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[[-3, -7, 6, 4, -3],\n [-7, -11, -2, -2, -1],\n [6, -2, 14, 3, 2],\n [4, -2, 3, 4, -2],\n [-3, -1, 2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 348 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 4, -1, 3, 4],\n [-9, 8, 14, 6, 13],\n [-6, 4, 3, -10, -7],\n [-11, 14, 1, 1, 11],\n [2, -3, -3, -4, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 279 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -14, 12, -6, 6],\n [0, 5, -4, 1, -7],\n [0, 0, -6, -1, -5],\n [0, 0, 0, -8, -2],\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"
... | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -10, 13, 15, 9],\n [0, 7, 2, 6, 9],\n [0, 0, 8, -7, -9],\n [0, 0, 0, -9, -14],\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"
}
] | 528 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -1, -14, -8, 13],\n [-13, -14, 6, -14, 10],\n [-1, -2, 2, -4, 6],\n [10, 4, 5, -7, 5],\n [-14, -11, 0, 4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 302 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -8, -5, -1, -3],\n [-8, 15, 0, 6, -3],\n [-5, 0, -8, 8, -7],\n [-1, 6, 8, -3, -1],\n [-3, -3, -7, -1, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 196 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -4, -2, -3, -2],\n [-4, -2, -2, 2, -10],\n [-2, -2, 5, 7, -6],\n [-3, 2, 7, -12, -6],\n [-2, -10, -6, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 664 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 9, 15, 8, -11],\n [4, -12, 15, -4, 13],\n [8, 6, -6, 4, 5],\n [0, -8, -12, -13, -6],\n [3, 13, -13, 10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 607 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -3, -7, -14, -7],\n [0, -10, 5, 9, 12],\n [0, 0, -1, 2, 14],\n [0, 0, 0, -7, -9],\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"
}
] | 250 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[15, -1, -13, -4, -8],\n [0, -7, 12, -14, 8],\n [0, 0, 9, -10, 8],\n [0, 0, 0, 8, -11],\n [0, 0, 0, 0, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 240 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 12, -6, 0, 4],\n [12, -13, 2, 5, 2],\n [-6, 2, -3, 0, -12],\n [0, 5, 0, -7, -1],\n [4, 2, -12, -1, -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}",
"role":... | 148 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 2, -9, 8, 14],\n [-1, 5, -3, 2, 10],\n [11, -11, 15, 5, 2],\n [10, -7, 12, 15, 11],\n [-15, 10, 11, -7, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 386 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, -1, -13, 3, 3],\n [15, 1, -15, 3, 4],\n [9, 13, -6, -3, 14],\n [-3, 14, 11, 4, -4],\n [9, -2, -3, 5, 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":... | 451 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-13, 8, 3, -8, 6],\n [8, 12, -4, 5, -5],\n [3, -4, 2, 11, 0],\n [-8, 5, 11, -4, -2],\n [6, -5, 0, -2, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 534 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 3, 11, 2, -2],\n [-2, 0, -7, -7, 5],\n [-6, -12, -1, 8, 1],\n [-9, 10, -5, 5, -5],\n [-8, 3, 5, 1, 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": "u... | 823 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 2, -1, 0, 3],\n [2, -7, 4, -4, 10],\n [-1, 4, 5, 0, 6],\n [0, -4, 0, 11, -2],\n [3, 10, 6, -2, -13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 301 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -4, 0, 13, 2],\n [-4, 4, -4, 0, -10],\n [0, -4, 2, 2, -8],\n [13, 0, 2, 13, 4],\n [2, -10, -8, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 208 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-13, -15, 9, -4, 0],\n [0, -10, -5, 13, 3],\n [0, 0, 6, -12, -10],\n [0, 0, 0, -10, 7],\n [0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 4, -2, 0, 7],\n [4, -10, -10, -2, -2],\n [-2, -10, -6, -14, -8],\n [0, -2, -14, -9, 12],\n [7, -2, -8, 12, -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}",
"... | 136 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[15, 3, -5, -4, 2],\n [0, 6, 5, 5, -15],\n [0, 0, -1, -15, -6],\n [0, 0, 0, 6, 11],\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": "user"... | 680 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-13, -10, -2, 8, -5],\n [0, -10, 11, -11, -14],\n [0, 0, -8, -14, 6],\n [0, 0, 0, -9, 13],\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"
