messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -5, 0, -1],\n [-5, 5, -2, 3],\n [0, -2, 9, 8],\n [-1, 3, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
698
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -2, 2, 0],\n [-2, 4, -4, 6],\n [2, -4, -4, -8],\n [0, 6, -8, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
536
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -3, 0, -7],\n [0, -12, 1, -6],\n [0, 0, -10, -11],\n [0, 0, 0, 2]]\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[[-3, -6, -6, -4],\n [-5, 8, 1, 9],\n [-8, 6, -5, -8],\n [-6, 1, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
271
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 10, 8, 0],\n [10, 11, -3, -8],\n [8, -3, -5, -1],\n [0, -8, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
874
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 0, -8, 0],\n [0, 11, -2, 4],\n [-8, -2, 0, -4],\n [0, 4, -4, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
192
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 10, -2, 12],\n [0, -2, 5, -6],\n [0, 0, -4, 11],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
640
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -1, 2, -4],\n [0, -8, -1, -9],\n [0, 0, 10, -6],\n [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"
}
] |
720
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 2, -12, -3],\n [2, 6, 1, 0],\n [-12, 1, 5, 2],\n [-3, 0, 2, -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"
}
] |
158
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -11, 5, 7],\n [-12, 3, 5, -10],\n [6, -11, -7, 0],\n [9, 12, -8, 0]]\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"
}
] |
18
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 11, 10, 2],\n [0, 7, -5, 7],\n [0, 0, -9, -8],\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"
}
] |
930
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 8, 8, -7],\n [0, -9, -1, -9],\n [0, 0, -4, 4],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
976
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 2, -4, -6],\n [2, 7, -2, -1],\n [-4, -2, 12, 4],\n [-6, -1, 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"
}
] |
592
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 10, 9, -1],\n [8, 10, 7, -7],\n [-7, -10, 1, -11],\n [12, 6, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
796
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -1, 4, 0],\n [-1, -5, -3, -2],\n [4, -3, 6, -10],\n [0, -2, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -8, -6, 2],\n [-8, -6, 6, -4],\n [-6, 6, 12, 2],\n [2, -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"
}
] |
272
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 0, 5, 8],\n [0, -8, -3, 0],\n [5, -3, -7, 0],\n [8, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
962
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 12, -1, -4],\n [0, 1, 4, -11],\n [0, 0, 9, 5],\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"
}
] |
720
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, -3, -12, 5],\n [0, -3, -6, 4],\n [0, 0, 5, -6],\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"
}
] |
320
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 6, -3, -4],\n [6, -7, 4, -5],\n [-3, 4, 3, 0],\n [-4, -5, 0, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
612
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, -4, -1, 4],\n [-4, -10, -2, 8],\n [-1, -2, 3, 0],\n [4, 8, 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"
}
] |
864
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 1, 6, 1],\n [-2, -12, 0, 8],\n [-8, -6, 6, -10],\n [11, 11, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
188
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -9, 4, 7],\n [0, -3, 7, 1],\n [0, 0, -10, 7],\n [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"
}
] |
560
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 0, 2, -6],\n [0, -3, 2, 4],\n [2, 2, -12, 6],\n [-6, 4, 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"
}
] |
136
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[4, 4, -3, 5],\n [-11, -9, 7, -1],\n [-1, 1, -12, 9],\n [-8, 2, 5, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
234
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 1, 4, -11],\n [1, 5, 12, 5],\n [5, -7, -10, -5],\n [6, -5, -3, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
950
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 10, -9, -3],\n [6, -8, 8, 1],\n [-10, -10, 8, 8],\n [-3, 0, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
402
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, -4, 11, -2],\n [-3, 7, -1, 9],\n [-6, 11, -12, 3],\n [5, 7, -4, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
582
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 11, -10, -7],\n [0, -7, -4, -2],\n [0, 0, -3, -9],\n [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"
}
] |
168
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 6, 10, 5],\n [0, -4, 8, 3],\n [0, 0, -9, 3],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
320
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -12, -6, -6],\n [-10, -12, -11, -10],\n [-8, -9, 4, 3],\n [12, 4, -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"
}
] |
884
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -11, 10, 6],\n [0, -8, -11, -3],\n [0, 0, -7, -8],\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"
}
] |
864
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 10, -8, -5],\n [5, 1, 10, 11],\n [2, -11, -7, 12],\n [-12, -9, -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"
}
] |
303
