messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 1, 0, 2],\n [0, -6, -1, -12],\n [0, 0, 1, 12],\n [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"
}
] |
432
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -6, -5, 7],\n [0, 3, 5, -11],\n [-6, -4, 5, 0],\n [-9, 2, -8, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
835
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 10, 5, 1],\n [2, 7, 8, 6],\n [0, 12, 10, 10],\n [-9, 12, 7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
24
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 0, 6, -4],\n [0, -3, 0, -10],\n [6, 0, 9, 2],\n [-4, -10, 2, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
418
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 0, -1, -5],\n [7, -10, 12, -12],\n [-1, 0, 2, 11],\n [3, -6, 7, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
792
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -4, 12, 9],\n [2, -7, 11, 8],\n [2, 12, -10, 11],\n [-12, 5, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, -2, -2, 2],\n [-2, 2, 2, 0],\n [-2, 2, -2, 10],\n [2, 0, 10, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
512
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -5, -4, -2],\n [-5, -9, -10, 2],\n [-4, -10, -9, -2],\n [-2, 2, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, 0, 6, -2],\n [0, 6, 2, -7],\n [6, 2, 8, -2],\n [-2, -7, -2, -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"
}
] |
268
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, -9, -5],\n [-4, 3, -4, -2],\n [-9, -4, -1, -2],\n [-5, -2, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
259
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 4, -4, -8],\n [4, -1, 1, -4],\n [-4, 1, -2, -1],\n [-8, -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"
}
] |
24
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 10, 2, 5],\n [10, 4, 1, 8],\n [2, 1, -12, 0],\n [5, 8, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
485
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -3, 2, -4],\n [-3, -3, 8, 8],\n [2, 8, -11, 6],\n [-4, 8, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
582
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 7, 8, -8],\n [7, -2, -2, 3],\n [8, -2, -12, -2],\n [-8, 3, -2, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
496
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -4, 0, -2],\n [-4, -11, -1, -5],\n [-8, -3, -5, 12],\n [7, -9, -5, 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": "user"
}
] |
386
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -7, 8, 3],\n [-10, -2, -12, 2],\n [2, 12, 7, 3],\n [9, -10, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
164
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -2, 4, -2],\n [-2, 10, 2, -8],\n [4, 2, 0, -10],\n [-2, -8, -10, -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": "user"
}
] |
280
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 7, 0, 6],\n [7, -10, 2, -1],\n [0, 2, -2, 10],\n [6, -1, 10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
636
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, -3, 8, 0],\n [-3, 10, 0, -1],\n [8, 0, 7, -8],\n [0, -1, -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"
}
] |
840
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -4, -6, -4],\n [-4, 6, -4, -4],\n [-6, -4, 4, 0],\n [-4, -4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -5, 9, -5],\n [0, -4, 7, 12],\n [0, 0, 7, -8],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
888
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -6, 9, 10],\n [2, 5, 10, 10],\n [-2, -5, -4, 12],\n [1, -12, -10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
194
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 0, 0, -2],\n [0, -8, -4, -11],\n [0, 0, 7, -3],\n [0, 0, 0, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
896
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -10, -7, -11],\n [0, -1, 8, -1],\n [0, 0, 2, 6],\n [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": "user"
}
] |
200
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 10, -9, -2],\n [-3, -3, 11, -12],\n [-4, 7, 5, 4],\n [-12, -9, 0, 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": "user"
}
] |
767
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, -3, -2, 0],\n [-9, -6, 3, 2],\n [8, -3, 2, -12],\n [-3, 7, -8, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
624
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -11, 8, 0],\n [1, -7, 12, 3],\n [-7, 0, -1, 4],\n [10, -11, -10, -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": "user"
}
] |
171
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 1, -1, -2],\n [1, 6, -6, -8],\n [-1, -6, 2, 1],\n [-2, -8, 1, -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": "user"
}
] |
887
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, -2, -6, -1],\n [-2, 8, -4, 0],\n [-6, -4, -10, -2],\n [-1, 0, -2, -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": "user"
}
] |
16
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -9, 5, -11],\n [0, 7, 7, 5],\n [0, 0, -12, 1],\n [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": "user"
}
] |
560
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -5, -5, 0],\n [0, -9, -3, -7],\n [0, 0, -9, 1],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
199
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 0, -4, -8],\n [0, 3, -10, 1],\n [-4, -10, 1, 6],\n [-8, 1, 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": "user"
}
] |
156
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 10, 3, -11],\n [0, -3, -2, -7],\n [0, 0, 6, 9],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
920
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -2, 8, -4],\n [-2, 3, 2, -8],\n [8, 2, 0, -4],\n [-4, -8, -4, 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": "user"
