messages
listlengths 1
1
| ground_truth
stringclasses 992
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[12, 6, 0, 4],\n [0, 3, 7, -8],\n [0, 0, 12, 10],\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"
}
] |
568
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 12, -3, 9],\n [2, 6, 9, 12],\n [-6, -7, -10, -4],\n [-10, 12, 8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
495
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, -3, -7, -8],\n [0, 7, 7, -1],\n [0, 0, 7, 0],\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"
}
] |
71
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[2, -10, -6, 0],\n [-3, -6, -7, -5],\n [10, 8, 4, -8],\n [11, -8, -8, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
828
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -2, -7, 5],\n [-11, 12, 3, -10],\n [-1, 6, 3, 2],\n [-7, -8, 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"
}
] |
516
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 3, 3, -8],\n [11, 7, -6, 5],\n [1, -9, -11, -2],\n [-5, 6, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 2, -3, 6],\n [2, 0, 12, -8],\n [-3, 12, 9, 0],\n [6, -8, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
388
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 12, 5, 4],\n [0, 2, 2, -9],\n [0, 0, -7, 12],\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"
}
] |
608
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -9, -11, -1],\n [0, -9, -8, -1],\n [0, 0, -10, -3],\n [0, 0, 0, 10]]\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[[-9, 1, 10, -1],\n [0, 2, -8, 4],\n [0, 0, 5, -11],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 11, -8, 3],\n [0, -10, 6, -7],\n [0, 0, -5, -11],\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"
}
] |
600
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -3, 1, 4],\n [-3, 12, 0, 4],\n [1, 0, 12, -8],\n [4, 4, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
688
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 4, -7, 6],\n [0, -12, -1, -6],\n [-4, -2, 5, 5],\n [-11, 0, -11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
816
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 2, 0, 5],\n [2, 0, 1, 4],\n [0, 1, 8, -4],\n [5, 4, -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"
}
] |
299
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, 3, -7],\n [0, -5, 7, 9],\n [0, 0, -4, -6],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
500
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[3, 6, 5, 1],\n [0, 6, 6, 10],\n [0, 0, 12, -3],\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"
}
] |
160
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -4, 2, 1],\n [-4, 10, 0, 4],\n [2, 0, 4, -6],\n [1, 4, -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"
}
] |
976
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -3, 11, 5],\n [-12, -2, 12, 5],\n [12, 5, -9, -6],\n [6, -10, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
676
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, -9, -10, 6],\n [9, -4, 8, -7],\n [5, -8, 10, -9],\n [10, 11, -12, -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"
}
] |
448
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -3, -5, -9],\n [-11, -2, -4, 2],\n [-9, -5, -8, -8],\n [8, 3, -10, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
491
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -2, -3, 12],\n [0, -8, -3, 1],\n [5, -4, -4, -5],\n [6, 6, -9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
436
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[1, 3, -9, 7],\n [-1, 5, 6, -6],\n [-9, -7, 7, -3],\n [-11, 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"
}
] |
712
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-5, -6, 9, -6],\n [-6, 2, 2, -4],\n [9, 2, -12, -2],\n [-6, -4, -2, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
186
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 11, 9, -2],\n [4, 0, 5, 12],\n [5, 9, 0, -11],\n [5, 4, 1, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
452
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 6, -3, 12],\n [10, 8, 5, -10],\n [9, 2, 2, -1],\n [-4, 5, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
699
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 4, 7, -2],\n [0, 7, -4, 7],\n [0, 0, 8, -2],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
664
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 9, 2, -9],\n [0, 3, -2, -3],\n [0, 0, 11, 12],\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"
}
] |
175
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, -4, 10, 6],\n [4, -4, -8, -9],\n [4, 10, 0, 11],\n [-5, 6, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
824
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 10, -2, 2],\n [10, 9, -6, -7],\n [-2, -6, 3, -1],\n [2, -7, -1, -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"
}
] |
293
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 6, -1, -1],\n [-5, 7, -3, 0],\n [12, -11, -3, -10],\n [6, 1, 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"
}
] |
371
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[9, -8, 5, 12],\n [0, -12, -7, -6],\n [0, 0, -7, -4],\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"
}
] |
268
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 5, -11, 3],\n [-3, -11, -2, -7],\n [9, 11, -12, 11],\n [-1, 9, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
208
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 11, -4, -10],\n [0, 6, 10, 5],\n [0, 0, -12, -6],\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"
}
] |
456
