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[ { "content": "What is the determinant of the matrix:\n[[-4, -10, 8, -6],\n [0, 10, 4, 4],\n [0, 0, -4, 8],\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" } ]
440
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 0, 0, -6],\n [0, 3, -7, -2],\n [0, -7, -6, 5],\n [-6, -2, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
228
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 6, 5, 8],\n [0, -7, 8, 0],\n [0, 0, 4, -9],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
616
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, -8, 7, -2],\n [6, -1, 5, 5],\n [10, -7, -3, 2],\n [10, 0, -11, 10]]? 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": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, -11, 12, -4],\n [-12, 0, 10, 12],\n [7, 0, 9, 2],\n [1, -9, 9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
402
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 0, 6, 10],\n [0, 7, 1, -4],\n [0, 0, 10, 1],\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" } ]
200
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 0, 4, -4],\n [0, 3, -5, -2],\n [4, -5, -3, -1],\n [-4, -2, -1, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
36
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, 0, -2, 0],\n [0, -10, 4, 1],\n [-2, 4, 7, -9],\n [0, 1, -9, -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" } ]
720
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 3, 5, 4],\n [0, -12, -8, 12],\n [0, 0, -10, -5],\n [0, 0, 0, 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" } ]
160
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 3, -11, -5],\n [-4, 10, 8, -6],\n [6, -9, -5, 2],\n [-5, -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" } ]
772
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -1, -8, 2],\n [0, 6, 3, -3],\n [0, 0, -4, 12],\n [0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
120
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, -4, 4, -3],\n [-4, 3, -6, -2],\n [4, -6, -4, -1],\n [-3, -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" } ]
116
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, -8, 5, 1],\n [-9, 5, 0, 5],\n [-8, 6, 12, -12],\n [-8, 0, 8, -6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
444
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, -8, 1, 7],\n [-8, -4, -5, 12],\n [1, -5, 5, 7],\n [7, 12, 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" } ]
605
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -10, 0, 5],\n [-10, 2, -5, -12],\n [0, -5, -8, -8],\n [5, -12, -8, 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" } ]
489
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, 2, -12, 5],\n [0, -6, 12, 6],\n [0, 0, 10, 5],\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" } ]
880
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -9, -9, -8],\n [0, -12, -8, -7],\n [0, 0, 3, 5],\n [0, 0, 0, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
324
MATH
[ { "content": "What is the determinant of the matrix:\n[[-9, 7, -3, -3],\n [0, -3, 1, -4],\n [0, 0, -3, 10],\n [0, 0, 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" } ]
838
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 1, -1, 8],\n [1, 12, -10, -2],\n [-1, -10, -6, 4],\n [8, -2, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
750
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -6, 10, 12],\n [9, 8, -12, 8],\n [-10, -9, -7, 7],\n [11, -7, 12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
650
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 5, 10, 7],\n [7, 4, -7, -1],\n [-2, 3, 7, -7],\n [10, -10, 12, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
183
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, -7, -5, 0],\n [0, 7, 3, -2],\n [0, 0, 4, 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" } ]
112
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 11, -4, -2],\n [0, -2, -8, -3],\n [0, 0, 6, -1],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
712
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -5, -10, 2],\n [1, 1, 3, -11],\n [-7, 0, -2, 8],\n [7, 12, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
365
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -2, 11, 7],\n [0, -2, 8, 9],\n [0, 0, 1, 7],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, 12, -6, -12],\n [-1, 5, 7, 8],\n [12, 0, 8, -11],\n [0, 12, -4, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
272
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -7, 6, 7],\n [-5, 9, 10, -8],\n [1, -9, 6, 9],\n [10, -10, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
776
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, 2, 6, 8],\n [2, -8, 3, 12],\n [6, 3, -6, 7],\n [8, 12, 7, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
988
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -3, -7, 5],\n [0, -3, 11, 5],\n [0, 0, 1, 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" } ]
18
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 10, -11, 9],\n [0, -7, -2, -6],\n [0, 0, -8, 7],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
344
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, -8, -10, -3],\n [0, 3, -10, 11],\n [0, 0, -10, -10],\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" } ]
810
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 9, 9, -2],\n [4, 7, 9, 10],\n [-2, 12, -2, -9],\n [-11, 11, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
644
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -11, 6, 1],\n [10, 2, 11, 3],\n [-1, -11, 3, 0],\n [-11, -5, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