}
] |
80
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 6, 6, -5],\n [6, -12, -4, -4],\n [6, -4, -11, -4],\n [-5, -4, -4, -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"
}
] |
324
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -10, 10, 6],\n [-3, -5, -3, -2],\n [4, 9, 0, 4],\n [11, 5, 11, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, 6, 5, -5],\n [2, 7, 2, 8],\n [8, -2, -12, -2],\n [-6, -6, 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"
}
] |
984
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -3, -2, 4],\n [-1, -1, -12, -12],\n [-1, 4, 8, -6],\n [-12, 1, -4, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
312
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -12, 6, -4],\n [0, -1, -7, -8],\n [0, 0, -1, -11],\n [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"
}
] |
991
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 7, -6, -2],\n [7, 9, 8, -1],\n [-6, 8, 6, 8],\n [-2, -1, 8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
210
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 5, -8, -2],\n [-9, 1, 12, -11],\n [2, 5, -4, -11],\n [-1, 9, -5, -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": "user"
}
] |
745
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 7, 0, -4],\n [7, -9, 8, 6],\n [0, 8, 11, 7],\n [-4, 6, 7, 3]]\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[[-5, -8, -2, -11],\n [7, 6, 3, 3],\n [0, -1, -9, 1],\n [6, 12, -10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
175
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -1, 11, -6],\n [0, 6, -11, -9],\n [0, 0, 8, -12],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
184
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 2, 6, -10],\n [-7, 7, -2, 4],\n [5, 2, 9, -5],\n [8, 8, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
682
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 11, 5, 12],\n [-2, -3, 9, -9],\n [-9, 8, -10, -4],\n [-5, 1, -7, 0]]\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": "Determine the value of det(A) where A =\n[[-5, -3, 12, 3],\n [0, -2, 2, -2],\n [0, 0, 10, -1],\n [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": "user"
}
] |
800
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 0, -2, 3],\n [6, 12, 9, -9],\n [9, 2, 7, 6],\n [-2, -3, 11, -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"
}
] |
904
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 4, 2, 4],\n [4, 5, 10, -4],\n [2, 10, 3, -3],\n [4, -4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
764
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -4, 10, -5],\n [0, -8, 3, 3],\n [0, 0, 11, 12],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
112
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -2, 7, 11],\n [-2, 0, -6, 6],\n [7, -6, 4, -4],\n [11, 6, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
684
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -10, 5, 4],\n [0, 0, 7, 9],\n [-12, -3, 7, -12],\n [0, -2, -4, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
968
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 11, -12, 11],\n [-10, -6, 1, 0],\n [8, -10, 9, -8],\n [-10, 12, 4, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
706
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 12, -12, -11],\n [-8, -12, 8, 12],\n [-6, -9, -8, -5],\n [10, 10, -11, 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": "user"
}
] |
456
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -9, 4, -10],\n [0, 7, 10, 10],\n [0, 0, 1, -7],\n [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": "user"
}
] |
972
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -6, -9, 3],\n [-7, 6, 0, 0],\n [-1, 12, -2, 1],\n [6, 12, -12, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
736
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 1, -6, 5],\n [-5, 6, 2, -5],\n [-7, -4, -3, 0],\n [-12, 3, -1, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
765
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, 5, -5, 3],\n [6, -4, -8, 2],\n [6, -6, 10, 12],\n [-7, -10, -4, 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": "user"
}
] |
168
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 4, -3, 8],\n [0, -2, 0, -7],\n [0, 0, 5, -12],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
860
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -3, -2, 3],\n [-3, 11, 6, 2],\n [-2, 6, 7, 2],\n [3, 2, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
735
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -4, -7, 9],\n [0, 11, 5, 11],\n [0, 0, 2, 2],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
924
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -11, 0, 0],\n [-11, -12, -10, 3],\n [0, -10, -9, -7],\n [0, 3, -7, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
120
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 4, -4, -1],\n [0, -9, -6, 8],\n [0, 0, 10, -2],\n [0, 0, 0, -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": "user"
}
] |
10
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 12, -4, 10],\n [5, 1, 3, -12],\n [0, -5, 8, -12],\n [-6, -3, 9, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
229
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 6, 12, -9],\n [0, 3, 4, 7],\n [0, 0, 5, 7],\n [0, 0, 0, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
460
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 11, -7, 5],\n [3, -3, 12, 12],\n [-8, -11, -1, 6],\n [1, -9, 6, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
82
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -11, -12, -4],\n [-11, 9, 3, -10],\n [-12, 3, -7, -6],\n [-4, -10, -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": "user"
}
] |
778
