messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1 value |
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[
{
"content": "What is the determinant of the matrix:\n[[-14, 13, 12, -5, -10, -3],\n [-4, 14, 6, -13, -2, -11],\n [8, 11, -7, 8, -3, -15],\n [3, 5, -12, 6, -3, -9],\n [-6, 14, -10, -9, -1, -15],\n [-3, -4, 8, 12, 1, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer ... | 819 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -2, -2, -1, 10, -2],\n [-2, 15, -2, -2, 8, 4],\n [-2, -2, 0, -1, 2, -2],\n [-1, -2, -1, -6, -4, 2],\n [10, 8, 2, -4, -13, -2],\n [-2, 4, -2, 2, -2, 5]]\n\nPresent the answer in La... | 432 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -12, 5, -7, 3, 10],\n [0, 13, 12, -9, -14, 10],\n [0, 0, 3, 4, 3, -11],\n [0, 0, 0, 1, -10, 8],\n [0, 0, 0, 0, -8, -15],\n [0, 0, 0, 0, 0, 15]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex for... | 720 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 1, -3, -8, -3, -8],\n [0, 7, 12, 6, 15, -3],\n [0, 0, -5, -2, 4, -4],\n [0, 0, 0, -2, -9, 10],\n [0, 0, 0, 0, 8, -6],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed... | 80 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -1, 12, -5, 1, 9],\n [-1, -8, 0, 4, -3, -8],\n [12, 0, -8, -8, 1, 7],\n [-5, 4, -8, -8, 6, 2],\n [1, -3, 1, 6, 12, 3],\n [9, -8, 7, 2, 3, -13]]\n\nPresent the answer in LaTex forma... | 55 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-15, -2, -4, -10, -3, -2],\n [-2, 11, 6, -3, -4, -2],\n [-4, 6, -10, -10, -12, 0],\n [-10, -3, -10, 1, -12, 10],\n [-3, -4, -12, -12, -15, -7],\n [-2, -2, 0, 10, -7, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaT... | 308 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -8, 2, -12, 5, 8],\n [-8, -1, 10, 11, -4, -12],\n [2, 10, 14, 3, -12, 2],\n [-12, 11, 3, -2, 4, 8],\n [5, -4, -12, 4, 8, -2],\n [8, -12, 2, 8, -2, -13]]\n\nPresent the answer in LaT... | 987 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 7, -10, 4, 12, 1],\n [0, -3, 6, 3, 12, 13],\n [0, 0, 11, -10, -8, -11],\n [0, 0, 0, -4, 12, 13],\n [0, 0, 0, 0, -7, -14],\n [0, 0, 0, 0, 0, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex fo... | 616 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 8, 2, 4, 5, 4],\n [8, -9, 5, 12, -8, 5],\n [2, 5, 1, 3, -4, -4],\n [4, 12, 3, 9, -2, 2],\n [5, -8, -4, -2, 3, 8],\n [4, 5, -4, 2, 8, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{... | 563 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 15, 1, -12, -14, -14],\n [-14, 8, -11, 5, -9, -4],\n [-3, 9, -7, 8, 14, 1],\n [3, 6, 11, 10, -15, -12],\n [10, -5, -8, 5, 13, -11],\n [-4, 13, -1, -8, 11, 6]]\n\nPresent the answer... | 11 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 8, -12, -15, -11, 10],\n [-13, -9, 2, -12, -5, 11],\n [10, -13, -6, -9, 6, -5],\n [13, -7, 12, -14, -5, 4],\n [10, 11, -15, -4, -5, -15],\n [-1, 6, 14, 2, -2, -11]]\n\nPresent the ... | 620 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-15, 1, 10, -11, 5, 6],\n [0, -10, 3, -4, 1, 8],\n [0, 0, 7, 14, 12, 8],\n [0, 0, 0, 5, 3, 10],\n [0, 0, 0, 0, 2, -3],\n [0, 0, 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: \... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, 10, 3, 10, -4, -2],\n [10, 12, 3, 8, -2, 2],\n [3, 3, 4, 0, -2, 6],\n [10, 8, 0, 1, 2, -11],\n [-4, -2, -2, 2, -9, -8],\n [-2, 2, 6, -11, -8, -13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex for... | 928 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -12, 12, -4, 0, 1],\n [-12, 8, -3, 2, -4, 0],\n [12, -3, 3, 0, 10, 15],\n [-4, 2, 0, -14, 2, -9],\n [0, -4, 10, 2, 6, 10],\n [1, 0, 15, -9, 10, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex... | 894 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, -15, 15, -12, 12, -15],\n [0, -2, 2, 15, -10, 5],\n [0, 0, -11, 10, -11, 3],\n [0, 0, 0, 13, 3, -11],\n [0, 0, 0, 0, 11, -10],\n [0, 0, 0, 0, 0, 9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTe... | 372 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 6, -1, 15, 4, -12],\n [0, -1, 6, -7, 9, -6],\n [-15, -14, 13, 11, -7, 4],\n [-12, 10, -9, -1, -8, 7],\n [-4, -7, -13, -10, 9, 11],\n [-1, 13, 3, -8, -14, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex form... | 544 