messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -7, 0, -4],\n [9, -3, 4, -3],\n [-12, -10, -11, -1],\n [8, 11, -11, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
848
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 4, -1, 8],\n [-3, 7, 3, 11],\n [-8, 9, 4, -7],\n [10, -1, 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"
}
] |
99
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 8, -9, 4],\n [-9, 10, -8, -9],\n [-11, 10, 12, 11],\n [3, 4, 8, -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"
}
] |
200
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 10, -11, 7],\n [0, 2, -3, -10],\n [0, 0, 2, 10],\n [0, 0, 0, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
44
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 2, -3, 2],\n [2, -9, -7, 2],\n [-3, -7, -2, -1],\n [2, 2, -1, -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"
}
] |
857
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -1, -10, -7],\n [0, -1, -3, 1],\n [0, 0, -1, -2],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
916
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 11, 6, 7],\n [0, 12, 9, 5],\n [0, 0, 5, 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"
}
] |
920
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 11, -4, -8],\n [7, 6, -3, 8],\n [6, 5, -5, -3],\n [-10, -10, 5, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
719
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 12, -5, 4],\n [0, 5, -9, 3],\n [0, 0, 7, 11],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
210
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -7, -2, 3],\n [-8, 1, -5, 2],\n [-10, -2, -10, -12],\n [0, -8, 12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
598
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -5, 4, 1],\n [-5, 8, 0, -2],\n [4, 0, -6, -1],\n [1, -2, -1, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
207
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, -10, -4, -4],\n [-10, 3, 4, 0],\n [-4, 4, -12, 6],\n [-4, 0, 6, 4]]? Round to the nearest integer, then express your answer modulo 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[[6, 9, 6, -3],\n [0, 9, -8, 10],\n [0, 0, -3, -1],\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"
}
] |
838
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, -1, -9, 4],\n [0, -12, 10, 5],\n [0, 0, -4, -6],\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"
}
] |
864
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 12, -6, 3],\n [0, 12, -2, 9],\n [0, 0, 9, -9],\n [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"
}
] |
464
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -8, -1, 2],\n [-8, -3, 1, 2],\n [-1, 1, -1, 0],\n [2, 2, 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"
}
] |
158
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -4, 0, -9],\n [10, -6, -4, 12],\n [11, -9, -11, -4],\n [-1, -9, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
872
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 2, 1, 7],\n [2, 1, -2, 0],\n [1, -2, 10, -1],\n [7, 0, -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": "user"
}
] |
669
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 6, -9, 10],\n [10, -7, 3, -9],\n [6, -4, -4, -2],\n [0, -8, -12, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
456
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 7, -11, 1],\n [-6, 8, -10, 4],\n [-7, 11, -5, -7],\n [-2, 12, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, 8, -1, 3],\n [8, -6, 0, -2],\n [-1, 0, -12, -2],\n [3, -2, -2, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
892
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 6, -2, -10],\n [0, 7, 11, -8],\n [0, 0, -10, 6],\n [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"
}
] |
120
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -3, -1, 4],\n [0, 10, -1, -5],\n [0, 0, -12, -9],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -4, 2, 0],\n [-4, 5, -2, -2],\n [2, -2, 4, 2],\n [0, -2, 2, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
56
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 9, 11, 2],\n [-3, 10, -5, 0],\n [12, -4, 9, -2],\n [-6, 2, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
790
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 2, 4, 8],\n [0, 3, -11, 4],\n [0, 0, 9, 7],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
972
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 12, 1, 3],\n [-12, -8, -1, -6],\n [1, 1, -3, -5],\n [8, 6, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
154
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -6, 7, -10],\n [-6, -11, -1, -4],\n [5, -11, 3, -4],\n [11, -4, -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"
}
] |
820
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -11, 11, 3],\n [0, 7, -3, -4],\n [0, 0, 11, 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"
}
] |
684
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, -4, 5, -6],\n [-4, -9, -9, -8],\n [5, -9, -3, 0],\n [-6, -8, 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"
}
] |
31
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, -3, 4, -3],\n [0, -6, -11, 4],\n [0, 0, -8, -8],\n [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"
}
] |
576
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 9, -9, 9],\n [0, -2, 12, -4],\n [0, 0, 6, -4],\n [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"
}
] |
152
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -2, 2, 3],\n [-2, 4, -4, -6],\n [2, -4, 2, -1],\n [3, -6, -1, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
