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[[5, 3, 5, -5],\n [0, -6, -6, 3],\n [0, 0, -11, -7],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
340
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -12, 4, -3],\n [-7, 11, -9, 8],\n [4, -5, -4, 7],\n [-11, -5, -8, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
928
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 8, -8, 10],\n [8, -2, -5, -1],\n [-8, -5, -5, 4],\n [10, -1, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 9, 8, -10],\n [10, -2, 7, -9],\n [8, 8, -4, 11],\n [12, 8, 3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
944
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 5, 12, -10],\n [9, -6, -10, -6],\n [2, -8, 8, -5],\n [1, 12, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
734
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 6, -4, -7],\n [-5, -9, 12, 9],\n [-1, -2, 1, 0],\n [-6, -1, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
29
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -6, -12, -7],\n [-7, 3, -8, 0],\n [-1, -9, 0, -1],\n [-1, 8, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
424
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -2, 7, -11],\n [0, 5, 2, -9],\n [0, 0, -4, 3],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
900
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, -6, -9, 11],\n [0, 6, 8, 4],\n [0, 0, 1, -1],\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"
}
] |
126
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -12, 0, 10],\n [10, -5, -2, -3],\n [-4, 7, -5, -6],\n [-7, 7, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
969
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -4, 1, -2],\n [-3, 5, 4, 7],\n [7, -1, 5, 4],\n [8, 7, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
880
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 11, 0, -3],\n [0, -1, -6, 8],\n [0, 0, 4, 10],\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"
}
] |
920
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, -8, 0, -5],\n [-8, -2, 2, -6],\n [0, 2, -9, 0],\n [-5, -6, 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"
}
] |
880
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 7, 1, 3],\n [-10, 6, 11, -4],\n [-11, -9, -10, -11],\n [6, 5, 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"
}
] |
534
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 7, -12, 5],\n [0, 1, -8, -4],\n [0, 0, -10, 5],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
900
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[12, -6, -12, 4],\n [4, -10, 8, -10],\n [9, 3, 0, -11],\n [-1, 2, 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"
}
] |
920
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-6, -3, -2, -2],\n [6, 8, -1, -3],\n [-11, 1, -6, 9],\n [-11, -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"
}
] |
601
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 4, 3, 2],\n [4, 2, 0, 2],\n [3, 0, -3, -9],\n [2, 2, -9, -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"
}
] |
12
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -8, -11, -4],\n [6, 11, 0, 1],\n [-9, 6, 9, -1],\n [4, -12, -12, 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"
}
] |
778
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[5, -6, 2, -7],\n [8, -4, 6, 0],\n [-6, 8, -11, 11],\n [9, -8, -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"
}
] |
980
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[4, 6, -6, -6],\n [-3, -11, -8, -5],\n [9, 4, 2, 6],\n [-4, 3, -1, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
742
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[6, 4, 7, -2],\n [4, -1, 7, 0],\n [7, 7, 0, -2],\n [-2, 0, -2, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
621
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -5, 12, -5],\n [0, -5, 8, 2],\n [0, 0, -10, 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"
}
] |
0
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-4, 2, 12, 2],\n [2, -8, -9, -2],\n [11, -8, 0, 2],\n [6, -7, 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"
}
] |
916
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 1, -10, -6],\n [4, 12, 4, 1],\n [12, -1, 1, -2],\n [3, -3, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
615
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -5, -9, 2],\n [-9, -6, 1, -10],\n [-6, 8, 2, 10],\n [12, -9, 7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
768
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, 12, 11, -8],\n [-9, -8, -11, -7],\n [-2, -3, 3, 7],\n [11, 5, -8, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
630
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 9, 7, 10],\n [0, 3, -4, -5],\n [0, 0, 5, -1],\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"
}
] |
845
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 0, -2, 8],\n [0, -10, 2, 12],\n [-2, 2, -1, -3],\n [8, 12, -3, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
778
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 11, -1, 9],\n [0, 1, -6, 2],\n [0, 0, 10, 12],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
800
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 7, 1, -6],\n [0, -12, -7, 3],\n [0, 0, 12, 7],\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"
}
] |
416
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, 0, 6],\n [-2, -5, -4, 6],\n [0, -4, 10, 0],\n [6, 6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
916
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[5, -9, -3, 0],\n [-5, -4, -2, -4],\n [-9, -8, -9, -9],\n [-7, 12, -8, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
284
