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[ { "content": "Determine the value of det(A) where A =\n[[-9, -6, -3],\n [-5, -2, 6],\n [5, -4, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
418
MATH
[ { "content": "Determine the value of det(A) where A =\n[[3, 2, -7],\n [2, 1, -2],\n [-7, -2, 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" } ]
993
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-1, 0, 0],\n [0, -7, -7],\n [0, -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" } ]
979
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -7, 0],\n [0, 1, 7],\n [0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -3, -6],\n [-4, 2, 8],\n [6, 10, 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" } ]
234
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -2, 10],\n [0, -8, 1],\n [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" } ]
64
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 2, 7],\n [2, -7, -6],\n [7, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
697
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 1, 3],\n [0, -9, 6],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
820
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-6, 0, 0],\n [0, -10, 0],\n [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" } ]
180
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, 0, -4],\n [0, 2, 8],\n [-4, 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" } ]
280
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -4, 9],\n [0, -8, 10],\n [0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
920
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 0, 8],\n [0, -1, 8],\n [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" } ]
100
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -4, -2],\n [-4, -9, 1],\n [-2, 1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
528
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, -7, -5],\n [0, -3, 10],\n [0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
928
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, -2, 0],\n [-2, -9, 6],\n [0, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
532
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-7, -1, -6],\n [0, 0, 10],\n [6, -8, -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" } ]
380
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 2, -6],\n [9, -10, 4],\n [-5, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
896
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -3, 2],\n [-3, -6, 0],\n [2, 0, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
297
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -6, 6],\n [0, 7, -10],\n [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" } ]
860
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 7, -2],\n [0, -8, 2],\n [3, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
546
MATH
[ { "content": "What is the determinant of the matrix:\n[[-5, -5, 4],\n [5, 5, 4],\n [-1, 3, -9]]? Round to the nearest integer, then express your answer modulo 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[[1, 7, 0],\n [0, -9, 10],\n [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" } ]
81
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 5, 3],\n [5, 4, -4],\n [3, -4, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
807
MATH
[ { "content": "What is the determinant of the matrix:\n[[-2, -6, -4],\n [-6, -3, 4],\n [-4, 4, 0]]? 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, 2],\n [-6, 10, 6],\n [-3, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
464
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 0, 8],\n [0, -3, 2],\n [8, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
198
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 4, 0],\n [4, -5, 2],\n [0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
696
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -1, -8],\n [-1, 2, -4],\n [-8, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
842
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 3, 4],\n [3, 4, 10],\n [4, 10, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
287
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-10, 2, -5],\n [2, 10, 2],\n [-5, 2, 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" } ]
918
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 5, 8],\n [0, -4, 6],\n [5, -10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
618
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -4, 0],\n [-4, -7, -5],\n [4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
632
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, 1, 4],\n [1, 2, 0],\n [4, 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" } ]
932
MATH
[ { "content": "Determine the value of det(A) where A =\n[[8, 5, 7],\n [0, 8, -3],\n [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" } ]
552
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[4, 6, -2],\n [0, -6, 8],\n [0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
144
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 6, 3],\n [-8, -10, 3],\n [0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
637
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 2, 7],\n [0, -6, -9],\n [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" } ]
216
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-8, 8, 4],\n [0, -10, 8],\n [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" } ]
240
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, -6, 8],\n [-4, 8, -8],\n [-2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
152
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -10, 10],\n [10, -2, 0],\n [2, -9, 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" } ]
140
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 0, -2],\n [0, 8, 2],\n [-2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
968
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -3, -2],\n [-3, -2, -3],\n [-2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
44
MATH
[ { "content": "Determine the value of det(A) where A =\n[[4, 8, 3],\n [-1, 3, -9],\n [-2, -10, -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" } ]
712
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -5, 2],\n [0, -6, -9],\n [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": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 9, 3],\n [-9, -1, -3],\n [-10, 9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
764
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -3, 0],\n [-9, -10, -2],\n [-3, 1, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
436
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 8, -7],\n [9, -10, 10],\n [9, -10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
342
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 4, 1],\n [4, 3, -7],\n [10, -9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
43
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -10, -10],\n [0, -7, -3],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
63
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-1, -5, 9],\n [0, -3, -8],\n [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" } ]
12
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -6, -3],\n [7, 7, 6],\n [-1, -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" } ]