752
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -9, 12, -3],\n [-6, -7, 1, 5],\n [8, -4, 8, 8],\n [7, 8, 8, 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" } ]
552
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -7, 5, 0],\n [11, -8, 0, 2],\n [3, -3, 11, -6],\n [6, -4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
784
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -10, 7, 4],\n [-10, 9, 3, 3],\n [7, 3, -3, -4],\n [4, 3, -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" } ]
600
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 2, -11, -7],\n [0, -8, 8, -7],\n [0, 0, 5, -7],\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" } ]
0
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -9, 6, -8],\n [12, -10, 9, -10],\n [10, -9, -6, -2],\n [0, -5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
298
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 10, 12, -2],\n [10, 12, 0, -1],\n [12, 0, 12, 2],\n [-2, -1, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
124
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, -2, 6, 4],\n [-2, -1, -5, -2],\n [6, -5, 0, -8],\n [4, -2, -8, -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" } ]
505
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 5, -3, 12],\n [0, 5, 0, 12],\n [0, 0, 1, -4],\n [0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
315
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -6, -4, -6],\n [-1, -10, -9, 3],\n [6, -6, -1, 2],\n [1, 2, 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" } ]
140
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, -5, -2, -9],\n [0, -4, -12, -12],\n [0, 0, 5, -4],\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" } ]
580
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -6, -6, -2],\n [-6, -9, 6, 1],\n [-6, 6, 5, -6],\n [-2, 1, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
827
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -7, 9, 11],\n [-6, -9, 2, -1],\n [9, 12, -9, 2],\n [1, 8, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
846
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 0, 6, 0],\n [0, -10, 0, 0],\n [6, 0, -7, -3],\n [0, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
340
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, -4, -7, 0],\n [-4, 8, 0, 0],\n [-7, 0, 5, -10],\n [0, 0, -10, 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" } ]
832
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -9, -5, -7],\n [0, -9, 11, 8],\n [0, 0, 12, -12],\n [0, 0, 0, 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" } ]
944
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 9, -1, 8],\n [0, 11, -1, 8],\n [0, 0, -4, 12],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
696
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, -4, -9, -1],\n [0, 4, -6, 12],\n [0, 0, 4, 12],\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" } ]
904
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -12, -12, 6],\n [0, -7, -4, -12],\n [0, 0, 7, 9],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
292
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 6, 3, -10],\n [-6, -8, 0, -9],\n [-3, -8, -7, 6],\n [4, 8, -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" } ]
810
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -4, 1, 3],\n [-4, 5, 6, 2],\n [1, 6, -1, -2],\n [3, 2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
323
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 5, 8, 10],\n [12, 3, 12, -1],\n [-6, -8, 10, 3],\n [-2, 8, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
512
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -2, 0, 2],\n [-2, 4, -3, -2],\n [0, -3, -7, -4],\n [2, -2, -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" } ]
684
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 4, 0, 0],\n [4, 0, -10, -4],\n [0, -10, -2, 4],\n [0, -4, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
676
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 8, 6, -3],\n [8, -1, -1, 2],\n [6, -1, -2, -11],\n [-3, 2, -11, -1]]\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[[2, 0, -3, 2],\n [0, -10, 5, -2],\n [-3, 5, -9, 3],\n [2, -2, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
128
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 1, -4, 9],\n [0, 8, 4, -5],\n [0, 0, -6, 0],\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" } ]
8
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, 11, -10, -11],\n [0, 5, -8, 10],\n [0, 0, 1, -12],\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" } ]
605
MATH
[ { "content": "Compute |A| for the matrix A =\n[[11, -7, 9, -12],\n [-6, 4, -4, -10],\n [9, -11, 11, 6],\n [9, 0, -3, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
328
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 0, -8, -8],\n [-8, -12, 9, -12],\n [-1, 3, -9, 8],\n [0, 12, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
773
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 2, -1, 8],\n [2, -2, -4, 7],\n [-1, -4, 6, -4],\n [8, 7, -4, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
395
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -2, 0, 4],\n [-2, 6, -2, -1],\n [0, -2, 11, 10],\n [4, -1, 10, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
555
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -4, 12, 1],\n [0, 5, -9, 3],\n [0, 0, 9, -9],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
730
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -4, 6, 8],\n [-3, -5, 8, -5],\n [-8, 5, 3, 4],\n [12, 2, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
988
