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[ { "content": "Compute |A| for the matrix A =\n[[-5, 9, -3, 11],\n [-11, -8, 12, 11],\n [1, 5, 7, 5],\n [-11, 10, -10, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
658
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -9, 12, 10],\n [0, 6, 4, -10],\n [0, 0, -10, 4],\n [0, 0, 0, -5]]\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[[8, 6, -2, -9],\n [9, 10, 4, -10],\n [12, -3, 3, -7],\n [9, 7, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
451
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 5, 7, 8],\n [0, 5, -9, -11],\n [0, 0, 3, 3],\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" } ]
660
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 8, 1, -2],\n [8, -3, 2, 11],\n [1, 2, 5, -4],\n [-2, 11, -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" } ]
517
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -12, 0, 2],\n [0, -5, -12, 5],\n [0, 0, -11, 5],\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" } ]
550
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 4, -4, 4],\n [4, 3, 2, -2],\n [-4, 2, 4, -2],\n [4, -2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
232
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, -7, 10, 2],\n [0, -5, -10, -7],\n [0, 0, 5, 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" } ]
700
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -1, -6, -8],\n [-1, 3, 10, 6],\n [-6, 10, 9, -2],\n [-8, 6, -2, 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" } ]
948
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, -3, -3, -7],\n [-3, 10, 2, 0],\n [-3, 2, 6, 0],\n [-7, 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" } ]
980
MATH
[ { "content": "Determine the value of det(A) where A =\n[[11, 2, 6, 7],\n [2, -8, -4, 10],\n [6, -4, 11, 0],\n [7, 10, 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" } ]
84
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, 1, -8, 9],\n [-1, 11, 9, -4],\n [1, 4, -4, 3],\n [12, -1, -4, 11]]\nRound to the nearest integer, then take the result modulo 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[[-7, 3, -5, 6],\n [3, -7, -2, 7],\n [-5, -2, -11, 0],\n [6, 7, 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" } ]
796
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -7, 11, -10],\n [-12, 9, -5, 12],\n [6, -11, 3, -11],\n [-9, -3, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
360
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-12, 0, -3, -7],\n [0, -5, 6, -5],\n [-3, 6, 10, 10],\n [-7, -5, 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" } ]
646
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 6, 2, -4],\n [6, 9, 4, 0],\n [2, 4, 12, -6],\n [-4, 0, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
932
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -8, -4, -6],\n [-8, 3, 2, 4],\n [-4, 2, 12, 8],\n [-6, 4, 8, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
824
MATH
[ { "content": "What is the determinant of the matrix:\n[[11, -3, -5, 8],\n [0, 11, 4, -1],\n [0, 0, 4, -9],\n [0, 0, 0, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
192
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, 4, 0, 2],\n [4, -11, -1, 0],\n [0, -1, 5, -12],\n [2, 0, -12, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 0, 1, -11],\n [0, 7, -11, 10],\n [0, 0, -9, 0],\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" } ]
575
MATH
[ { "content": "Determine the value of det(A) where A =\n[[12, -3, 8, 5],\n [-8, -12, 3, -7],\n [-4, 7, -6, -9],\n [12, -7, 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" } ]
904
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 0, 7, 0],\n [0, -10, 2, -6],\n [7, 2, -7, -2],\n [0, -6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
854
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 2, -12, -5],\n [0, -1, 6, 10],\n [0, 0, 11, -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" } ]
528
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 9, 5, 9],\n [0, 10, 10, 9],\n [0, 0, 1, -11],\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" } ]
250
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -10, 11, -11],\n [3, -4, 11, -1],\n [1, 10, 4, -1],\n [9, -9, -3, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
462
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, 12, -6, -2],\n [8, 5, 1, 6],\n [-4, -10, 8, 1],\n [12, 8, -3, -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" } ]
691
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 6, 1, -7],\n [6, 2, 2, 11],\n [12, -3, 11, -8],\n [10, -5, -5, 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" } ]
516
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -5, -3, -4],\n [0, 7, -6, -8],\n [0, 0, 4, 1],\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" } ]
896
MATH
[ { "content": "What is the determinant of the matrix:\n[[-7, -4, -3, -2],\n [-4, 1, 4, 0],\n [-3, 4, -12, 10],\n [-2, 0, 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" } ]
42
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 12, -12, 3],\n [0, 10, -3, -8],\n [0, 0, 3, 9],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
740
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 1, -1, 0],\n [0, 10, -11, -9],\n [0, 0, 2, 7],\n [0, 0, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
380
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -2, -4, 4],\n [-2, 8, -8, -2],\n [-4, -8, -9, 3],\n [4, -2, 3, -1]]? 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": "What is the determinant of the matrix:\n[[8, 11, 8, 12],\n [0, -1, 5, 1],\n [0, 0, -8, 1],\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" } ]
