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[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -5, 0, -1],\n [-5, 5, -2, 3],\n [0, -2, 9, 8],\n [-1, 3, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
698
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -2, 2, 0],\n [-2, 4, -4, 6],\n [2, -4, -4, -8],\n [0, 6, -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" } ]
536
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -3, 0, -7],\n [0, -12, 1, -6],\n [0, 0, -10, -11],\n [0, 0, 0, 2]]\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[[-3, -6, -6, -4],\n [-5, 8, 1, 9],\n [-8, 6, -5, -8],\n [-6, 1, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
271
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 10, 8, 0],\n [10, 11, -3, -8],\n [8, -3, -5, -1],\n [0, -8, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
874
MATH
[ { "content": "What is the determinant of the matrix:\n[[12, 0, -8, 0],\n [0, 11, -2, 4],\n [-8, -2, 0, -4],\n [0, 4, -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" } ]
192
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, 10, -2, 12],\n [0, -2, 5, -6],\n [0, 0, -4, 11],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
640
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, -1, 2, -4],\n [0, -8, -1, -9],\n [0, 0, 10, -6],\n [0, 0, 0, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
720
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, 2, -12, -3],\n [2, 6, 1, 0],\n [-12, 1, 5, 2],\n [-3, 0, 2, -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" } ]
158
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -11, 5, 7],\n [-12, 3, 5, -10],\n [6, -11, -7, 0],\n [9, 12, -8, 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" } ]
18
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, 11, 10, 2],\n [0, 7, -5, 7],\n [0, 0, -9, -8],\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" } ]
930
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 8, 8, -7],\n [0, -9, -1, -9],\n [0, 0, -4, 4],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
976
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 2, -4, -6],\n [2, 7, -2, -1],\n [-4, -2, 12, 4],\n [-6, -1, 4, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
592
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 10, 9, -1],\n [8, 10, 7, -7],\n [-7, -10, 1, -11],\n [12, 6, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
796
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -1, 4, 0],\n [-1, -5, -3, -2],\n [4, -3, 6, -10],\n [0, -2, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
100
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, -8, -6, 2],\n [-8, -6, 6, -4],\n [-6, 6, 12, 2],\n [2, -4, 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" } ]
272
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 0, 5, 8],\n [0, -8, -3, 0],\n [5, -3, -7, 0],\n [8, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
962
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 12, -1, -4],\n [0, 1, 4, -11],\n [0, 0, 9, 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" } ]
720
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -3, -12, 5],\n [0, -3, -6, 4],\n [0, 0, 5, -6],\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" } ]
320
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, 6, -3, -4],\n [6, -7, 4, -5],\n [-3, 4, 3, 0],\n [-4, -5, 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" } ]
612
MATH
[ { "content": "What is the determinant of the matrix:\n[[-11, -4, -1, 4],\n [-4, -10, -2, 8],\n [-1, -2, 3, 0],\n [4, 8, 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" } ]
864
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 1, 6, 1],\n [-2, -12, 0, 8],\n [-8, -6, 6, -10],\n [11, 11, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
188
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, -9, 4, 7],\n [0, -3, 7, 1],\n [0, 0, -10, 7],\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" } ]
560
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, 0, 2, -6],\n [0, -3, 2, 4],\n [2, 2, -12, 6],\n [-6, 4, 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" } ]
136
MATH
[ { "content": "What is the determinant of the matrix:\n[[4, 4, -3, 5],\n [-11, -9, 7, -1],\n [-1, 1, -12, 9],\n [-8, 2, 5, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
234
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 1, 4, -11],\n [1, 5, 12, 5],\n [5, -7, -10, -5],\n [6, -5, -3, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
950
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[7, 10, -9, -3],\n [6, -8, 8, 1],\n [-10, -10, 8, 8],\n [-3, 0, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
402
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -4, 11, -2],\n [-3, 7, -1, 9],\n [-6, 11, -12, 3],\n [5, 7, -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" } ]
582
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 11, -10, -7],\n [0, -7, -4, -2],\n [0, 0, -3, -9],\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" } ]
168
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 6, 10, 5],\n [0, -4, 8, 3],\n [0, 0, -9, 3],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
320
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, -12, -6, -6],\n [-10, -12, -11, -10],\n [-8, -9, 4, 3],\n [12, 4, -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" } ]
884
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -11, 10, 6],\n [0, -8, -11, -3],\n [0, 0, -7, -8],\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" } ]
864
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, 10, -8, -5],\n [5, 1, 10, 11],\n [2, -11, -7, 12],\n [-12, -9, -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" } ]