}
] | 200 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -2, 3, 3, -6],\n [-4, 3, 11, 2, -12],\n [6, -9, -5, -15, -3],\n [7, -3, 0, 14, -8],\n [4, -4, 12, 14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 72 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[13, 6, 4, 8, 11],\n [0, 11, 12, -8, 0],\n [0, 0, 12, -1, -4],\n [0, 0, 0, 9, -3],\n [0, 0, 0, 0, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 660 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 8, -6, -14, -11],\n [0, -15, 4, -15, -8],\n [0, 0, 1, 2, 14],\n [0, 0, 0, 13, -13],\n [0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 460 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 0, -1, 10, -15],\n [0, -15, 2, 7, -11],\n [0, 0, 8, -13, -4],\n [0, 0, 0, 4, 11],\n [0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 600 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, -6, -8, -2, -10],\n [-6, -3, 4, -2, -8],\n [-8, 4, 0, 1, 0],\n [-2, -2, 1, 2, 6],\n [-10, -8, 0, 6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 406 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 13, 14, 8, 5],\n [0, -8, 3, 4, 12],\n [0, 0, 4, 8, -11],\n [0, 0, 0, 11, -1],\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"... | 840 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, -8, -1, -10],\n [-12, 6, 15, 1, 11],\n [13, 6, -12, -14, -4],\n [12, -8, -2, -6, -9],\n [-13, 3, -4, 9, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 87 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -12, 12, -15, -9],\n [0, -13, -1, 9, 10],\n [0, 0, -5, -15, 1],\n [0, 0, 0, -5, 4],\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"
}
] | 600 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -8, -9, 0, 0],\n [-8, 10, 1, 6, 0],\n [-9, 1, -8, -4, 7],\n [0, 6, -4, 10, -4],\n [0, 0, 7, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 996 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 15, -3, -6, -9],\n [0, 3, 9, -8, -10],\n [0, 0, 9, -5, -6],\n [0, 0, 0, -8, -11],\n [0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 768 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[10, -4, 6, -7, 5],\n [-4, -1, 2, 0, 4],\n [6, 2, -11, 3, 0],\n [-7, 0, 3, 13, -6],\n [5, 4, 0, -6, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 854 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 4, 0, -4, 2],\n [4, 12, 0, -4, 2],\n [0, 0, 14, -2, 2],\n [-4, -4, -2, -9, 4],\n [2, 2, 2, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -4, -12, -1, -6],\n [-4, 15, -12, 6, -8],\n [-12, -12, 10, 13, 0],\n [-1, 6, 13, -6, 0],\n [-6, -8, 0, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 528 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 0, 0, -9, 4],\n [-3, -11, -11, -2, -15],\n [-11, 4, 8, -7, 6],\n [6, -11, 5, -4, 0],\n [7, 3, -11, -13, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 112 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 5, -14, 4, 15],\n [0, -4, -13, -5, -1],\n [0, 0, -15, -13, 14],\n [0, 0, 0, 7, -8],\n [0, 0, 0, 0, 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": "u... | 640 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 4, -6, -4, 3],\n [-6, 7, 11, 14, -5],\n [13, -12, 13, -7, -15],\n [-14, -9, 3, -12, 7],\n [-4, 9, -13, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 16 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -11, 10, 7, 11],\n [0, 4, 11, -6, 12],\n [0, 0, 4, 11, 10],\n [0, 0, 0, 5, 12],\n [0, 0, 0, 0, -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": "user... | 760 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 4, 2, 2, -3],\n [4, -8, -12, -2, 2],\n [2, -12, -4, 2, 0],\n [2, -2, 2, -13, -12],\n [-3, 2, 0, -12, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 448 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 0, 6, 2, -2],\n [0, -15, 0, 1, 0],\n [6, 0, 3, 8, -6],\n [2, 1, 8, -11, 0],\n [-2, 0, -6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 400 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, -7, 0, -2, 0],\n [-7, 5, 12, -1, -8],\n [0, 12, 7, 10, -3],\n [-2, -1, 10, -14, 0],\n [0, -8, -3, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 425 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 5, -8, -12, -9],\n [0, 3, -11, 15, -3],\n [0, 0, -14, -8, 11],\n [0, 0, 0, -6, -6],\n [0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 632 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -12, -7, -15, 3],\n [-8, -1, 10, 8, 8],\n [-3, -5, 0, -10, 6],\n [3, 6, -10, -1, -5],\n [-15, 1, 2, 8, -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}",