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, -7, -2, 2],\n [-7, 4, 4, 2],\n [-2, 4, -4, -1],\n [2, 2, -1, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
517
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 6, -3, 0],\n [6, 4, -2, -1],\n [-3, -2, -2, -5],\n [0, -1, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
547
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 4, -1, -4],\n [4, 10, -10, -4],\n [-1, -10, 10, 6],\n [-4, -4, 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"
}
] |
480
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 10, 5, 2],\n [11, 8, -6, -10],\n [-4, 1, 3, 10],\n [5, -9, -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"
}
] |
180
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -5, 6, -11],\n [0, -10, 6, -11],\n [0, 0, 2, -6],\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[[11, -1, 12, -10],\n [0, -11, -1, -11],\n [0, 0, 3, 2],\n [0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
822
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -9, -4, -12],\n [-11, 5, 0, -1],\n [9, 0, -1, 7],\n [-11, -1, 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"
}
] |
957
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 2, -1, 1],\n [2, -9, -3, -8],\n [-1, -3, -2, 8],\n [1, -8, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
699
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 3, 9, -2],\n [0, -10, -3, -2],\n [0, 0, -5, -1],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
200
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 4, -8, -6],\n [0, 9, 0, 12],\n [0, 0, 10, 1],\n [0, 0, 0, -4]]\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[[0, -12, -7, -9],\n [-5, -4, -8, 4],\n [3, -3, 9, -10],\n [0, -2, -7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
463
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, -2, 4, 2],\n [-2, 6, -7, -2],\n [4, -7, -4, -8],\n [2, -2, -8, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
376
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[12, 12, 10, 11],\n [0, -1, -12, -9],\n [0, 0, -3, 6],\n [0, 0, 0, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
324
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 11, -2, 4],\n [11, -1, -2, 1],\n [-2, -2, 12, 10],\n [4, 1, 10, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
776
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 2, 9, 6],\n [4, 2, 8, -5],\n [-7, 2, 3, -1],\n [-8, 11, -7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
833
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 6, 2, -10],\n [0, 11, 9, -8],\n [0, 0, -2, 8],\n [0, 0, 0, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
386
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-9, 0, -7, -2],\n [0, 9, -7, -12],\n [0, 0, 11, -4],\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"
}
] |
763
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -11, -12, -9],\n [-8, -10, -5, 2],\n [8, 9, 5, 6],\n [3, 6, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
873
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[10, -2, -2, -5],\n [-2, -5, -1, 7],\n [-2, -1, 8, -3],\n [-5, 7, -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"
}
] |
315
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -1, 2, 11],\n [-1, 10, 6, 3],\n [2, 6, 2, 4],\n [11, 3, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
486
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -3, -4, 0],\n [-2, 5, 9, 7],\n [10, 9, 4, 8],\n [0, 3, 5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
152
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[1, -10, -8, -1],\n [0, 5, 7, -8],\n [-9, 1, -3, -7],\n [1, 3, -2, 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"
}
] |
976
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -9, -1, -1],\n [11, 3, -11, 9],\n [-5, 12, -9, 7],\n [-7, -8, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
585
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 2, 8, 5],\n [2, -8, 4, 6],\n [8, 4, 9, 0],\n [5, 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"
}
] |
800
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[7, 8, 0, 1],\n [8, -3, -4, -3],\n [0, -4, -1, 3],\n [1, -3, 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"
}
] |
585
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -7, 3, -11],\n [0, 11, 12, -1],\n [0, 0, -10, 3],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
160
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -12, 5, 12],\n [0, 3, 8, -10],\n [0, 0, 2, 2],\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"
}
] |
340
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 4, -2, 0],\n [4, 8, -1, 8],\n [-2, -1, -7, 3],\n [0, 8, 3, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
691
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -8, 0, -11],\n [8, -11, -6, 9],\n [-3, -1, -7, 9],\n [-2, 6, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
261
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 4, -7, -7],\n [0, -12, 1, -11],\n [0, 0, 4, -3],\n [0, 0, 0, 10]]\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[[12, -11, 4, 6],\n [0, 4, 3, 8],\n [0, 0, 1, 2],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 0, -2, -2],\n [0, 0, 8, -8],\n [-2, 8, 7, 0],\n [-2, -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"
}
] |
976
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 5, 1, -4],\n [5, 9, 0, 3],\n [1, 0, 5, 6],\n [-4, 3, 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"
}
] |
53
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[12, 3, 0, 1],\n [3, 2, -3, 0],\n [0, -3, -11, 4],\n [1, 0, 4, 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"
}
] |
679
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -6, 0, -6],\n [-6, 1, -4, 9],\n [0, -4, 5, -4],\n [-6, 9, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