676
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 7, -3, 6],\n [7, 11, -6, -2],\n [-3, -6, -6, -1],\n [6, -2, -1, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
767
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 2, -1, -8],\n [2, 12, 8, 4],\n [-1, 8, 6, 2],\n [-8, 4, 2, 12]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -5, 3, 5],\n [-8, -2, 4, 3],\n [4, 3, 12, -11],\n [-12, -5, -11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
783
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -2, 6, 5],\n [-2, 3, -2, -2],\n [6, -2, 5, 4],\n [5, -2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
777
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, -2, 3, -6],\n [-2, -12, -2, 9],\n [3, -2, -6, 0],\n [-6, 9, 0, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
935
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 9, -11, 3],\n [0, 11, -12, -7],\n [0, 0, -1, -6],\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"
}
] |
66
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -2, -10, -9],\n [0, -2, 3, 7],\n [0, 0, -5, 3],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, 0, -5, -5],\n [11, 8, -6, -4],\n [-6, 12, -5, -4],\n [3, -9, 6, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
397
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 4, 1, 6],\n [4, 5, 5, -6],\n [1, 5, 5, 2],\n [6, -6, 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"
}
] |
246
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 9, -12, 3],\n [0, -7, 7, 12],\n [0, 0, 8, 10],\n [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": "user"
}
] |
968
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 4, 6, 9],\n [0, 12, 3, 12],\n [0, 0, -5, -7],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -8, -2, 4],\n [-8, -10, -4, 8],\n [-2, -4, 6, -11],\n [4, 8, -11, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
254
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 3, -1, 12],\n [0, -2, -8, -5],\n [0, 0, 9, 11],\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"
}
] |
568
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -2, -7, 9],\n [-2, 5, -2, -4],\n [-7, -2, -7, 6],\n [9, -4, 6, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
565
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, -12, -11, 12],\n [10, 11, -2, -7],\n [2, -3, -3, -8],\n [9, -4, -6, -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"
}
] |
799
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 9, -3, -12],\n [0, 8, -2, -3],\n [0, 0, 8, 7],\n [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"
}
] |
360
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -2, 8, 0],\n [-2, 8, 2, 0],\n [8, 2, 4, -9],\n [0, 0, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
780
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 12, 8, 11],\n [-5, 11, -9, 0],\n [2, 2, 8, 12],\n [-7, -6, 7, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 4, 0, -7],\n [0, -5, 5, -11],\n [0, 0, -9, 9],\n [0, 0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
945
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 11, 12, -7],\n [0, -5, 9, 6],\n [0, 0, -8, -9],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -5, -6, -5],\n [0, -1, 10, -1],\n [0, 0, 2, -9],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
780
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 0, -7, 8],\n [0, -3, -4, -4],\n [-7, -4, 7, -2],\n [8, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
614
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, 7, -3, 10],\n [8, 4, 0, 4],\n [-10, 4, -4, 6],\n [-2, -11, 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"
}
] |
952
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 0, -7, 1],\n [0, 6, -6, 0],\n [-7, -6, 8, 6],\n [1, 0, 6, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
618
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -2, 2, -10],\n [6, 3, 11, -3],\n [-11, -5, -5, 1],\n [-3, 10, -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"
}
] |
732
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -1, 12, -3],\n [0, -12, 2, -2],\n [0, 0, 1, 7],\n [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": "user"
}
] |
288
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -6, 3, -10],\n [-6, -9, 3, 0],\n [3, 3, 1, -1],\n [-10, 0, -1, -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"
}
] |
854
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -1, -6, -11],\n [12, -11, 3, 12],\n [-1, -3, -5, -6],\n [7, 7, 9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
37
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -5, -2, -3],\n [-5, 9, -6, 4],\n [-2, -6, 3, 2],\n [-3, 4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
29
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 6, -10, -10],\n [-9, -6, 0, -6],\n [9, -9, 4, 12],\n [-6, 8, 7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
142
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -5, -3, 6],\n [-5, 1, -8, 8],\n [-3, -8, -6, -3],\n [6, 8, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
266
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -6, 5, 1],\n [0, -11, 8, 2],\n [0, 0, -10, 10],\n [0, 0, 0, -12]]\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[[-5, 2, 6, 8],\n [0, -4, -12, -10],\n [0, 0, -10, 10],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
400
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -1, -4, -10],\n [-1, -5, -4, 6],\n [-4, -4, -5, 1],\n [-10, 6, 1, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
922