64
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 6, -2, 8],\n [6, -5, 0, -7],\n [-2, 0, 12, 0],\n [8, -7, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
192
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, -9, -3, 5],\n [-8, 5, 4, 9],\n [-8, 5, -3, -8],\n [1, -2, -9, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
874
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 12, 10, -2],\n [0, 5, 8, -5],\n [0, 0, -1, -7],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
360
MATH
[ { "content": "Determine the value of det(A) where A =\n[[10, 1, -10, 1],\n [-1, -3, -4, 3],\n [-10, 9, 8, 10],\n [-6, 10, -9, 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" } ]
749
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -1, -6, 0],\n [-1, 9, 8, 6],\n [-6, 8, 10, 6],\n [0, 6, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
496
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 1, -8, -5],\n [1, 1, 0, -4],\n [-8, 0, -12, -7],\n [-5, -4, -7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
885
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 5, 5, -3],\n [4, -2, -7, 6],\n [-12, -12, -1, 3],\n [2, -8, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
662
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 8, -9, 0],\n [8, 9, -5, -4],\n [-9, -5, -12, 11],\n [0, -4, 11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
384
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 5, -7, 0],\n [0, 6, 10, 3],\n [0, 0, 11, 6],\n [0, 0, 0, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
584
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -9, -3, 4],\n [0, 7, -6, -5],\n [0, 0, 3, -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" } ]
950
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -6, 6, 8],\n [0, -2, 0, -12],\n [0, 0, 4, -2],\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": "What is the determinant of the matrix:\n[[-1, -2, 2, -4],\n [-2, 0, -4, 0],\n [2, -4, 6, 0],\n [-4, 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" } ]
496
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 9, -7, 8],\n [0, -10, 1, 12],\n [0, 0, -7, -1],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
600
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 4, 8, -1],\n [0, 9, 8, 7],\n [0, 0, 10, 5],\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": "Determine the value of det(A) where A =\n[[2, 9, 2, 6],\n [1, -10, 7, -6],\n [-3, 6, 12, 6],\n [-7, 6, 7, -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" } ]
692
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -2, -2, -2],\n [-2, -1, -8, -1],\n [-2, -8, 7, -2],\n [-2, -1, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
568
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -1, 12, 4],\n [-1, 1, 2, 2],\n [12, 2, -5, 4],\n [4, 2, 4, -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[[-6, 8, 4, 4],\n [8, -5, -9, -3],\n [4, -9, -1, 10],\n [4, -3, 10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
162
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 12, 2, -4],\n [12, 5, 2, 4],\n [2, 2, 9, 10],\n [-4, 4, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
456
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 7, 10, 11],\n [0, -2, -7, 8],\n [0, 0, 5, 4],\n [0, 0, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
120
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -11, -10, 7],\n [0, 9, 11, -5],\n [0, 0, -5, -8],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
800
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -11, 1, -1],\n [-11, -5, 8, 10],\n [1, 8, -11, -6],\n [-1, 10, -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" } ]
716
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, -7, -4, 1],\n [-7, -9, 4, -8],\n [-4, 4, 9, 5],\n [1, -8, 5, 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" } ]
761
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -8, -11, -11],\n [0, -9, -1, -6],\n [0, 0, 3, -1],\n [0, 0, 0, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
650
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 11, 1, -4],\n [2, 7, -6, -7],\n [-12, -9, 4, -2],\n [-3, 9, 11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
438
MATH
[ { "content": "What is the determinant of the matrix:\n[[8, 12, -10, 5],\n [9, 6, -11, 2],\n [-7, 4, 12, -2],\n [-10, 7, 9, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
631
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -12, 12, 11],\n [0, -9, 4, 1],\n [0, 0, -2, -8],\n [0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
720
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 0, 1, 7],\n [0, -12, 4, -2],\n [1, 4, -10, -2],\n [7, -2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
260
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -8, 7, -1],\n [4, -12, 5, -3],\n [-9, 10, -6, -1],\n [12, -1, 7, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
823
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, -10, -2, -3],\n [0, 6, 2, 5],\n [0, 0, 11, 12],\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" } ]
40
MATH
[ { "content": "Compute |A| for the matrix A =\n[[8, 4, 12, 0],\n [-1, 7, 7, -8],\n [-1, 5, -12, -1],\n [5, 2, 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" } ]
412
MATH
[ { "content": "What is the determinant of the matrix:\n[[-4, -3, -4, 2],\n [-3, 4, -2, 10],\n [-4, -2, 1, 6],\n [2, 10, 6, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
242
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, -2, -4, 5],\n [-2, 2, 4, -6],\n [-4, 4, 11, -1],\n [5, -6, -1, -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" } ]
274