54
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -2, -7, 10],\n [0, 7, 9, 3],\n [0, 0, 11, -6],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
623
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -3, 7, -9],\n [-10, -8, -2, -7],\n [-3, -6, 9, -9],\n [4, 1, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
135
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -3, 12, 6],\n [8, -2, 12, -2],\n [3, -3, -3, -12],\n [0, -9, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
996
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[6, -9, -5, -5],\n [0, 1, 4, 8],\n [0, 0, -7, 9],\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"
}
] |
832
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-2, 6, 9, 6],\n [0, 6, -8, 10],\n [0, 0, 4, -2],\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"
}
] |
616
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-7, 2, -10, -2],\n [2, 3, 0, 1],\n [-10, 0, 7, 2],\n [-2, 1, 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"
}
] |
629
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 1, -1, -1],\n [1, -9, 0, 6],\n [-1, 0, -1, 4],\n [-1, 6, 4, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
559
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 0, 4, 2],\n [0, -2, -4, -10],\n [4, -4, 9, 2],\n [2, -10, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
298
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -3, -9, -6],\n [0, 9, 2, 12],\n [0, 0, 7, 2],\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"
}
] |
315
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -1, -11, 10],\n [0, 12, -7, 12],\n [0, 0, 6, -6],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
88
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -6, -2, -7],\n [2, -11, -6, 8],\n [3, -7, 4, -10],\n [-3, 9, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
338
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[-12, -2, 10, -2],\n [0, -1, -9, -6],\n [0, 0, 5, -9],\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"
}
] |
400
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -6, -1, 6],\n [-6, -11, 0, -2],\n [-1, 0, -1, 2],\n [6, -2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
84
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -12, -10, 7],\n [5, -7, 8, 3],\n [-7, -5, -4, 8],\n [9, -1, 6, -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"
}
] |
850
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 6, -8, -10],\n [-11, -12, -12, 3],\n [5, -12, -11, 0],\n [9, -10, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
320
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[10, 4, -1, 2],\n [12, -5, 9, 4],\n [-4, -3, -12, -12],\n [2, -9, 3, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
408
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 3, 6, 0],\n [3, 10, -8, -2],\n [6, -8, -10, 1],\n [0, -2, 1, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
721
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 1, 8, -9],\n [0, 5, 12, 9],\n [0, 0, 5, -5],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
100
|
MATH
|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -6, -1, -6],\n [0, 6, 7, -4],\n [0, 0, 2, 1],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
600
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[3, -3, 4, -10],\n [-9, -5, 3, 5],\n [-5, 7, -8, 3],\n [-10, -8, -7, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
520
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[7, -6, 9, 10],\n [0, 8, -6, 12],\n [0, 0, 1, -2],\n [0, 0, 0, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
664
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -4, -2, -4],\n [-4, -10, 5, 6],\n [-2, 5, 2, 6],\n [-4, 6, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
350
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 9, -11, -11],\n [6, -12, 0, 12],\n [-2, -8, 8, -9],\n [2, 8, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
364
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -2, 2, 10],\n [-2, 2, -1, 1],\n [2, -1, 3, 0],\n [10, 1, 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"
}
] |
614
|
MATH
|
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -7, -6, -3],\n [-10, 6, 11, -9],\n [-10, 11, 8, -8],\n [-8, 10, -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"
}
] |
854
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[8, -2, 6, -8],\n [0, 1, 3, 8],\n [0, 0, 12, -5],\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"
}
] |
616
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 2, 6, 11],\n [2, 7, 0, -4],\n [6, 0, 0, 6],\n [11, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
60
|
MATH
|
[
{
"content": "What is the determinant of the matrix:\n[[11, 6, -2, 7],\n [0, -4, 11, -8],\n [0, 0, 6, 8],\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"
}
] |
680
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[10, 1, -5, -10],\n [0, 2, -4, 9],\n [7, -4, 7, 8],\n [0, 5, 7, 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"
}
] |
236
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -6, 11, -2],\n [-8, 5, -9, 8],\n [8, 5, 12, 9],\n [4, 6, -10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
299
|
MATH
|
[
{
"content": "Determine the value of det(A) where A =\n[[11, -10, 9, 5],\n [-4, -2, 10, -2],\n [-11, -3, -10, -1],\n [9, -3, 8, 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"
}
] |
972
|
MATH
|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 4, 6, 0],\n [4, -2, 3, 2],\n [6, 3, -3, -8],\n [0, 2, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
108
|
MATH
|
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