messages
listlengths
1
1
ground_truth
stringclasses
992 values
dataset
stringclasses
1 value
[ { "content": "Determine the value of det(A) where A =\n[[5, -7, 1, -9],\n [0, 3, 6, 12],\n [0, 0, 5, 9],\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" } ]
625
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, 3, 7, 1],\n [-8, 2, -2, 2],\n [0, 2, -12, 5],\n [-6, 12, -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" } ]
500
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 2, 1, -2],\n [2, -12, 6, 4],\n [1, 6, -12, 2],\n [-2, 4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
112
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -9, 12, -3],\n [0, -2, -6, 4],\n [0, 0, 7, -9],\n [0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
386
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 4, 1, 10],\n [0, -3, 8, 7],\n [0, 0, -10, -5],\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" } ]
180
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 11, 4, 0],\n [-11, 6, -12, 7],\n [6, -10, -4, -4],\n [9, -1, 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" } ]
712
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 0, -7, 2],\n [-3, 11, -12, 3],\n [1, -4, 0, 6],\n [10, 0, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
246
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -2, 4, -3],\n [3, 0, -12, -7],\n [-12, -5, 4, 8],\n [11, -1, 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" } ]
880
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 5, 12, -6],\n [2, -11, -8, 1],\n [4, 10, 2, 1],\n [-9, -5, -5, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
132
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, 11, 7, -10],\n [4, -10, 11, -2],\n [-1, -6, -10, 12],\n [0, 2, 0, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
586
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, 3, -6, 6],\n [-4, -10, -8, -7],\n [10, -8, -1, 7],\n [7, -11, -9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
209
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -11, 5, -3],\n [12, -4, 9, -9],\n [-12, 1, -11, 3],\n [-6, 5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
968
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -12, -6, -4],\n [-12, -6, 10, 5],\n [6, 7, 9, -7],\n [11, 0, 7, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
510
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -4, -12, -8],\n [-4, 9, 1, 2],\n [2, -5, -4, 2],\n [-9, -3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
858
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 0, 11, -9],\n [1, -6, 6, -8],\n [-8, 9, -5, -8],\n [-6, 4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
531
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -5, 8, -5],\n [0, -3, -3, 5],\n [0, 0, -5, -1],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
450
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, -12, 8, -2],\n [1, -6, 1, -8],\n [7, 2, 6, 9],\n [0, -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" } ]
280
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -4, 12, -4],\n [-4, 7, 2, -4],\n [12, 2, 3, -3],\n [-4, -4, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
612
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 8, 0, 5],\n [0, -12, 10, 8],\n [0, 0, 4, 0],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
656
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -5, -3, 1],\n [8, 11, -5, 0],\n [8, -9, -4, 3],\n [-6, 12, -10, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
895
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -5, 5, 3],\n [0, -3, -8, 1],\n [0, 0, 4, -12],\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" } ]
976
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 2, -2, -4],\n [2, -2, -2, 4],\n [-2, -2, 0, -2],\n [-4, 4, -2, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
592
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -7, 9, 1],\n [0, -9, 6, -3],\n [0, 0, 2, -1],\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" } ]
648
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 12, 3, -9],\n [-2, -8, 12, -3],\n [-3, 9, 8, 4],\n [-2, 3, -6, -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" } ]
351
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -3, 12, -1],\n [3, 12, 2, 6],\n [-5, -1, -10, 8],\n [12, -7, -2, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
310
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 4, 6, -2],\n [4, -7, 1, -2],\n [6, 1, -9, 2],\n [-2, -2, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 7, -11, -6],\n [7, 6, -4, 7],\n [-10, -2, -2, -3],\n [1, -12, 7, -11]]\nRound to the nearest integer, then take the result modulo 1000.\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[[5, -3, -9, 5],\n [-1, 10, -7, 4],\n [-5, -2, -9, 12],\n [9, -6, -9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
460
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -2, -9, -3],\n [1, -8, 11, -1],\n [-4, -10, -8, -5],\n [11, -12, 9, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
532
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 8, 6, -12],\n [0, -10, 12, 1],\n [0, 0, 9, 12],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 5, 0, 1],\n [5, -3, -1, 2],\n [0, -1, 0, -8],\n [1, 2, -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" } ]
747
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, -10, 6, 4],\n [3, -3, -7, 4],\n [-9, 0, -9, 8],\n [-5, -4, 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" } ]
524
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 11, -3, -7],\n [0, -12, -6, 7],\n [0, 0, -8, 2],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