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, 10, 7, 6],\n [-6, -10, 6, 6],\n [-8, -6, 7, 6],\n [11, -4, 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"
}
] |
760
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -12, 4, 6],\n [0, 4, 10, -8],\n [0, 0, 2, 7],\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"
}
] |
56
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -2, -4, 1],\n [4, 5, -11, 10],\n [-9, -11, -1, 7],\n [-5, 3, -4, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
729
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 1, 2, -8],\n [1, 1, -11, 2],\n [2, -11, 9, -1],\n [-8, 2, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
207
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -2, -3, -2],\n [0, -2, 12, 11],\n [0, 0, -5, 0],\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"
}
] |
330
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -7, 0, 2],\n [-7, -1, -2, -2],\n [0, -2, 11, 4],\n [2, -2, 4, 4]]\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[[-4, -3, 2, 4],\n [-7, 1, 11, 1],\n [-9, 5, 5, -8],\n [2, 9, -10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
642
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 1, -5, -8],\n [1, 2, 6, 6],\n [-5, 6, 0, 0],\n [-8, 6, 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"
}
] |
946
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -12, 6, -1],\n [0, -5, 4, -6],\n [0, 0, 8, 11],\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"
}
] |
920
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, 9, -6, -9],\n [0, 5, -6, 7],\n [0, 0, -12, 2],\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"
}
] |
880
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, 0, 4, 9],\n [0, 2, 0, 0],\n [4, 0, 9, -10],\n [9, 0, -10, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
732
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 8, 4, 0],\n [8, -12, -2, -5],\n [4, -2, -12, 3],\n [0, -5, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
392
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, -7, 9, 8],\n [6, -3, -1, 6],\n [10, -5, -5, -5],\n [9, 1, 9, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
870
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -11, 6, 8],\n [-3, 6, -9, -5],\n [10, -8, 7, -11],\n [1, 9, -9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
470
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, -5, -12, 7],\n [0, 7, -4, 12],\n [0, 0, -7, -7],\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"
}
] |
352
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -4, 10, 0],\n [-4, 11, 0, -2],\n [10, 0, -4, 4],\n [0, -2, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
632
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 10, 2, 0],\n [10, -10, 6, 3],\n [2, 6, 6, 3],\n [0, 3, 3, -7]]? Round to the nearest integer, then express your answer 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[[-8, 2, -1, 0],\n [0, 7, 0, 12],\n [0, 0, 11, 7],\n [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"
}
] |
920
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 10, 8, -10],\n [-11, 12, 9, -6],\n [4, -6, 11, 2],\n [-12, 7, -11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
746
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 0, 6, -5],\n [0, 12, -6, 7],\n [0, 0, -1, 6],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
576
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, 3, 9, -4],\n [5, 3, -4, -8],\n [-4, -9, 10, -11],\n [-6, 10, -6, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
625
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 0, -9, -5],\n [0, -1, -2, -8],\n [-9, -2, -8, 8],\n [-5, -8, 8, -7]]? 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": "Compute |A| for the matrix A =\n[[10, 3, 5, -12],\n [-3, -5, 9, -12],\n [1, -12, -5, -8],\n [3, 5, 4, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
531
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 10, 11, -9],\n [0, -7, -1, -11],\n [0, 0, 10, 11],\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"
}
] |
620
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -2, -6, -9],\n [0, 8, 9, -7],\n [0, 0, 7, -11],\n [0, 0, 0, 9]]\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[[2, 0, -10, -2],\n [0, -3, 2, 4],\n [-10, 2, -7, 12],\n [-2, 4, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
912
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 10, -4, -12],\n [0, 9, -3, -4],\n [0, 0, 10, -8],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
930
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -2, 9, 0],\n [0, 5, 7, 2],\n [0, 0, -5, 4],\n [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"
}
] |
100
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 0, 7, 6],\n [3, 11, 1, 7],\n [-2, -4, -8, 4],\n [-2, -5, 12, -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"
}
] |
674
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -6, -1, -2],\n [-6, 5, 4, -5],\n [-1, 4, -6, 1],\n [-2, -5, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
654
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -3, 2, 6],\n [-3, 1, 6, 4],\n [2, 6, -2, -4],\n [6, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -10, -4, -6],\n [0, 8, -6, -12],\n [0, 0, -4, -6],\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"
}
] |
760
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -2, -2, 2],\n [-2, 5, -8, -10],\n [-2, -8, -7, -9],\n [2, -10, -9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
590
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 1, 1, -7],\n [1, 8, 5, 0],\n [1, 5, 2, 2],\n [-7, 0, 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"
}
] |
637
