messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -8, 9, 12],\n [0, 1, -10, 5],\n [0, 0, -10, -11],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
340
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 10, 1, 6],\n [0, -9, -11, -5],\n [0, 0, 11, 6],\n [0, 0, 0, 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"
}
] |
684
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -1, 6, 2],\n [0, -11, 12, 3],\n [0, 0, -12, -6],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
336
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -6, 6, -2],\n [-6, -7, 1, 10],\n [6, 1, 6, -6],\n [-2, 10, -6, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
544
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 8, 2, -7],\n [0, 5, -5, -2],\n [0, 0, -12, -4],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 2, -4, -6],\n [2, 5, -2, 4],\n [-4, -2, -10, 0],\n [-6, 4, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
820
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 12, 9, -4],\n [-10, -3, 11, -4],\n [1, 4, -5, -12],\n [1, 9, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
495
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 1, 9, -1],\n [2, 9, 10, -12],\n [0, 3, 6, -8],\n [0, -10, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -8, -4, 0],\n [-8, -12, 10, 7],\n [-4, 10, -8, -1],\n [0, 7, -1, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
616
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -8, 12, -12],\n [4, 5, 11, 9],\n [-7, 2, 7, -9],\n [1, -11, 1, -5]]\nRound to the nearest integer, then take the result modulo 1000.\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, 0, 0, -6],\n [0, 1, 5, -3],\n [0, 5, 7, 2],\n [-6, -3, 2, 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"
}
] |
632
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -8, 7, 0],\n [-8, -12, 8, 4],\n [7, 8, 10, 2],\n [0, 4, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
688
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-11, -11, 11, -7],\n [-3, 11, -6, -8],\n [7, 4, 8, 2],\n [-11, -3, -10, 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"
}
] |
84
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, 1, -7, 4],\n [0, 1, 7, -1],\n [0, 0, 3, 1],\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"
}
] |
925
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 9, 4, 6],\n [2, 1, 5, 12],\n [-4, 4, 10, 6],\n [-6, -11, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
192
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -9, -2, 4],\n [0, -7, -9, 12],\n [0, 0, -12, -1],\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"
}
] |
720
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -5, -6, -7],\n [5, 10, -2, -4],\n [-4, -9, 9, -6],\n [6, -8, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
443
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 8, 0, -6],\n [8, -10, -1, 4],\n [0, -1, -8, 10],\n [-6, 4, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
808
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -11, -11, 0],\n [-12, -1, 9, 4],\n [3, -11, 9, 3],\n [-7, 4, -1, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
915
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 0, 0, -4],\n [0, -2, -7, 2],\n [0, -7, -6, 4],\n [-4, 2, 4, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
537
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -11, 4, 5],\n [11, -10, 4, -3],\n [-8, -5, -10, -7],\n [9, -6, 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"
}
] |
134
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -2, 4, 2],\n [-2, -4, -4, -5],\n [4, -4, -3, 1],\n [2, -5, 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"
}
] |
85
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, -7, -1, -6],\n [-7, 7, 4, -4],\n [-1, 4, -1, -10],\n [-6, -4, -10, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
344
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 8, 10, 8],\n [-11, -4, -1, -4],\n [-12, 11, 1, 4],\n [10, -7, -3, -9]]? Round to the nearest integer, then express your answer modulo 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[[-1, -3, -7, 7],\n [0, 8, -6, 3],\n [0, 0, 4, 6],\n [0, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
256
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -2, 5, -6],\n [0, 10, 10, 5],\n [0, 0, -9, 9],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -12, -10, -10],\n [5, 12, 7, 4],\n [7, 12, 9, -7],\n [-4, 0, 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"
}
] |
412
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 2, -9, 6],\n [0, 9, -12, -1],\n [0, 0, -11, -9],\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"
}
] |
594
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -6, -9, -9],\n [-7, 2, 4, -3],\n [-4, 7, 4, 1],\n [11, -7, 3, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
647
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -3, -8, 12],\n [-2, 7, 2, 0],\n [-2, 0, -2, 7],\n [-12, -4, 11, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
417
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -4, -2, -2],\n [1, -11, -2, -1],\n [2, 10, 7, 3],\n [-7, -10, -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"
}
] |
680
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -9, -7, 9],\n [0, 11, -1, 8],\n [0, 0, 7, -5],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
155
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 0, 3, -1],\n [12, -8, -1, 0],\n [-1, 1, -8, -2],\n [3, -8, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
755
