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[[2, 10, 4, -4],\n [6, -3, 9, 10],\n [12, 12, -10, -12],\n [-10, -5, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
516
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -7, -5, -10],\n [0, -1, -5, 8],\n [0, 0, 7, 3],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
245
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 0, 6, 6],\n [0, 2, -2, 4],\n [6, -2, 1, 4],\n [6, 4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
672
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -4, -10, -7],\n [0, 6, 8, -9],\n [-12, 5, 0, -4],\n [3, 10, 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"
}
] |
810
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -4, 12, 2],\n [-4, 0, -4, 1],\n [12, -4, -10, -4],\n [2, 1, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
866
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, 0, 3, -4],\n [0, 3, -10, -8],\n [0, 0, 12, 12],\n [0, 0, 0, 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": "Determine the value of det(A) where A =\n[[-11, 5, 5, 4],\n [0, -3, 8, -5],\n [0, 0, 2, 0],\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"
}
] |
406
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -2, -12, -1],\n [0, -2, 10, -12],\n [0, 0, -9, -7],\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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 0, 8, -2],\n [0, -4, 0, -11],\n [0, 0, 9, 5],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
324
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -5, -9, -11],\n [-7, 7, -1, 8],\n [-1, -9, 12, -3],\n [9, 4, 4, -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"
}
] |
889
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 5, 11, 3],\n [8, -7, -9, -2],\n [11, 11, 12, 1],\n [2, 11, -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": "user"
}
] |
940
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 4, 0, 2],\n [4, -11, -12, -2],\n [0, -12, -11, -2],\n [2, -2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
923
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 4, -8, -11],\n [-1, -8, 0, 10],\n [-11, 1, -11, 4],\n [4, -2, -8, -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"
}
] |
850
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -6, -2, -10],\n [0, -7, -2, 2],\n [0, 0, -4, 9],\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"
}
] |
976
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -9, 10, -1],\n [0, -3, 1, -9],\n [0, 0, -10, 0],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
740
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 5, 4, -1],\n [0, -4, 3, -7],\n [0, 0, 6, 1],\n [0, 0, 0, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
984
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -7, -11, -1],\n [-12, -10, 0, 4],\n [-10, 1, 5, -11],\n [9, 12, -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"
}
] |
180
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 0, 4, 7],\n [0, 1, 8, -5],\n [4, 8, -6, -4],\n [7, -5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
42
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 2, -3, -6],\n [0, 8, -9, -7],\n [0, 0, 2, 7],\n [0, 0, 0, 3]]\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[[-3, 4, 7, 9],\n [0, -8, -9, 8],\n [0, 0, 10, 11],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
920
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -7, -6, 12],\n [0, 7, -11, 6],\n [0, 0, 4, 2],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
804
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 11, -11, 5],\n [0, 3, -1, -8],\n [0, 0, 5, 4],\n [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"
}
] |
940
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -1, 10, -1],\n [0, -10, -5, -11],\n [0, 0, -1, -11],\n [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"
}
] |
970
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 2, -8, 4],\n [2, 9, 5, -8],\n [-8, 5, 9, 5],\n [4, -8, 5, -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"
}
] |
885
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -12, 0, 3],\n [-1, 12, -11, -3],\n [-7, 10, 10, -11],\n [10, 1, 12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
755
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, -1, -3, -7],\n [0, -9, 4, 8],\n [0, 0, 9, 2],\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"
}
] |
570
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -2, 10, 0],\n [10, -5, 7, -1],\n [5, 12, -1, -11],\n [-10, 9, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
374
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 12, -11, -2],\n [7, 5, 0, -8],\n [-7, -3, -7, -6],\n [-12, 9, 12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
723
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 0, 0, -8],\n [0, 3, 4, 2],\n [0, 4, 7, 2],\n [-8, 2, 2, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
636
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 10, -7, -10],\n [0, 3, 4, -6],\n [0, 0, -7, -11],\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"
}
] |
680
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 1, -11, -10],\n [0, -9, -10, 12],\n [0, 0, -5, 0],\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"
}
] |
620
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -5, -11, 8],\n [4, 3, -11, 3],\n [1, -8, -5, 12],\n [0, -4, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
465
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, -2, 1, 5],\n [7, 7, 2, -6],\n [2, -9, -4, 7],\n [5, 2, -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"
}
] |
797