"rol... | 550 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -11, -7, 6, 14],\n [0, 1, 13, 8, -10],\n [0, 0, 8, -10, -3],\n [0, 0, 0, -11, -11],\n [0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 112 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 2, -4, 2, 8],\n [14, -4, -14, 3, 9],\n [-14, 3, 13, -8, -13],\n [-9, 6, 14, 0, -5],\n [-5, 10, -14, 10, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 408 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -2, -2, -15, 6],\n [-2, -15, -3, 0, 2],\n [-2, -3, -5, -1, 6],\n [-15, 0, -1, 0, 0],\n [6, 2, 6, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 964 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -11, -1, -10, -9],\n [5, 15, 5, 11, -13],\n [11, -6, 1, 9, 6],\n [12, -10, -15, -7, -9],\n [-8, -15, 8, -10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 826 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -8, 3, 9, 1],\n [-8, 14, 4, -2, -11],\n [3, 4, -11, -6, -4],\n [9, -2, -6, -7, -5],\n [1, -11, -4, -5, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 515 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -12, -1, -12, -4],\n [0, -9, -6, 15, 6],\n [0, 0, -9, 8, -5],\n [0, 0, 0, 2, -10],\n [0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 592 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -10, -5, -6, -3],\n [0, -3, -15, -2, -12],\n [0, 0, 15, -13, -1],\n [0, 0, 0, 7, 6],\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... | 640 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -7, 8, 13, -6],\n [8, 12, -8, 7, 15],\n [15, 11, 1, 2, -12],\n [15, -10, -10, -6, 3],\n [8, 13, -4, -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}",
"rol... | 627 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 0, 13, -5, -7],\n [-7, 10, -7, -8, 13],\n [-3, 9, 1, 14, -5],\n [-13, 12, 8, -15, 1],\n [-7, 3, -4, 12, 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... | 420 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -10, -2, 4, -11],\n [-10, 12, 0, -8, -12],\n [-2, 0, 4, -3, 10],\n [4, -8, -3, -3, 8],\n [-11, -12, 10, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 948 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 3, 10, -12, 2],\n [0, 8, -4, -13, -5],\n [-5, -2, 4, -2, 12],\n [-12, 1, -15, -8, 11],\n [-2, -3, -13, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 266 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -4, 12, -1, 10],\n [4, 4, -11, 3, -9],\n [-6, -4, 15, -3, 13],\n [0, -13, 13, -12, -1],\n [4, 11, -6, 11, 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}",
"r... | 192 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -11, 0, 3, -3],\n [0, 5, -15, -5, -13],\n [0, 0, 8, 6, 11],\n [0, 0, 0, 15, -3],\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"
}
] | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -2, -6, -2, 0],\n [0, 14, -14, 5, -9],\n [0, 0, 10, -4, -13],\n [0, 0, 0, -5, -4],\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"
... | 500 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, 10, 4, -2, -1],\n [10, -8, 4, 14, -6],\n [4, 4, 11, -8, 14],\n [-2, 14, -8, -10, -7],\n [-1, -6, 14, -7, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 616 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 1, 4, -10, 11],\n [1, -4, -4, -2, 0],\n [4, -4, 11, 8, -3],\n [-10, -2, 8, 8, -12],\n [11, 0, -3, -12, 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... | 364 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, 8, -9, 6, 13],\n [0, 10, -10, 15, -2],\n [0, 0, -6, 14, 0],\n [0, 0, 0, -13, 2],\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"
}
] | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -13, 3, -15, -1],\n [-4, -12, -2, -15, -7],\n [7, 4, -6, 15, -14],\n [-2, -9, -3, 2, 0],\n [9, -8, 14, -7, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 504 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -6, 11, -1, -5],\n [-6, -4, 0, 6, -4],\n [11, 0, 2, -8, -8],\n [-1, 6, -8, 4, 2],\n [-5, -4, -8, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 152 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -5, -11, 10, 3],\n [0, 4, 15, 13, -5],\n [0, 0, 10, 11, 15],\n [0, 0, 0, 1, -3],\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"
}
] | 720 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 5, 10, -14, 0],\n [5, -13, 10, 14, -6],\n [10, 10, -9, 3, 2],\n [-14, 14, 3, -14, 12],\n [0, -6, 2, 12, 14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 530 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-13, 6, -10, 10, 1],\n [6, -15, -10, -2, 4],\n [-10, -10, -13, -5, 10],\n [10, -2, -5, -8, 3],\n [1, 4, 10, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 537 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 6, 7, -5, -3],\n [6, -10, 0, 9, 5],\n [7, 0, -11, 10, -6],\n [-5, 9, 10, 9, 4],\n [-3, 5, -6, 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"
}
] | 84 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -5, 5, 3, 9],\n [0, 9, -12, -8, -9],\n [0, 0, 12, -10, 10],\n [0, 0, 0, -15, -3],\n [0, 0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[14, -8, -4, -1, -12],\n [0, -2, -11, 5, -8],\n [0, 0, -11, -8, 6],\n [0, 0, 0, -5, -15],\n [0, 0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 860 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -12, 2, -10, -5],\n [-12, 0, 3, 4, 2],\n [2, 3, -11, -9, -3],\n [-10, 4, -9, -14, -3],\n [-5, 2, -3, -3, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 199 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 6, 12, -1, 0],\n [-5, 13, -9, -1, 12],\n [7, -9, 9, 3, 5],\n [2, -11, -12, 7, -14],\n [8, -13, -7, -4, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 390 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 6, 14, 9, -6],\n [15, 9, 0, -1, 5],\n [-7, 2, 0, -7, 6],\n [3, 2, -8, 15, 9],\n [-15, -11, -14, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 512 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-14, 8, 1, 15, -13],\n [0, -12, -12, -10, 4],\n [0, 0, 10, 9, -12],\n [0, 0, 0, -2, 11],\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": "us... | 680 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 13, 12, -7, 1],\n [0, 3, -11, -8, -4],\n [0, 0, 12, -11, -11],\n [0, 0, 0, -10, 13],\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"
}
] | 600 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-14, -4, -6, 4, 6],\n [-4, -13, 2, 0, 5],\n [-6, 2, 15, -3, 0],\n [4, 0, -3, 8, 0],\n [6, 5, 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"
}
] | 218 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -7, 8, 7, 0],\n [0, -8, 5, -11, -8],\n [0, 0, 5, -6, -8],\n [0, 0, 0, 4, -13],\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"
}
] | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 14, -15, -6, -7],\n [0, 15, 14, -9, -1],\n [0, 0, -6, -12, -15],\n [0, 0, 0, -11, -3],\n [0, 0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 640 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-13, 8, 10, 6, 0],\n [8, 12, 4, -4, -2],\n [10, 4, -3, -7, -2],\n [6, -4, -7, 0, -10],\n [0, -2, -2, -10, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 264 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 0, 15, -4, -8],\n [0, -11, 5, 13, -15],\n [0, 0, -12, -9, 1],\n [0, 0, 0, 9, 14],\n [0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 940 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -3, -3, 5, -6],\n [-3, -11, -8, 0, 4],\n [-3, -8, 3, -1, 2],\n [5, 0, -1, -9, -7],\n [-6, 4, 2, -7, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 321 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -1, -3, 14, 5],\n [0, -10, 7, -9, -5],\n [0, 0, 1, 13, -1],\n [0, 0, 0, -3, -6],\n [0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 630 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -14, 8, -8, -12],\n [6, 12, -11, 10, -12],\n [7, 11, -10, 7, -11],\n [6, -3, 9, 9, -7],\n [-13, -6, -6, -1, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 144 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 10, 6, -9, -2],\n [10, -3, 1, 8, -9],\n [6, 1, 7, -4, -2],\n [-9, 8, -4, -3, -8],\n [-2, -9, -2, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 652 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 11, 6, -15, -11],\n [0, 2, -8, -7, -14],\n [0, 0, -9, 1, -11],\n [0, 0, 0, 6, -8],\n [0, 0, 0, 0, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 728 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -13, -9, 14, 12],\n [5, 4, -9, 6, -11],\n [13, -4, -5, 12, 0],\n [4, 12, 2, 13, 11],\n [8, -14, 12, -3, 13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, -1, 7, 5, -14],\n [6, 7, 9, 10, 11],\n [3, -2, 6, 8, 12],\n [14, 4, 2, 7, 14],\n [-8, 2, 9, 13, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 71 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, 7, -4, 5, -9],\n [-2, -12, 3, 9, -11],\n [2, -5, 12, -12, -3],\n [-2, -15, 2, 7, -5],\n [-7, 8, -2, -11, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 493 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 0, 10, -10, 14],\n [-11, 3, -5, -6, -2],\n [-12, 0, -7, -1, -11],\n [15, 8, -5, 9, -7],\n [0, 5, -10, 5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 160 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 2, -5, -4, 3],\n [2, -4, 4, 12, -4],\n [-5, 4, -3, 10, 6],\n [-4, 12, 10, -3, 7],\n [3, -4, 6, 7, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 648 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -1, 1, 8, 3],\n [-4, -2, 8, 1, 13],\n [2, 6, 4, -1, -10],\n [1, 12, -13, 13, 7],\n [12, -8, 0, -9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 134 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 0, -2, -2, 0],\n [0, -13, 1, -1, -10],\n [-2, 1, 13, -11, -2],\n [-2, -1, -11, 7, 13],\n [0, -10, -2, 13, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 476 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -2, -10, 2, -4],\n [-2, 7, 0, -9, -3],\n [-10, 0, -1, 4, 0],\n [2, -9, 4, -3, -3],\n [-4, -3, 0, -3, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 940 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 6, -1, -4, 0],\n [6, -14, 7, 0, -4],\n [-1, 7, 7, 10, 8],\n [-4, 0, 10, -3, 8],\n [0, -4, 8, 8, -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": "u... | 782 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, -6, 10, 0, -7],\n [0, 9, -7, -14, -10],\n [0, 0, 2, 10, 6],\n [0, 0, 0, 3, -15],\n [0, 0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 626 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 6, 11, 14, 6],\n [6, -7, 10, 8, 14],\n [6, -11, 0, -7, 6],\n [-11, -12, 12, 7, 2],\n [8, 0, 12, -6, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 392 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -5, -3, -9, 14],\n [-7, 2, -13, -7, 8],\n [13, -15, 8, -13, 11],\n [-3, -7, -12, -1, -15],\n [-6, 6, 0, -12, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 680 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 6, -6, 2, 4],\n [6, -10, -6, -2, -8],\n [-6, -6, -2, -4, 2],\n [2, -2, -4, 3, -3],\n [4, -8, 2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 696 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 2, -6, -2, 0],\n [2, -4, 8, -4, 8],\n [-6, 8, -11, 5, -2],\n [-2, -4, 5, -14, 0],\n [0, 8, -2, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 568 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, 1, 2, -15, -14],\n [-4, 8, -13, -9, 11],\n [-11, 13, 2, -11, 14],\n [4, -5, 7, -15, 11],\n [-11, 1, 4, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 443 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[13, 10, 11, 9, -5],\n [10, -1, 2, -1, 4],\n [11, 2, 0, 2, -14],\n [9, -1, 2, 1, 9],\n [-5, 4, -14, 9, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 849 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 10, -2, -4, -2],\n [10, -11, 2, 7, -1],\n [-2, 2, 15, 4, -2],\n [-4, 7, 4, 7, -2],\n [-2, -1, -2, -2, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 415 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.