520
MATH
[ { "content": "Compute |A| for the matrix A =\n[[7, -3, -3],\n [0, -8, 4],\n [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" } ]
280
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 8, -9],\n [0, -5, 2],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
950
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, 0, -4],\n [0, 1, -8],\n [-4, -8, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
550
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -6, 0],\n [-6, 1, 2],\n [0, 2, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
72
MATH
[ { "content": "Compute |A| for the matrix A =\n[[9, 2, -8],\n [0, -10, -5],\n [0, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
900
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -5, -5],\n [6, 2, 6],\n [1, -7, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
176
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -4, -2],\n [0, 8, -8],\n [0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-5, -4, 10],\n [0, 3, 2],\n [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" } ]
865
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-2, -7, -7],\n [-9, 0, 3],\n [8, 10, 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" } ]
18
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-2, 9, -7],\n [-3, -10, -6],\n [10, -9, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
538
MATH
[ { "content": "Determine the value of det(A) where A =\n[[-8, -2, -6],\n [-2, 2, 4],\n [-6, 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" } ]
252
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 2, 3],\n [2, -1, 8],\n [3, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
361
MATH
[ { "content": "What is the determinant of the matrix:\n[[-6, 4, 0],\n [4, 2, 6],\n [0, 6, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
160
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -1, 4],\n [-1, 9, -2],\n [4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
956
MATH
[ { "content": "What is the determinant of the matrix:\n[[10, 5, -9],\n [-3, 8, -1],\n [10, 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" } ]
612
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 6, 2],\n [0, 1, -9],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
998
MATH
[ { "content": "Determine the value of det(A) where A =\n[[7, 1, 5],\n [0, 10, -6],\n [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" } ]
70
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 7, 10],\n [0, 8, 0],\n [0, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
160
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 9, 9],\n [0, -1, 10],\n [0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
50
MATH
[ { "content": "What is the determinant of the matrix:\n[[6, 9, -7],\n [0, -5, -5],\n [0, 0, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
210
MATH
[ { "content": "What is the determinant of the matrix:\n[[3, 9, -8],\n [-1, 9, -1],\n [7, -8, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
173
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-4, 4, -8],\n [0, 4, -1],\n [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" } ]
32
MATH
[ { "content": "Compute |A| for the matrix A =\n[[4, 0, -1],\n [0, -9, 0],\n [-1, 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" } ]
865
MATH
[ { "content": "What is the determinant of the matrix:\n[[-8, -4, -2],\n [-4, 6, 6],\n [-2, 6, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
744
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, -9, -4],\n [-9, -10, 10],\n [-4, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
380
MATH
[ { "content": "Compute |A| for the matrix A =\n[[5, -10, -6],\n [0, -3, 10],\n [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" } ]
135
MATH
[ { "content": "What is the determinant of the matrix:\n[[5, 3, -7],\n [0, 3, -8],\n [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" } ]
940
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, -2, -7],\n [-2, 4, -4],\n [6, 1, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
262
MATH
[ { "content": "What is the determinant of the matrix:\n[[0, 8, 2],\n [-1, 10, -5],\n [4, 5, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
702
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 9, 3],\n [9, 2, 1],\n [3, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
843
MATH
[ { "content": "Compute |A| for the matrix A =\n[[0, -9, -7],\n [-10, 3, 7],\n [6, 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" } ]
258
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 2, 0],\n [2, -8, 8],\n [10, 8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
308
MATH
[ { "content": "Compute |A| for the matrix A =\n[[1, 3, -8],\n [0, -8, -4],\n [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" } ]
48
MATH
[ { "content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -6, 8],\n [-6, -8, 0],\n [8, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
232
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -5, 0],\n [-7, -4, -10],\n [-8, 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" } ]
126
MATH
[ { "content": "Determine the value of det(A) where A =\n[[1, -3, -3],\n [0, -7, 4],\n [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" } ]
979
MATH
[ { "content": "Compute |A| for the matrix A =\n[[3, -1, -2],\n [0, 9, 7],\n [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" } ]
27
MATH
[ { "content": "What is the determinant of the matrix:\n[[2, 5, -2],\n [0, 1, 8],\n [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" } ]
2
MATH
[ { "content": "What is the determinant of the matrix:\n[[-10, 3, 0],\n [3, -10, 4],\n [0, 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" } ]
706
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -7, 4],\n [-9, -10, -1],\n [-7, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
127
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 8, -6],\n [8, 10, 0],\n [-6, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
880
MATH
[ { "content": "What is the determinant of the matrix:\n[[7, -9, 10],\n [0, 1, -7],\n [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" } ]
930
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-3, -3, -10],\n [0, -2, -1],\n [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" } ]
18
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 4, 2],\n [4, 10, 6],\n [2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
744
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 1, -2],\n [-8, 5, 7],\n [0, 7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
516
MATH
[ { "content": "What is the determinant of the matrix:\n[[-3, 3, -8],\n [0, -5, -10],\n [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" } ]
880
MATH
[ { "content": "Compute |A| for the matrix A =\n[[-6, -5, -5],\n [0, 7, 6],\n [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" } ]
874
MATH
[ { "content": "Determine the value of det(A) where A =\n[[5, -2, -4],\n [-2, -7, 1],\n [-4, 1, 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" } ]
772
MATH
[ { "content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 10, 0],\n [10, -5, -4],\n [0, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
MATH