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, 3, 6, 1],\n [-7, 8, -3, -1],\n [12, -5, -3, -5],\n [-10, 8, 12, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
938
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -6, 12, 2],\n [10, -7, 11, 6],\n [-3, 8, -3, 0],\n [2, -3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
518
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 12, -1, -10],\n [7, 4, -6, -2],\n [-6, 8, 1, 12],\n [-12, 7, -3, -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"
}
] |
400
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 1, 10, -3],\n [0, 2, -3, 5],\n [-1, -9, -12, 12],\n [-3, -5, 7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
651
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -11, -2, 0],\n [4, -7, 9, 3],\n [11, -2, -5, 5],\n [0, 3, 12, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
714
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -6, 2, 9],\n [-6, 12, 4, 0],\n [2, 4, 4, -6],\n [9, 0, -6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
640
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, -9, 8, 10],\n [0, -10, -2, -6],\n [0, 0, 11, 5],\n [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"
}
] |
30
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 9, 7, 3],\n [9, -8, -9, -4],\n [7, -9, 4, 0],\n [3, -4, 0, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
681
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -7, 1, -2],\n [-7, -5, -8, 5],\n [1, -8, 2, 4],\n [-2, 5, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
871
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[1, -4, -2, 3],\n [-4, -1, 0, -2],\n [-2, 0, -10, 0],\n [3, -2, 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"
}
] |
486
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, -8, -1, 10],\n [-1, -11, 0, -11],\n [-3, -9, -4, 9],\n [-12, 7, -5, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
790
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[0, 1, 2, 1],\n [1, 1, 2, 4],\n [2, 2, 10, -8],\n [1, 4, -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"
}
] |
298
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 11, 7, 1],\n [-9, 11, -8, -5],\n [-9, 5, -2, 9],\n [-8, 3, 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"
}
] |
126
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -2, 6, 7],\n [0, -5, -3, -5],\n [0, 0, -7, 6],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
210
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -2, -10, -10],\n [-4, -9, -8, 0],\n [-5, 5, 7, 12],\n [-5, -5, 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"
}
] |
402
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -12, -12, -9],\n [0, 12, -10, -2],\n [0, 0, -1, -11],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 10, -4, 6],\n [10, -3, 8, 2],\n [-4, 8, -4, 3],\n [6, 2, 3, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
236
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 2, 10, 1],\n [0, 3, 6, 10],\n [0, 0, -6, 7],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
162
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -12, -8, 0],\n [3, -1, 8, -10],\n [5, 7, 6, 8],\n [-6, -7, -11, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
744
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 1, -8, -10],\n [2, 11, -6, -1],\n [-11, -7, 1, 3],\n [6, -11, 0, 12]]\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, 2, 0, -4],\n [2, 10, 2, -2],\n [0, 2, -12, 5],\n [-4, -2, 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": "user"
}
] |
930
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 8, 1, 10],\n [0, -7, -6, 1],\n [0, 0, 5, -4],\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"
}
] |
800
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -3, 8, 8],\n [-3, -11, 2, 2],\n [8, 2, -6, 2],\n [8, 2, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
870
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, -2, -4, -7],\n [-2, -5, -3, 12],\n [7, -3, 0, -10],\n [-11, 0, 11, 1]]\nRound to the nearest integer, then take the result modulo 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[[-5, 4, 5, 8],\n [0, -6, 4, -5],\n [0, 0, 1, 8],\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"
}
] |
240
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 2, 2, -10],\n [2, 0, 6, 8],\n [2, 6, 6, -1],\n [-10, 8, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
116
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -11, -2, 3],\n [0, -4, 4, 2],\n [0, 0, 5, -1],\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"
}
] |
440
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -3, -6, -4],\n [0, -8, 0, 3],\n [0, 0, -7, 11],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
152
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 6, -6, 4],\n [6, 12, 0, -5],\n [-6, 0, -4, 6],\n [4, -5, 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"
}
] |
916
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 0, 0, -4],\n [0, 1, -2, -6],\n [0, -2, -9, 0],\n [-4, -6, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
208
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -10, 7, -8],\n [0, 9, 7, -4],\n [0, 0, -4, 1],\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"
}
] |
644
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[8, -7, 2, 3],\n [-7, -12, -5, 7],\n [9, -10, -11, 4],\n [-3, -4, 1, 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"
}
] |
784
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 0, -2, -8],\n [0, 1, -1, 2],\n [-2, -1, -2, 2],\n [-8, 2, 2, 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"
}
] |
194
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -7, 10, -2],\n [0, 10, 3, 10],\n [0, 0, 5, 4],\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"