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-11, -9, -7, -2],\n [-9, 2, 0, 4],\n [-7, 0, 9, -2],\n [-2, 4, -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" } ]
850
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -6, 9, -6],\n [-6, -10, 8, -8],\n [7, 6, 4, -2],\n [-9, -7, -8, 9]]\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[[0, -2, 6, -4],\n [-2, 10, 0, 1],\n [6, 0, -12, -2],\n [-4, 1, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
948
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 7, 11, -1],\n [7, 11, 6, 3],\n [-12, 9, 7, -8],\n [6, -11, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
688
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -1, 6, -10],\n [0, -3, -7, 12],\n [0, 0, -12, -11],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
892
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 10, 4, 10],\n [0, 3, -6, -1],\n [0, 0, -1, 1],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
54
MATH
[ { "content": "Compute |A| for the matrix A =\n[[2, -1, 2, -9],\n [-1, -3, 2, 4],\n [2, 2, 0, -2],\n [-9, 4, -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" } ]
424
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, -4, 5, -3],\n [-4, -7, 4, 0],\n [5, 4, 4, -1],\n [-3, 0, -1, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
212
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, 0, 0, -8],\n [0, -12, 8, -2],\n [0, 8, 11, -2],\n [-8, -2, -2, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
220
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 0, -1, -1],\n [0, 1, 7, 4],\n [-1, 7, 0, 4],\n [-1, 4, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
43
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -9, -2, 7],\n [0, -8, 2, 12],\n [0, 0, 8, -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" } ]
384
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 0, 4, 0],\n [-10, 0, 4, 2],\n [7, -2, -6, 1],\n [8, -3, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
80
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-12, -8, -2, -11],\n [0, -9, 8, -10],\n [0, 0, 6, -8],\n [0, 0, 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" } ]
464
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -8, 6, -5],\n [-2, -4, -6, -6],\n [10, -4, 10, -4],\n [6, 3, -5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
336
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -9, 9, -7],\n [6, 2, -12, -4],\n [6, -1, -3, 9],\n [2, 8, 9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
850
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, 8, -3, 3],\n [8, 0, 8, -2],\n [-3, 8, 2, -3],\n [3, -2, -3, -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" } ]
236
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, -4, -12, 4],\n [0, 1, 1, 9],\n [0, 0, 1, -1],\n [0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
45
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 0, 6, 5],\n [0, -10, 8, 7],\n [6, 8, 7, 3],\n [5, 7, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
856
MATH
[ { "content": "What is the determinant of the matrix:\n[[1, 7, 4, 2],\n [7, 6, -3, -4],\n [4, -3, -6, -8],\n [2, -4, -8, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
220
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, 7, -8, 8],\n [3, -1, 2, -7],\n [-2, -8, 2, -12],\n [-2, -6, 9, -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" } ]
348
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 11, 8, -5],\n [0, 2, 3, 2],\n [0, 0, 3, 0],\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" } ]
18
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, -8, 6, -1],\n [-8, -1, -2, 9],\n [6, -2, -5, -10],\n [-1, 9, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
587
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -3, -8, 4],\n [-3, -6, -1, -3],\n [-8, -1, 10, 6],\n [4, -3, 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" } ]
106
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, -5, 2, 3],\n [0, 9, 1, 10],\n [0, 0, 4, 4],\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" } ]
564
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -1, -5, -12],\n [8, -5, -3, -1],\n [4, -8, 0, 11],\n [-3, 12, -12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
722
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-4, 6, -4, 0],\n [6, -1, 4, 2],\n [-4, 4, 11, -3],\n [0, 2, -3, 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" } ]
720
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 8, 0, 2],\n [8, 1, 9, 1],\n [0, 9, 5, -2],\n [2, 1, -2, 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" } ]
421
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 0, 2, 0],\n [0, -1, -4, 9],\n [2, -4, 10, 4],\n [0, 9, 4, -8]]\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[[-10, -10, 9, -9],\n [10, -12, 2, 5],\n [12, -1, -12, 6],\n [-1, 7, 11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
437
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 0, 12, -9],\n [0, -1, 3, -3],\n [0, 0, 1, 4],\n [0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, 2, -2, 4],\n [0, -3, 5, 2],\n [2, 5, -6, 10],\n [11, 10, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
856
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-5, 1, 7, -8],\n [0, 11, -5, 8],\n [0, 0, -5, -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" } ]
375
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 2, -12, -7],\n [0, 7, -3, -5],\n [0, 0, 4, 3],\n [0, 0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
680
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-9, -8, 2, 10],\n [-8, 2, 1, 6],\n [2, 1, -7, -1],\n [10, 6, -1, -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" } ]
442
MATH