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, -2, -3, -2],\n [-2, 1, -3, -4],\n [-3, -3, 12, 11],\n [-2, -4, 11, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
423
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -7, -7, 0],\n [0, -12, 7, 4],\n [0, 0, -9, 5],\n [0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 7, -9, 11],\n [0, 9, 9, 5],\n [0, 0, -2, -5],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
352
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 2, -1, -4],\n [2, -3, 0, 5],\n [-1, 0, -12, -4],\n [-4, 5, -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"
}
] |
283
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, -2, 8],\n [-4, -4, 0, 0],\n [-2, 0, -2, 2],\n [8, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
608
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -2, 8, 7],\n [-2, 6, 0, 0],\n [8, 0, 0, 6],\n [7, 0, 6, 10]]\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[[10, -4, 6, 12],\n [-10, -8, 7, 1],\n [6, -8, 12, -6],\n [1, -12, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
392
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 7, -4, 4],\n [0, 9, -7, 10],\n [4, -12, 10, -2],\n [3, -4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
274
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -7, 0, 0],\n [-7, -11, -3, -6],\n [0, -3, 6, -8],\n [0, -6, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
479
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -2, 0, 0],\n [-2, 6, -1, 5],\n [0, -1, 2, 8],\n [0, 5, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
688
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 5, -6, 0],\n [5, -2, -2, 3],\n [-6, -2, 4, 3],\n [0, 3, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
297
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -2, -4, 0],\n [-2, -3, -4, -8],\n [-4, -4, -3, 0],\n [0, -8, 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"
}
] |
850
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 7, -9, 3],\n [0, -4, -1, -1],\n [0, 0, 9, 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"
}
] |
840
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, 5, -10, 11],\n [-11, 1, 0, 1],\n [-2, -10, 4, -4],\n [-3, -5, -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"
}
] |
704
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[2, 0, 3, -1],\n [0, -3, 2, -8],\n [3, 2, -12, -6],\n [-1, -8, -6, 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"
}
] |
476
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 10, -12, -11],\n [0, 10, 8, 11],\n [0, 0, -2, 8],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
920
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -4, 12, 5],\n [0, -12, -9, 1],\n [0, 0, 6, -1],\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"
}
] |
280
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -6, 6, 2],\n [-6, 4, 6, 7],\n [6, 6, 2, 4],\n [2, 7, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
830
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -8, 3, 1],\n [-8, 8, -8, -2],\n [3, -8, -8, -2],\n [1, -2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
532
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[8, -12, 5, -9],\n [0, -8, -11, -10],\n [0, 0, 4, 8],\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"
}
] |
208
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, -4, -1, 4],\n [-4, 7, 11, 2],\n [-1, 11, 12, -2],\n [4, 2, -2, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
94
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 0, 6, 4],\n [0, 11, 8, -4],\n [6, 8, 6, -8],\n [4, -4, -8, 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"
}
] |
236
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 4, -7, 1],\n [0, -10, 3, -1],\n [0, 0, -12, -6],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 1, 8, -2],\n [-4, 2, 11, 6],\n [4, -6, 8, -12],\n [-7, -7, -6, -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"
}
] |
410
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 9, 4, 6],\n [-2, 3, 5, 8],\n [-9, -3, 7, 6],\n [9, 3, -9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
512
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 1, 6, -2],\n [0, 10, 7, -5],\n [0, 0, -3, 3],\n [0, 0, 0, -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"
}
] |
700
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -11, -1, -1],\n [8, 4, -5, 6],\n [10, 9, -10, 11],\n [6, 0, 11, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, 11, -3, 5],\n [0, -3, 5, 4],\n [0, 0, 2, -1],\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"
}
] |
736
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -2, -6, -5],\n [0, 11, -4, -10],\n [0, 0, 7, 8],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
308
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -7, -2, -11],\n [5, 0, 0, 6],\n [-4, -12, -2, 2],\n [4, -7, -4, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
142
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 0, -6, -2],\n [0, -8, 7, 0],\n [-6, 7, 6, -8],\n [-2, 0, -8, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
103
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -12, 3, 11],\n [3, -1, 7, 6],\n [-1, -4, 8, 0],\n [7, -12, -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"
}
] |
405
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, -5, -8, -4],\n [9, 8, 10, -6],\n [11, 3, 10, 3],\n [-2, -3, 3, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
445
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 12, 4, -9],\n [0, -2, -3, -5],\n [0, 0, 1, -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"
}
] |
958