}
] |
750
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -2, 9, 5],\n [-2, 7, 2, 4],\n [9, 2, -12, 4],\n [5, 4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
685
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 3, -1, 0],\n [1, 9, 4, -4],\n [3, 10, -12, 3],\n [-5, 0, -8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
636
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 6, -4, -8],\n [6, -11, 0, -8],\n [-4, 0, -7, -2],\n [-8, -8, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
708
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 4, 1, 0],\n [4, 9, 2, -8],\n [1, 2, -9, 0],\n [0, -8, 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"
}
] |
936
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -6, -8, 10],\n [-2, 11, 8, -10],\n [-6, 3, 7, 7],\n [-11, 6, 6, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
108
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 4, 12, -11],\n [0, 6, 0, 9],\n [0, 0, -6, 9],\n [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"
}
] |
812
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 0, -1, -6],\n [0, 0, 3, -6],\n [-1, 3, 12, -1],\n [-6, -6, -1, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
844
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, 10, 9, -11],\n [0, -10, 8, 10],\n [0, 0, 11, -11],\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": "Determine the value of det(A) where A =\n[[2, 8, 0, -5],\n [0, -6, -1, -5],\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"
}
] |
144
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -7, -6, -3],\n [-9, 11, -12, -4],\n [-11, -5, -5, -10],\n [-7, -11, -5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
373
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 3, 7, 4],\n [0, 1, 4, -6],\n [0, 0, 5, 10],\n [0, 0, 0, -6]]\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[[8, 8, -6, -1],\n [8, 2, 0, 0],\n [-6, 0, 6, -1],\n [-1, 0, -1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
692
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -9, 6, -1],\n [0, -7, 3, 4],\n [0, 0, 1, 9],\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"
}
] |
916
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -4, 8, -4],\n [-4, -9, 0, -7],\n [8, 0, -3, -2],\n [-4, -7, -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"
}
] |
496
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 5, -2, 4],\n [5, 6, 8, 0],\n [-2, 8, 9, -5],\n [4, 0, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
709
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -2, 9, 2],\n [-2, 8, 2, -1],\n [9, 2, -5, -2],\n [2, -1, -2, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
898
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 2, -12, -12],\n [0, 4, -2, -3],\n [0, 0, 11, -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"
}
] |
264
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -8, 1, -12],\n [0, 10, 7, -9],\n [0, 0, -4, 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"
}
] |
600
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 4, 5, -11],\n [4, -3, -12, -4],\n [5, -12, 5, 10],\n [-11, -4, 10, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
53
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -10, -2, 1],\n [-10, 12, 0, -5],\n [-2, 0, 9, -10],\n [1, -5, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
307
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -3, -5, -6],\n [0, 9, -3, 10],\n [0, 0, -10, -1],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, 10, 11, -10],\n [0, 5, -10, -1],\n [0, 0, 1, 7],\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"
}
] |
850
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 4, 8, -7],\n [2, -4, -7, 4],\n [7, -10, 9, -9],\n [5, 10, -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"
}
] |
428
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 3, 8, -12],\n [-3, 1, 9, 9],\n [-1, 3, -8, -11],\n [0, 3, 12, 11]]\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": "Compute |A| for the matrix A =\n[[6, 4, -10, -11],\n [4, -2, -2, -4],\n [-10, -2, 8, 2],\n [-11, -4, 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"
}
] |
964
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -2, 6, -6],\n [-2, 7, -5, -4],\n [6, -5, -5, 8],\n [-6, -4, 8, 4]]? Round to the nearest integer, then express your answer modulo 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[[0, -10, 0, -7],\n [-10, 0, 4, 0],\n [0, 4, 3, -10],\n [-7, 0, -10, -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"
}
] |
484
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 7, 12, -9],\n [5, -8, 6, -4],\n [-9, 5, -12, 0],\n [-4, 4, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
422
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -4, 7, -12],\n [0, 8, 7, -1],\n [0, 0, -6, 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"
}
] |
80
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, -4, -6, 2],\n [-4, 1, -8, 6],\n [-6, -8, 6, 10],\n [2, 6, 10, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
482
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -8, -12, 7],\n [0, 11, 8, -8],\n [0, 0, -5, -4],\n [0, 0, 0, 10]]\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[[10, -3, 10, -6],\n [-4, 3, 1, 7],\n [-3, -7, -1, 7],\n [-8, 3, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
565
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, 0, 3, -1],\n [0, 11, -4, 0],\n [3, -4, -8, 2],\n [-1, 0, 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"
}
] |
366
|
MATH
|
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