303
MATH
[ { "content": "What is the determinant of the matrix:\n[[9, 10, 7, 6],\n [-6, -10, 6, 6],\n [-8, -6, 7, 6],\n [11, -4, 6, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
760
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, -12, 4, 6],\n [0, 4, 10, -8],\n [0, 0, 2, 7],\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" } ]
56
MATH
[ { "content": "What is the determinant of the matrix:\n[[-12, -2, -4, 1],\n [4, 5, -11, 10],\n [-9, -11, -1, 7],\n [-5, 3, -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" } ]
729
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 1, 2, -8],\n [1, 1, -11, 2],\n [2, -11, 9, -1],\n [-8, 2, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
207
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -2, -3, -2],\n [0, -2, 12, 11],\n [0, 0, -5, 0],\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" } ]
330
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -7, 0, 2],\n [-7, -1, -2, -2],\n [0, -2, 11, 4],\n [2, -2, 4, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
528
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, -3, 2, 4],\n [-7, 1, 11, 1],\n [-9, 5, 5, -8],\n [2, 9, -10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
642
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 1, -5, -8],\n [1, 2, 6, 6],\n [-5, 6, 0, 0],\n [-8, 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" } ]
946
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-7, -12, 6, -1],\n [0, -5, 4, -6],\n [0, 0, 8, 11],\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" } ]
920
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 9, -6, -9],\n [0, 5, -6, 7],\n [0, 0, -12, 2],\n [0, 0, 0, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Determine the value of det(A) where A =\n[[9, 0, 4, 9],\n [0, 2, 0, 0],\n [4, 0, 9, -10],\n [9, 0, -10, 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" } ]
732
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 8, 4, 0],\n [8, -12, -2, -5],\n [4, -2, -12, 3],\n [0, -5, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
392
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, -7, 9, 8],\n [6, -3, -1, 6],\n [10, -5, -5, -5],\n [9, 1, 9, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
870
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -11, 6, 8],\n [-3, 6, -9, -5],\n [10, -8, 7, -11],\n [1, 9, -9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
470
MATH
[ { "content": "Compute |A| for the matrix A =\n[[6, -5, -12, 7],\n [0, 7, -4, 12],\n [0, 0, -7, -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" } ]
352
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -4, 10, 0],\n [-4, 11, 0, -2],\n [10, 0, -4, 4],\n [0, -2, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
632
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, 10, 2, 0],\n [10, -10, 6, 3],\n [2, 6, 6, 3],\n [0, 3, 3, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
552
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, 2, -1, 0],\n [0, 7, 0, 12],\n [0, 0, 11, 7],\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" } ]
920
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 10, 8, -10],\n [-11, 12, 9, -6],\n [4, -6, 11, 2],\n [-12, 7, -11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
746
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 0, 6, -5],\n [0, 12, -6, 7],\n [0, 0, -1, 6],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
576
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 3, 9, -4],\n [5, 3, -4, -8],\n [-4, -9, 10, -11],\n [-6, 10, -6, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
625
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 0, -9, -5],\n [0, -1, -2, -8],\n [-9, -2, -8, 8],\n [-5, -8, 8, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
397
MATH
[ { "content": "Compute |A| for the matrix A =\n[[10, 3, 5, -12],\n [-3, -5, 9, -12],\n [1, -12, -5, -8],\n [3, 5, 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" } ]
531
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 10, 11, -9],\n [0, -7, -1, -11],\n [0, 0, 10, 11],\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" } ]
620
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -2, -6, -9],\n [0, 8, 9, -7],\n [0, 0, 7, -11],\n [0, 0, 0, 9]]\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[[2, 0, -10, -2],\n [0, -3, 2, 4],\n [-10, 2, -7, 12],\n [-2, 4, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
912
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 10, -4, -12],\n [0, 9, -3, -4],\n [0, 0, 10, -8],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
930
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -2, 9, 0],\n [0, 5, 7, 2],\n [0, 0, -5, 4],\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" } ]
100
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, 0, 7, 6],\n [3, 11, 1, 7],\n [-2, -4, -8, 4],\n [-2, -5, 12, -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" } ]
674
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -6, -1, -2],\n [-6, 5, 4, -5],\n [-1, 4, -6, 1],\n [-2, -5, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
654
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, -3, 2, 6],\n [-3, 1, 6, 4],\n [2, 6, -2, -4],\n [6, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -10, -4, -6],\n [0, 8, -6, -12],\n [0, 0, -4, -6],\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" } ]
760
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -2, -2, 2],\n [-2, 5, -8, -10],\n [-2, -8, -7, -9],\n [2, -10, -9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
590