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 11, -2, -2],\n [-10, 5, 8, -10],\n [12, 12, -11, -5],\n [5, 8, -9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
198
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 4, 6, 11],\n [0, 8, 1, 9],\n [0, 0, -3, -6],\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"
}
] |
288
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, -4, -12, 0],\n [0, -6, 0, -2],\n [0, 0, 12, 7],\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"
}
] |
640
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -8, -10, 0],\n [0, 8, -10, -3],\n [0, 0, 9, -1],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
728
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 10, 2, 2],\n [10, -1, 4, 10],\n [2, 4, -12, -6],\n [2, 10, -6, 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"
}
] |
620
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 1, 5, 7],\n [0, -8, -5, -1],\n [0, 0, 5, -2],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
640
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -2, 9, 12],\n [12, 8, 1, -1],\n [-5, -9, -7, 6],\n [5, -9, 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"
}
] |
529
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -8, 8, 6],\n [-8, 9, 4, 2],\n [8, 4, -7, -7],\n [6, 2, -7, 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"
}
] |
964
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, -5, 5, 3],\n [0, -11, -5, 1],\n [0, 0, -4, 9],\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"
}
] |
580
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 4, -1, 6],\n [0, 6, 9, -3],\n [0, 0, 4, -2],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
360
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, -9, -8, -8],\n [-9, -10, -3, 8],\n [-8, -3, -12, -6],\n [-8, 8, -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"
}
] |
390
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, 9, -5, -5],\n [6, -8, -9, -6],\n [10, -6, -10, -1],\n [-7, -9, -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}",
"role": "user"
}
] |
247
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 5, 10, 2],\n [0, -10, -7, -11],\n [0, 0, 5, -11],\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"
}
] |
800
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -6, -2, -4],\n [3, 9, 0, 6],\n [6, 8, -2, -8],\n [-3, 5, -5, -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"
}
] |
100
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, 11, -12],\n [4, 4, -12, 1],\n [5, 7, 0, -1],\n [5, -5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
652
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, -4, 12, -3],\n [0, 5, -5, -11],\n [0, 0, -3, -7],\n [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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -3, -3, 5],\n [-2, -11, 3, -11],\n [-9, -7, 6, 2],\n [8, -3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
698
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 11, -10, -4],\n [0, 12, 8, 4],\n [0, 0, 9, 9],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
880
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 7, -6, 0],\n [-3, -3, 9, 4],\n [10, -6, -3, -3],\n [-10, 9, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
353
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 9, -5, 10],\n [0, 6, -2, 0],\n [0, 0, -9, -3],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
812
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 0, -2, -6],\n [0, -1, 2, 5],\n [-2, 2, 5, 2],\n [-6, 5, 2, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 4, -3, -6],\n [4, -5, -3, -2],\n [-3, -3, -6, 2],\n [-6, -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"
}
] |
184
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 6, 11, -2],\n [6, 8, -1, 10],\n [11, -1, 5, -3],\n [-2, 10, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
490
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -12, 1, -9],\n [0, -8, 2, -8],\n [0, 0, -5, 10],\n [0, 0, 0, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
880
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 6, -12, 10],\n [-9, 10, -7, -1],\n [-8, 6, 1, 1],\n [0, 8, -7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
212
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 10, 1, 12],\n [-7, 7, -3, -3],\n [10, 10, 12, -6],\n [7, 1, 1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
240
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -1, -4, 8],\n [-1, 10, 7, 2],\n [-12, -3, 3, 9],\n [1, -5, -9, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
415
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -11, -7, -10],\n [0, -8, -2, -3],\n [0, 0, 4, 7],\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"
}
] |
576
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 1, 0, -10],\n [1, 5, 0, 5],\n [0, 0, 10, 4],\n [-10, 5, 4, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
66
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 9, 3, -2],\n [9, 11, -6, 4],\n [3, -6, 4, 0],\n [-2, 4, 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"
}
] |
791
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -7, 7, 6],\n [0, -12, -8, -5],\n [-4, -4, 0, -4],\n [-2, -9, -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"
}
] |
444
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 5, 6, -8],\n [5, -9, 8, -8],\n [6, 8, -2, 2],\n [-8, -8, 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"
}
] |
108
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -2, -2, -4],\n [-2, 0, 6, 7],\n [-2, 6, -6, -4],\n [-4, 7, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
560
|
MATH
|
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