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, -11, -8, 10],\n [8, 1, 10, -7],\n [-11, -6, -3, -4],\n [3, -9, 3, -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"
}
] |
274
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[4, 10, 3, -1],\n [0, 8, 4, -2],\n [0, 0, 10, 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"
}
] |
480
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -8, 10, -2],\n [0, 3, -12, 11],\n [0, 0, -2, -3],\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"
}
] |
832
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, -3, -3, 8],\n [0, -5, 9, -4],\n [0, 0, -2, -7],\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"
}
] |
160
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 3, -9, 9],\n [0, -11, -12, -9],\n [0, 0, -6, 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"
}
] |
304
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, -4, 9, -9],\n [0, 5, -4, 9],\n [0, 0, -8, 1],\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"
}
] |
400
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 9, 8, 4],\n [12, -7, -9, 9],\n [-11, -5, 8, -1],\n [-8, -5, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
677
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, -8, 2, -4],\n [-8, 7, 0, 6],\n [2, 0, -10, 2],\n [-4, 6, 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"
}
] |
750
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 12, 0, 10],\n [-1, 0, -12, 9],\n [5, -11, 4, 3],\n [5, 10, -12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
828
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[0, -10, 8, 12],\n [-7, 4, -3, 4],\n [11, 8, 0, 12],\n [-4, -3, -5, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
540
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 11, -1, 4],\n [0, -4, 1, 10],\n [0, 0, 1, 1],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
784
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, 0, 8, 5],\n [0, -12, 10, 8],\n [8, 10, -8, 0],\n [5, 8, 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"
}
] |
372
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 1, 4, 0],\n [1, 5, -6, -4],\n [4, -6, -3, -2],\n [0, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
144
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -4, 1, 2],\n [-4, 12, -3, -8],\n [1, -3, -9, 8],\n [2, -8, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
942
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -4, -10, 7],\n [-4, 1, -2, -4],\n [-10, -2, -8, 4],\n [7, -4, 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"
}
] |
52
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 2, 0, -2],\n [2, 12, -6, -3],\n [0, -6, 2, -6],\n [-2, -3, -6, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
860
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 7, 11, 6],\n [7, 3, -6, -2],\n [11, -6, 6, -2],\n [6, -2, -2, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
236
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, 9, 5, -5],\n [7, 8, -9, 6],\n [-8, 3, -11, -2],\n [-1, -3, 8, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
290
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[5, 11, 4, -8],\n [0, 7, -5, 10],\n [0, 0, -4, 9],\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"
}
] |
120
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 7, -8, 4],\n [0, -12, -5, 5],\n [0, 0, 9, 5],\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"
}
] |
972
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -9, 10, 10],\n [-5, -12, 5, 2],\n [6, -4, -7, -7],\n [7, -5, 12, -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"
}
] |
880
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, 11, -2, -9],\n [0, 12, 2, -5],\n [0, 0, 6, 5],\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"
}
] |
408
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, 11, -5, 11],\n [-9, -7, 9, 9],\n [7, -8, 8, -7],\n [9, -5, 4, -1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
607
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 6, -11, -12],\n [0, -7, -7, 6],\n [0, 0, -1, -9],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
461
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-11, -3, -2, -2],\n [-3, -4, 1, 0],\n [-2, 1, -4, -4],\n [-2, 0, -4, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
849
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[9, 12, 11, -10],\n [0, -4, 0, -11],\n [0, 0, 2, -12],\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": "Compute |A| for the matrix A =\n[[-9, -4, -5, -8],\n [8, -9, -2, 7],\n [-4, 3, -10, -7],\n [6, -11, -8, -1]]\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": "Compute |A| for the matrix A =\n[[0, 6, -4, 2],\n [6, 11, 0, 2],\n [-4, 0, -9, -7],\n [2, 2, -7, 6]]\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": "Compute |A| for the matrix A =\n[[3, 2, -6, 2],\n [2, -7, 2, 6],\n [-6, 2, 2, -7],\n [2, 6, -7, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
889
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -8, -2, -1],\n [-8, 5, 6, 5],\n [-2, 6, 12, -9],\n [-1, 5, -9, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -8, 11, -9],\n [1, 12, 9, -8],\n [3, -3, -11, -8],\n [-10, 9, 11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
162
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -4, -8, -5],\n [0, 7, 0, -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"
}
] |
992
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, -8, -7, 8],\n [0, -12, -2, -2],\n [0, 0, -3, -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"
}
] |
56
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, 5, 6, 11],\n [0, 7, 7, -5],\n [0, 0, -3, -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"
}
] |
147