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 8, -4, -7],\n [8, 7, 6, 2],\n [-4, 6, 1, 2],\n [-7, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
69
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 1, -8, -9],\n [0, 11, 7, 1],\n [0, 0, 3, 6],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
505
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -8, -8, -2],\n [-8, 3, 8, 0],\n [-8, 8, 11, -4],\n [-2, 0, -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" } ]
719
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -4, -1, -10],\n [-4, 1, -10, 12],\n [-1, -10, 10, 7],\n [-10, 12, 7, -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" } ]
516
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 8, 10, 12],\n [8, 7, -1, 4],\n [5, -10, -6, -5],\n [-11, -1, 5, -2]]\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[[8, -7, 11, 1],\n [6, -3, -8, 8],\n [-12, 7, -8, 11],\n [-7, -8, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
189
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, -11, 2, 11],\n [-12, -12, -10, -4],\n [-5, 7, 10, 6],\n [4, -3, -7, 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" } ]
742
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 2, 0, 1],\n [2, -5, 0, 2],\n [0, 0, -5, 2],\n [1, 2, 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" } ]
556
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 7, 6, 1],\n [12, 3, -5, 8],\n [6, -12, -1, -9],\n [-8, 10, 9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
990
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -4, 2, -6],\n [0, -12, 8, 2],\n [0, 0, 11, 6],\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" } ]
752
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -7, 4, -9],\n [2, -11, -1, -8],\n [-5, -7, 4, 8],\n [-6, -7, 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" } ]
386
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -12, -6, -10],\n [0, -12, 9, 7],\n [0, 0, -4, -12],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
568
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -8, 7, 1],\n [12, -1, 3, 11],\n [-11, 10, -8, -8],\n [-6, -9, 12, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
95
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -11, -5, 12],\n [0, -4, 1, -3],\n [0, 0, -4, 3],\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" } ]
384
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-9, 10, 5, 3],\n [-7, -12, -3, -5],\n [-4, 7, 5, -3],\n [-9, -7, -8, 9]]\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[[-3, -7, -11, -6],\n [-7, -4, -6, 7],\n [7, -10, 6, 0],\n [-5, 3, -8, 6]]\nRound to the nearest integer, then take the result 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[[-7, -1, 0, -2],\n [-1, 6, 2, 7],\n [0, 2, -9, -8],\n [-2, 7, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
107
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -1, -2, 5],\n [0, -2, -7, -1],\n [0, 0, 1, -4],\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" } ]
952
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -11, -2, 5],\n [-11, -2, 5, -8],\n [-2, 5, -1, 2],\n [5, -8, 2, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
989
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -6, -4, 0],\n [-6, 4, 2, -8],\n [-4, 2, 10, 2],\n [0, -8, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
980
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 0, -7, -4],\n [-9, 12, -6, -7],\n [6, 5, -10, 4],\n [4, 7, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
176
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -11, -2, 0],\n [3, -10, -11, -2],\n [0, -12, -5, 5],\n [-10, -11, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 2, -1, 3],\n [0, -10, 2, -9],\n [0, 0, -8, 12],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
280
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, -4, 11, 8],\n [-5, -12, 4, 5],\n [10, -12, 3, -3],\n [3, -5, 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" } ]
580
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -5, 10, 0],\n [0, -9, -11, -4],\n [0, 0, -10, 9],\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" } ]
930
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 7, -9, 9],\n [2, 0, 0, 5],\n [-10, 4, 0, 0],\n [-12, 5, 4, -11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
754
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, -12, 8, -9],\n [7, 0, 6, -10],\n [10, 12, 9, 8],\n [7, 9, 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" } ]
945
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 10, 5, 5],\n [10, 5, 1, -7],\n [5, 1, 2, 1],\n [5, -7, 1, -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" } ]
735
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 8, -6, 12],\n [0, 2, -7, -4],\n [0, 0, 12, 3],\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" } ]
704
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, 9, 8, -9],\n [0, -11, -12, -8],\n [0, 0, -9, 7],\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" } ]
30
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -8, 4, -4],\n [0, 8, 4, -5],\n [0, 0, -8, 8],\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" } ]
552
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 10, -10, 9],\n [9, -9, 12, -10],\n [5, 8, -11, 3],\n [0, -4, 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" } ]
622
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 2, 3, 4],\n [2, -8, 0, -6],\n [3, 0, -2, 5],\n [4, -6, 5, 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" } ]
552
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, -1, 7, -10],\n [0, -2, 3, 6],\n [0, 0, 3, 3],\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" } ]
792
MATH