\n [0, 0, 9, 9, 12],\n [0, 0, 0, -2, -12],\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"
}
] | 380 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 7, 1, 1, -15],\n [-5, 9, -2, 4, -8],\n [-15, 10, 11, -8, 9],\n [-12, -5, 4, -9, 0],\n [-9, 14, -8, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 450 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 7, -11, -2, 13],\n [4, -15, 1, 0, -5],\n [2, 0, -9, -4, -12],\n [6, -11, 6, -13, 0],\n [9, 1, -6, -9, 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"... | 182 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -11, -3, 0, -2],\n [0, 12, 12, -1, -1],\n [0, 0, 6, 0, -9],\n [0, 0, 0, 4, 5],\n [0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 656 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 12, 8, 0, -10],\n [12, 4, 3, -4, -1],\n [8, 3, 0, -11, -8],\n [0, -4, -11, -11, -2],\n [-10, -1, -8, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 780 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-13, 4, 6, -8, 3],\n [4, -5, 2, -9, 2],\n [6, 2, 4, 0, -4],\n [-8, -9, 0, -4, -2],\n [3, 2, -4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 548 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, 0, -13, 6, 1],\n [0, 5, 3, 4, 13],\n [0, 0, 6, 4, 13],\n [0, 0, 0, 2, 0],\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"
}
] | 800 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 0, 2, -8, 1],\n [0, 14, -15, 2, 9],\n [2, -15, 1, -3, 2],\n [-8, 2, -3, -12, -1],\n [1, 9, 2, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 386 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 8, 1, 6, 12],\n [0, -8, 0, 2, 13],\n [0, 0, 7, -4, 13],\n [0, 0, 0, 2, 12],\n [0, 0, 0, 0, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 896 | MATH |
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