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -3, -9, 10],\n [0, -1, -7, -12],\n [0, 0, -9, -6],\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"
}
] |
693
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -2, 3, -5],\n [-7, 9, -12, -1],\n [-12, 8, -2, 1],\n [-6, 9, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
237
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 6, 2, -10],\n [11, 1, 10, -10],\n [4, 4, -2, 9],\n [-7, 4, 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"
}
] |
210
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 0, -4, 4],\n [0, 11, -2, 2],\n [-4, -2, -3, -2],\n [4, 2, -2, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
330
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-10, -8, -8, 3],\n [12, -7, -1, 11],\n [-5, 1, 4, -3],\n [-12, 2, 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"
}
] |
99
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 8, 0, 0],\n [8, 0, -5, 5],\n [0, -5, 9, -11],\n [0, 5, -11, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
308
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[9, -9, 8, -3],\n [0, 8, -4, -4],\n [0, 0, 7, 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"
}
] |
992
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-1, -4, -12, -3],\n [0, -12, -2, 4],\n [0, 0, 2, -6],\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"
}
] |
24
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, -10, -5, 0],\n [10, 5, -10, -7],\n [1, 11, -5, -4],\n [1, -2, 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"
}
] |
435
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-6, 11, -7, 11],\n [12, 0, 6, -6],\n [-9, 3, 1, 6],\n [-12, -5, 11, -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"
}
] |
260
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 3, -12, -9],\n [0, -7, 6, -1],\n [0, 0, -11, 2],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
693
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[6, 8, 5, 0],\n [0, 5, 1, -11],\n [0, 0, -4, -10],\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"
}
] |
40
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -6, 4, 5],\n [-6, 7, 6, -6],\n [4, 6, -6, -4],\n [5, -6, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
22
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, -4, -12, 1],\n [-10, -8, 8, 0],\n [-7, 1, 9, 6],\n [-1, -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"
}
] |
968
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -11, 0, 2],\n [0, 8, 7, -1],\n [0, 0, -10, -2],\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"
}
] |
480
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -8, -10, -2],\n [0, 9, 5, 11],\n [0, 0, 8, -11],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
184
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -3, 0, 4],\n [-3, 6, 4, -4],\n [0, 4, 2, 0],\n [4, -4, 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"
}
] |
134
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 8, -2, 11],\n [-9, 12, -10, -7],\n [0, 1, -9, 3],\n [9, 4, 2, 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"
}
] |
718
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 2, 6, 4],\n [2, -10, -6, -2],\n [6, -6, -2, -2],\n [4, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
40
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 5, 5, -7],\n [0, 8, 4, -6],\n [0, 0, 3, -4],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
712
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -2, 6, -2],\n [-2, 8, -6, -5],\n [6, -6, 4, 1],\n [-2, -5, 1, -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"
}
] |
16
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 10, -2, -2],\n [-9, 5, -5, -10],\n [-8, 3, 1, -5],\n [-8, 4, -2, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
716
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -4, -4, 11],\n [12, 9, 9, -11],\n [-2, 3, 6, 12],\n [-2, 8, -1, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
776
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -10, -11, 0],\n [0, -9, 4, 3],\n [0, 0, 4, -10],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
604
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 10, 2, 6],\n [0, 6, 2, -5],\n [0, 0, -9, -3],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
782
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 0, -2, 1],\n [0, -7, -5, -6],\n [-2, -5, 9, 1],\n [1, -6, 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"
}
] |
49
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 1, 0, -12],\n [0, -1, 10, 7],\n [0, 0, -4, -2],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -1, 12, -7],\n [-8, -2, 11, -7],\n [5, -10, 12, -2],\n [-12, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
700
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 7, -4, -12],\n [-2, -2, -9, 9],\n [4, -9, 3, 7],\n [-3, 0, 5, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
588
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -5, 1, 10],\n [0, -12, -12, 8],\n [0, 0, -6, 8],\n [0, 0, 0, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
320
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -8, -12, -5],\n [-12, -3, 6, 3],\n [-3, -9, -6, -10],\n [-4, 7, 4, 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"
}
] |
620
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -2, -1, -8],\n [0, 8, 1, -7],\n [0, 0, -4, 5],\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"
}
] |
80
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[2, 0, 9, 3],\n [0, 6, -6, -3],\n [0, 0, -11, -8],\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"
}
] |
528
|
MATH
|
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