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -4, 5, 6],\n [-4, 9, 5, -2],\n [5, 5, -7, 8],\n [6, -2, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
849
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 1, -2, -9],\n [0, -8, 9, -12],\n [1, 6, -3, 10],\n [-2, -10, 9, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
307
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 4, -6, 8],\n [-8, -9, -10, 5],\n [-3, -7, -12, 1],\n [5, -7, 4, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
120
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 11, -7, 9],\n [0, -4, -10, -1],\n [0, 0, 12, 8],\n [0, 0, 0, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
464
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -2, 0, 6],\n [-2, -1, -2, 4],\n [0, -2, 12, 6],\n [6, 4, 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": "user"
}
] |
316
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -6, -7, 2],\n [8, 4, -1, 4],\n [-8, -11, 3, 7],\n [-7, -11, -5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
583
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -2, 8, 0],\n [-2, -6, -1, -6],\n [8, -1, -6, -3],\n [0, -6, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
344
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 0, -1, -6],\n [0, -10, 4, 2],\n [-1, 4, 0, 4],\n [-6, 2, 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"
}
] |
350
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 12, -7, -12],\n [-1, -7, 0, -5],\n [8, 1, -9, 11],\n [-9, -2, -5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
320
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -2, 6, -5],\n [-2, 9, 1, 8],\n [6, 1, 12, 7],\n [-5, 8, 7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
368
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, -9, 9, -12],\n [0, -4, -12, 3],\n [0, 0, 7, -7],\n [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": "user"
}
] |
552
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 6, -4, 0],\n [6, 12, -2, 9],\n [-4, -2, 10, 11],\n [0, 9, 11, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
742
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -5, 4, -1],\n [-5, 2, -2, 2],\n [4, -2, -9, -8],\n [-1, 2, -8, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
469
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 4, -2, -2],\n [11, 8, -12, 9],\n [-7, 7, -6, 7],\n [-1, -3, 1, -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": "user"
}
] |
629
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 7, -2, -8],\n [-3, -3, -4, 5],\n [8, 8, 7, 11],\n [-6, 2, 12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
532
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -4, 0, 4],\n [-4, 10, -4, 2],\n [0, -4, 0, 6],\n [4, 2, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
472
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 7, 2, 4],\n [-2, 2, 0, -2],\n [1, -3, 7, 9],\n [-11, -9, -8, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
480
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -2, 4, 8],\n [-2, -3, -4, 9],\n [4, -4, -3, 0],\n [8, 9, 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": "user"
}
] |
305
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -8, 7, 6],\n [0, -9, -12, 3],\n [0, 0, -1, -11],\n [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": "user"
}
] |
360
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 8, 12, 4],\n [8, 3, 2, 0],\n [12, 2, 4, 4],\n [4, 0, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
312
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 11, -9, -10],\n [-6, -5, -10, 4],\n [-6, 7, -10, 10],\n [11, -6, 2, -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"
}
] |
98
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 3, 8, -4],\n [0, -4, 6, 1],\n [0, 0, 12, 9],\n [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"
}
] |
616
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -7, 5, -3],\n [0, -2, -5, -1],\n [0, 0, -11, 8],\n [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"
}
] |
990
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 11, -7, -10],\n [-9, 8, 6, -10],\n [8, 3, -10, -11],\n [-12, -2, 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"
}
] |
138
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -12, -3, -8],\n [0, 3, 3, -5],\n [0, 0, -11, 9],\n [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": "user"
}
] |
733
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 0, -6, -9],\n [0, 12, 12, -9],\n [0, 0, 6, -10],\n [0, 0, 0, -10]]? Round to the nearest integer, then express your answer modulo 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[[-12, -1, -10, -7],\n [0, 7, 10, 3],\n [0, 0, -7, -5],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
412
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -8, -10, 8],\n [0, 10, -8, 2],\n [0, 0, -6, -8],\n [0, 0, 0, 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": "user"
}
] |
700
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -3, 12, 7],\n [-6, 5, 6, -9],\n [-10, 7, -1, 8],\n [-11, 5, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
392
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 6, 1, -11],\n [0, 8, 5, -11],\n [0, 0, -6, 5],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
696
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 9, 8, 11],\n [-1, 8, -6, 8],\n [10, 11, 9, 4],\n [-3, 10, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
981
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 6, -9, 6],\n [6, 1, 6, 5],\n [-9, 6, 8, 2],\n [6, 5, 2, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
135
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 2, 11, 1],\n [-9, -4, -3, -1],\n [9, -2, -1, -3],\n [8, -10, 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"
}
] |
288
|
MATH
|
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