288
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 9, 1, -2],\n [1, -1, 1, 6],\n [-6, 4, -3, -7],\n [0, 0, 7, 7]]\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[[-6, 10, -2, 4],\n [0, -8, -7, -12],\n [0, 0, -2, 8],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
520
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 0, 4, 1],\n [0, 3, 5, 12],\n [0, 0, -5, -5],\n [0, 0, 0, 4]]\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, 4, -2],\n [-4, -5, -6, -6],\n [4, -6, 2, 0],\n [-2, -6, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
518
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 12, -11, 9],\n [0, -4, -1, 8],\n [0, 0, 1, -2],\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" } ]
940
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 4, -10, 6],\n [4, 5, -1, -2],\n [-10, -1, 0, 2],\n [6, -2, 2, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
296
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 0, 8, 7],\n [0, -4, 11, -9],\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" } ]
520
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, -10, -5, -11],\n [0, 10, 4, 7],\n [0, 0, -11, 10],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 4, -4, -2],\n [4, -12, -3, 0],\n [-4, -3, 11, 6],\n [-2, 0, 6, -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" } ]
158
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 4, -7, 4],\n [4, -8, -2, 9],\n [-7, -2, 2, 2],\n [4, 9, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
61
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -7, 9, 7],\n [1, 8, -7, 7],\n [3, 8, -5, -12],\n [0, -3, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
237
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -8, -10, 12],\n [0, 11, 4, -5],\n [0, 0, -12, 8],\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" } ]
56
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 8, -1, 9],\n [0, -2, -2, -2],\n [0, 0, -5, 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" } ]
300
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, 1, 2, 10],\n [11, 9, -8, -11],\n [-8, -10, 9, -2],\n [-11, 8, -5, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
467
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -3, 4, -7],\n [-9, -6, -4, -1],\n [-10, 12, -2, -2],\n [4, 9, -12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
870
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 5, 5, -8],\n [0, 7, 6, 0],\n [0, 0, -7, -9],\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" } ]
236
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 6, 0, 0],\n [6, -3, -4, 2],\n [0, -4, 8, 8],\n [0, 2, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
656
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -11, -12, -5],\n [0, 0, -12, -2],\n [5, 9, 11, 7],\n [9, -6, -8, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
738
MATH
[ { "content": "Compute |A| for the matrix A =\n[[12, 1, 7, -12],\n [0, 6, -5, -4],\n [0, 0, -7, 11],\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" } ]
48
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 8, 1, -7],\n [0, -1, 3, 3],\n [0, 0, 5, -6],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
330
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, -5, 1, -2],\n [-5, -8, 0, -2],\n [1, 0, 1, 2],\n [-2, -2, 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" } ]
812
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 12, 3, 11],\n [0, -5, 12, 7],\n [0, 0, 8, 11],\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" } ]
360
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -2, -6, 6],\n [-3, -5, 6, 1],\n [-7, -7, -12, -5],\n [-11, 6, 10, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
312
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -1, -10, 4],\n [6, 1, -12, 0],\n [9, 7, 5, -3],\n [3, 4, -4, 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" } ]
949
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, -8, -3, -11],\n [0, 2, -10, 9],\n [0, 0, -12, 11],\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" } ]
856
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 9, 6, 2],\n [9, -3, 8, 1],\n [6, 8, -1, 2],\n [2, 1, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
495
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, -2, 10, 5],\n [-2, 0, 5, 0],\n [10, 5, -10, 0],\n [5, 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" } ]
660
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -1, -10, 0],\n [0, 3, 1, 3],\n [0, 0, -5, 11],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
270
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -4, 6, 8],\n [0, -10, 11, 7],\n [0, 0, -8, -4],\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" } ]
800
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -5, 8, 6],\n [0, 4, -6, -12],\n [0, 0, 12, 9],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
576
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -12, 2, -5],\n [-1, 12, -2, 7],\n [-3, 3, -1, -5],\n [9, 5, 11, -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" } ]
380
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 3, -9, -2],\n [4, 6, -1, 9],\n [-5, -9, -5, 0],\n [7, -2, 11, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
78
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -11, -4, -3],\n [0, 1, 3, -7],\n [-5, 3, 5, 12],\n [0, 7, 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" } ]
804
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 9, -11, -1],\n [10, 8, -11, 2],\n [-3, -5, -1, -8],\n [-12, -1, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