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -9, -5, 3],\n [0, -12, -7, 7],\n [0, 0, 2, -9],\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"
}
] |
56
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 6, 7, 11],\n [0, 5, 9, 0],\n [0, 0, -11, 0],\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"
}
] |
835
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -5, 7, 8],\n [-5, 2, -1, 8],\n [7, -1, 1, -12],\n [8, 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}",
"role": "user"
}
] |
486
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -2, 2, 0],\n [-2, 9, 0, -9],\n [2, 0, -10, 5],\n [0, -9, 5, -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": "user"
}
] |
176
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 3, 12, 7],\n [0, 1, 10, -10],\n [0, 0, -7, 7],\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"
}
] |
98
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 2, -2, 0],\n [2, 5, -1, 2],\n [-2, -1, 6, -7],\n [0, 2, -7, -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"
}
] |
144
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -4, -6, -3],\n [0, -3, -9, 3],\n [0, 0, -9, -3],\n [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"
}
] |
299
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 4, -2, 0],\n [4, -7, 6, -4],\n [-2, 6, -8, -2],\n [0, -4, -2, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
148
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -11, -10, 7],\n [0, -8, -7, 3],\n [0, 0, 3, -12],\n [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"
}
] |
240
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 5, -10, -10],\n [0, 10, 7, 11],\n [0, 0, -5, 11],\n [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"
}
] |
150
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -1, 2, -2],\n [-1, -9, 8, 0],\n [2, 8, -8, 6],\n [-2, 0, 6, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -5, 2, -11],\n [2, 9, -4, -5],\n [7, -11, 8, 5],\n [12, -8, 12, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
78
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[7, 11, -7, -8],\n [-5, -9, 10, -11],\n [0, 10, 12, -1],\n [1, -3, 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}",
"role": "user"
}
] |
580
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 3, 7, 0],\n [3, 10, -4, 6],\n [7, -4, 2, -3],\n [0, 6, -3, -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"
}
] |
609
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, -9, -1, 2],\n [0, 7, -9, -6],\n [0, 0, 7, -1],\n [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"
}
] |
58
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -3, -12, 6],\n [0, -9, 7, -11],\n [0, 0, 4, -2],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
288
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, 7, -10, 12],\n [0, 5, -11, -5],\n [0, 0, 5, -2],\n [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"
}
] |
475
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -4, 0, -6],\n [-4, 1, 0, -8],\n [0, 0, -8, -2],\n [-6, -8, -2, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
552
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 10, 0, 6],\n [10, 9, 3, 0],\n [0, 3, 6, 10],\n [6, 0, 10, 4]]? 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": "Determine the value of det(A) where A =\n[[-7, 0, -4, -2],\n [0, -7, -6, 6],\n [-4, -6, 7, -2],\n [-2, 6, -2, 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"
}
] |
53
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 10, 10, 7],\n [6, 1, 12, -10],\n [4, -8, 10, 8],\n [2, 5, 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"
}
] |
224
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 12, 2, -12],\n [8, 8, -10, 7],\n [2, -3, -12, 10],\n [11, 10, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
262
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -9, -2, 10],\n [9, -7, -10, 12],\n [-2, -7, 7, 5],\n [6, 3, -8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
589
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 10, 2, -2],\n [-2, 11, -6, -10],\n [10, 8, 7, 12],\n [0, -3, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
956
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 11, 9, 0],\n [0, 1, -4, 12],\n [0, 0, 6, 4],\n [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"
}
] |
150
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -5, -4, -1],\n [-8, 4, -8, 2],\n [-8, 8, -9, 4],\n [-11, -11, -6, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
58
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 4, 0, 0],\n [4, -5, 4, 3],\n [0, 4, 7, -6],\n [0, 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"
}
] |
573
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -5, -12, -2],\n [0, -4, -4, 3],\n [0, 0, 5, 6],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -4, 1, 6],\n [0, 5, -5, 4],\n [0, 0, 11, 2],\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"
}
] |
940
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -1, -7, -5],\n [0, -4, -10, 2],\n [0, 0, -5, -7],\n [0, 0, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -6, 4, 1],\n [-6, -7, -2, -2],\n [4, -2, 4, 8],\n [1, -2, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
24
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -1, -2, 3],\n [-9, -1, 9, 3],\n [-11, 11, -8, 1],\n [9, -2, 2, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
197
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 4, 11, 3],\n [-2, 7, -12, 6],\n [7, -1, -11, 10],\n [7, -8, -12, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
877
|
MATH
|
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