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 2, 2, 0],\n [2, -11, 6, -1],\n [2, 6, -12, -7],\n [0, -1, -7, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
333
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[11, 9, -12, -5],\n [0, -5, -12, 3],\n [0, 0, 4, 9],\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"
}
] |
220
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -7, 0, -10],\n [-7, 6, -6, -12],\n [0, -6, 1, -2],\n [-10, -12, -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"
}
] |
589
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 5, 2, -6],\n [0, -10, 10, 10],\n [0, 0, -1, -5],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
660
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[3, 2, 0, 6],\n [2, -5, -1, -8],\n [0, -1, -8, 7],\n [6, -8, 7, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
593
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 2, 2, 4],\n [2, -11, -6, 0],\n [2, -6, -8, 6],\n [4, 0, 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"
}
] |
668
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -6, 8, 6],\n [0, -4, -9, 1],\n [0, 0, 10, -1],\n [0, 0, 0, 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"
}
] |
960
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -9, -8, 7],\n [11, -4, 0, 7],\n [11, 7, -4, 7],\n [9, -2, 11, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
379
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 6, 5, 9],\n [0, -11, -8, 12],\n [0, 0, 2, -8],\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"
}
] |
472
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 1, 8, -10],\n [0, 10, -1, -2],\n [0, 0, -7, 9],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
630
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 0, -7, 0],\n [12, 0, 6, 7],\n [3, -9, -9, -5],\n [0, -9, -7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
887
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 0, 4, 11],\n [0, -6, -9, 10],\n [0, 0, 9, -4],\n [0, 0, 0, -4]]\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[[-5, 10, 11, 0],\n [0, 3, 0, 0],\n [0, 0, 7, 7],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
790
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, -10, 1, -10],\n [-4, -3, -8, 11],\n [6, -11, -4, -5],\n [-10, -9, -7, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
914
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 5, 11, -7],\n [10, 2, 4, -3],\n [-11, 9, -12, 6],\n [11, 11, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
732
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 3, -4, 2],\n [3, 8, 6, -4],\n [-4, 6, 1, -9],\n [2, -4, -9, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
356
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 4, 8, -4],\n [-7, -4, 0, 10],\n [-4, -8, -2, 2],\n [6, -5, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
408
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 2, -2, -6],\n [2, 0, -2, 2],\n [-2, -2, 3, -1],\n [-6, 2, -1, -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"
}
] |
924
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -9, 1, 6],\n [0, -1, 8, 5],\n [0, 0, -4, 7],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
840
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-8, 4, 8, 6],\n [4, -10, 1, 4],\n [8, 1, -7, -3],\n [6, 4, -3, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
324
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -9, -9, 12],\n [-8, -7, -4, 0],\n [-12, 9, 6, 2],\n [8, 2, 7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
492
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -3, -4, 3],\n [-3, 10, 4, 4],\n [-4, 4, 4, 2],\n [3, 4, 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"
}
] |
44
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-3, 8, -6, -2],\n [8, -4, 4, 4],\n [-6, 4, 2, -7],\n [-2, 4, -7, -1]]? 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[[3, 12, 2, 11],\n [0, 4, 9, -9],\n [0, 0, 9, 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"
}
] |
784
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -2, 5, 9],\n [0, -4, -6, -11],\n [0, 0, 5, 11],\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"
}
] |
760
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -10, 2, 2],\n [0, -10, -8, -1],\n [0, 0, 7, -4],\n [0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
960
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 7, 6, -4],\n [0, 1, -11, 4],\n [0, 0, 12, -6],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
460
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, -3, 7, -6],\n [1, -6, 6, -11],\n [9, -1, 0, -5],\n [-2, 3, 4, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
723
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, 9, -6, 5],\n [0, 10, -11, -4],\n [0, 0, 6, 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"
}
] |
480
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, -3, 2, 1],\n [-3, 11, 8, -2],\n [2, 8, 5, 6],\n [1, -2, 6, 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"
}
] |
417
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 2, -7, -10],\n [0, 10, 10, -9],\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"
}
] |
240
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -1, 4, -2],\n [-1, 7, -8, 4],\n [4, -8, -8, 6],\n [-2, 4, 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"
}
] |
340
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -8, 0, -3],\n [-8, -9, 4, 4],\n [0, 4, -12, 7],\n [-3, 4, 7, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
127
|
MATH
|
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