257
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 10, 9, -2],\n [0, 1, 5, -11],\n [0, 0, -10, -7],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
700
MATH
[ { "content": "What is the determinant of the matrix:\n[[-1, 5, 12, -11],\n [10, 11, 1, -6],\n [6, 11, -2, 5],\n [-3, 6, -8, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
133
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 11, 0, -1],\n [4, 9, 9, 12],\n [-3, 2, 4, 0],\n [7, 4, -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" } ]
653
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -3, -10, -2],\n [-1, 3, 2, 8],\n [4, -5, -5, 8],\n [12, 9, 5, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
258
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 8, 12, -11],\n [0, -9, -11, -6],\n [0, 0, -10, 12],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 5, 11, -12],\n [-8, 5, 11, -3],\n [5, -3, -4, -5],\n [2, 4, -11, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
627
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -6, -8, -1],\n [0, -9, 10, 5],\n [0, 0, 7, 7],\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" } ]
567
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -2, -12, 4],\n [9, -7, -3, 8],\n [-8, 4, -11, 3],\n [0, 12, -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" } ]
157
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -4, 2, 0],\n [-4, 0, -11, -2],\n [2, -11, 1, 4],\n [0, -2, 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" } ]
989
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 3, 7, 3],\n [3, 0, -4, 10],\n [-5, 9, -4, -2],\n [-11, 0, -4, 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" } ]
857
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 2, 10, -6],\n [0, 2, 2, -12],\n [0, 0, 11, -9],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
210
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, 3, -3, -8],\n [0, 1, -10, -5],\n [0, 0, -3, 12],\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" } ]
832
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 0, 6, 7],\n [0, 7, -2, 0],\n [6, -2, 3, 2],\n [7, 0, 2, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
539
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -1, 2, 3],\n [0, -12, -3, 7],\n [0, 0, 8, 6],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
832
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, 4, -11, 9],\n [0, 3, -3, 0],\n [0, 0, 4, 5],\n [0, 0, 0, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
560
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -2, 6, 8],\n [-2, -12, -4, 1],\n [6, -4, 7, -6],\n [8, 1, -6, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
419
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 6, 0, 1],\n [6, -5, 0, 0],\n [0, 0, 3, 8],\n [1, 0, 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" } ]
777
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, -6, 2, 6],\n [-6, 3, -7, -2],\n [2, -7, 7, -3],\n [6, -2, -3, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
58
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 7, 2, 1],\n [0, -9, -10, -10],\n [0, 0, 12, -9],\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" } ]
224
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -12, -1, 5],\n [0, -9, 8, 6],\n [0, 0, -1, -10],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
252
MATH
[ { "content": "Determine the value of det(A) where A =\n[[0, 6, -6, 2],\n [6, -2, -8, 2],\n [-6, -8, 12, 0],\n [2, 2, 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" } ]
608
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, -2, 2, 6],\n [-2, -1, 4, -6],\n [2, 4, -10, 5],\n [6, -6, 5, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
856
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 12, 6, 10],\n [-7, -7, -7, 2],\n [0, -7, 3, -5],\n [-7, 2, -1, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
472
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, -10, 7, 5],\n [-9, -2, 12, 10],\n [6, -7, -9, -7],\n [-9, -1, 4, -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" } ]
371
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 11, -9, -3],\n [7, -2, 12, 8],\n [-6, -7, -4, 10],\n [6, 7, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
999
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, 8, 6, -8],\n [8, 6, 2, 4],\n [6, 2, 3, 6],\n [-8, 4, 6, -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" } ]
72
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, -1, 4, 0],\n [7, -1, 12, -8],\n [10, 0, 6, 8],\n [7, 4, 5, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
210
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 9, 10, -8],\n [0, -1, 6, 3],\n [0, 0, 1, -2],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 6, -8, 1],\n [0, -1, 1, 1],\n [0, 0, 8, -9],\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" } ]
960
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, 6, 2, 5],\n [6, -11, 6, 6],\n [2, 6, -2, 4],\n [5, 6, 4, 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" } ]
254
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 0, -3, -5],\n [0, 9, -2, -6],\n [-3, -2, 6, -6],\n [-5, -6, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
832
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, -9, 10, -11],\n [0, 9, -4, 6],\n [0, 0, 9, 2],\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" } ]
757
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 6, 12, 7],\n [0, -8, 8, 1],\n [0, 0, -9, -3],\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" } ]
960
MATH