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 1, 1, -7],\n [1, 8, 5, 0],\n [1, 5, 2, 2],\n [-7, 0, 2, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
637
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 11, -2, -2],\n [-10, 5, 8, -10],\n [12, 12, -11, -5],\n [5, 8, -9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
198
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, 4, 6, 11],\n [0, 8, 1, 9],\n [0, 0, -3, -6],\n [0, 0, 0, 6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
288
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, -4, -12, 0],\n [0, -6, 0, -2],\n [0, 0, 12, 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" } ]
640
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -8, -10, 0],\n [0, 8, -10, -3],\n [0, 0, 9, -1],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
728
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-11, 10, 2, 2],\n [10, -1, 4, 10],\n [2, 4, -12, -6],\n [2, 10, -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" } ]
620
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 1, 5, 7],\n [0, -8, -5, -1],\n [0, 0, 5, -2],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
640
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -2, 9, 12],\n [12, 8, 1, -1],\n [-5, -9, -7, 6],\n [5, -9, 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" } ]
529
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, -8, 8, 6],\n [-8, 9, 4, 2],\n [8, 4, -7, -7],\n [6, 2, -7, 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" } ]
964
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -5, 5, 3],\n [0, -11, -5, 1],\n [0, 0, -4, 9],\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, 4, -1, 6],\n [0, 6, 9, -3],\n [0, 0, 4, -2],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
360
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, -9, -8, -8],\n [-9, -10, -3, 8],\n [-8, -3, -12, -6],\n [-8, 8, -6, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
390
MATH
[ { "content": "Determine the value of det(A) where A =\n[[6, 9, -5, -5],\n [6, -8, -9, -6],\n [10, -6, -10, -1],\n [-7, -9, -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" } ]
247
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 5, 10, 2],\n [0, -10, -7, -11],\n [0, 0, 5, -11],\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" } ]
800
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, -6, -2, -4],\n [3, 9, 0, 6],\n [6, 8, -2, -8],\n [-3, 5, -5, -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" } ]
100
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, 11, -12],\n [4, 4, -12, 1],\n [5, 7, 0, -1],\n [5, -5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
652
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, -4, 12, -3],\n [0, 5, -5, -11],\n [0, 0, -3, -7],\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[[-2, -3, -3, 5],\n [-2, -11, 3, -11],\n [-9, -7, 6, 2],\n [8, -3, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
698
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 11, -10, -4],\n [0, 12, 8, 4],\n [0, 0, 9, 9],\n [0, 0, 0, 10]]\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[[5, 7, -6, 0],\n [-3, -3, 9, 4],\n [10, -6, -3, -3],\n [-10, 9, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
353
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 9, -5, 10],\n [0, 6, -2, 0],\n [0, 0, -9, -3],\n [0, 0, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
812
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 0, -2, -6],\n [0, -1, 2, 5],\n [-2, 2, 5, 2],\n [-6, 5, 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" } ]
5
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 4, -3, -6],\n [4, -5, -3, -2],\n [-3, -3, -6, 2],\n [-6, -2, 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" } ]
184
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, 6, 11, -2],\n [6, 8, -1, 10],\n [11, -1, 5, -3],\n [-2, 10, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
490
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, -12, 1, -9],\n [0, -8, 2, -8],\n [0, 0, -5, 10],\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" } ]
880
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 6, -12, 10],\n [-9, 10, -7, -1],\n [-8, 6, 1, 1],\n [0, 8, -7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
212
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 10, 1, 12],\n [-7, 7, -3, -3],\n [10, 10, 12, -6],\n [7, 1, 1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
240
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, -1, -4, 8],\n [-1, 10, 7, 2],\n [-12, -3, 3, 9],\n [1, -5, -9, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
415
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-3, -11, -7, -10],\n [0, -8, -2, -3],\n [0, 0, 4, 7],\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" } ]
576
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, 1, 0, -10],\n [1, 5, 0, 5],\n [0, 0, 10, 4],\n [-10, 5, 4, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
66
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-10, 9, 3, -2],\n [9, 11, -6, 4],\n [3, -6, 4, 0],\n [-2, 4, 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" } ]
791
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -7, 7, 6],\n [0, -12, -8, -5],\n [-4, -4, 0, -4],\n [-2, -9, -6, -1]]\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": "What is the determinant of the matrix:\n[[-5, 5, 6, -8],\n [5, -9, 8, -8],\n [6, 8, -2, 2],\n [-8, -8, 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" } ]
108
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -2, -2, -4],\n [-2, 0, 6, 7],\n [-2, 6, -6, -4],\n [-4, 7, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
560
MATH