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 9, 2, -2, -6, -11],\n [0, 1, 11, -7, -10, 0],\n [0, 0, -8, -11, 3, 14],\n [0, 0, 0, 4, 10, -2],\n [0, 0, 0, 0, 8, -5],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex format... | 472 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -7, 7, 11, 6, 13],\n [0, -2, 7, -12, 8, 5],\n [0, 0, 10, 9, -11, 6],\n [0, 0, 0, 12, 8, 13],\n [0, 0, 0, 0, -7, -5],\n [0, 0, 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: ... | 440 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -7, 0, 3, -1, -13],\n [0, -8, -14, 11, -13, -10],\n [0, 0, -11, -5, -14, -14],\n [0, 0, 0, 4, 6, 3],\n [0, 0, 0, 0, -7, -5],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex f... | 648 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 8, -2, 0, 0, 4],\n [8, 2, 3, -2, 10, 2],\n [-2, 3, -13, -10, 4, -5],\n [0, -2, -10, -3, -3, 2],\n [0, 10, 4, -3, -9, 5],\n [4, 2, -5, 2, 5, 14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{You... | 457 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -11, 0, -13, -12, -4],\n [0, -5, 1, -7, 1, 12],\n [0, 0, 3, -13, 9, -15],\n [0, 0, 0, 15, -6, 2],\n [0, 0, 0, 0, -10, -11],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format:... | 750 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -2, 12, 4, 6, -5],\n [0, 8, -3, 10, -6, -2],\n [0, 0, 6, -9, 9, 10],\n [0, 0, 0, 8, 10, 15],\n [0, 0, 0, 0, -15, -6],\n [0, 0, 0, 0, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 320 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -1, 6, -9, 9, 7],\n [15, -5, -2, 6, 11, 6],\n [-10, 14, 13, -11, -9, -9],\n [9, 3, 11, -7, 4, -3],\n [-4, 9, -9, -5, 4, 15],\n [-6, -2, 1, -13, -13, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\bo... | 128 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, -3, -5, 2, 2, -3],\n [-3, 0, -4, -8, 6, -4],\n [-5, -4, -13, 0, -3, 2],\n [2, -8, 0, 12, 0, 4],\n [2, 6, -3, 0, -14, 4],\n [-3, -4, 2, 4, 4, 9]]\n\nPresent the answer in LaTex format: \\... | 684 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -8, 6, 13, 1, 0],\n [2, -1, -6, 14, -8, 4],\n [-14, 12, 7, 0, 12, 1],\n [-1, -1, 8, 3, 9, 14],\n [7, -6, 12, 8, -12, 11],\n [15, 13, 4, -1, 11, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Y... | 700 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -8, -12, -2, -4, -14],\n [-8, -14, 8, 8, 6, 8],\n [-12, 8, 14, 8, -4, 11],\n [-2, 8, 8, 3, -6, 4],\n [-4, 6, -4, -6, -6, 0],\n [-14, 8, 11, 4, 0, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaT... | 64 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -7, 0, 12, -6, -8],\n [0, 3, 3, 4, -7, 14],\n [0, 0, -14, -6, 9, 11],\n [0, 0, 0, -8, -9, -2],\n [0, 0, 0, 0, 3, -9],\n [0, 0, 0, 0, 0, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 88 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -6, 1, 4, -12, -14],\n [0, -5, 6, 10, -3, -13],\n [-12, 8, 8, -10, 8, -4],\n [4, 14, -9, 3, 12, 2],\n [6, -13, 10, 9, 6, -11],\n [14, 12, -9, 4, -12, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in... | 264 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 13, -3, 3, 1, -6],\n [12, 3, -10, 0, 7, 3],\n [5, 10, 6, -12, -4, 12],\n [9, -8, -1, 12, -1, 1],\n [14, -12, -7, 6, 5, 8],\n [-14, 8, 5, 14, -7, 15]]\n\nPresent the answer in LaTex form... | 310 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[1, -2, -2, -6, -10, 4],\n [-2, -10, 0, 12, -4, 0],\n [-2, 0, -9, -2, 2, 6],\n [-6, 12, -2, -6, 12, 1],\n [-10, -4, 2, 12, -4, 2],\n [4, 0, 6, 1, 2, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex for... | 768 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -14, -12, -7, 7, -3],\n [2, -5, 1, -10, 6, 7],\n [-12, -13, -9, 13, 11, 5],\n [9, 10, 11, -10, 6, 8],\n [-11, -13, -8, 3, -12, 8],\n [2, 10, -1, 10, -5, -1]]\n\nPresent the answer ... | 775 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, -1, 2, 6, 2, -6],\n [-1, 0, 6, 9, 6, -10],\n [2, 6, -9, 7, 2, -5],\n [6, 9, 7, 14, -2, 0],\n [2, 6, 2, -2, 13, -11],\n [-6, -10, -5, 0, -11, -14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 341 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 8, 3, 11, 9, 6],\n [5, -15, -9, 13, 5, -8],\n [3, 8, -11, 0, 6, -10],\n [-14, -13, -10, 13, 3, 15],\n [-1, -14, 11, -2, -3, 12],\n [-11, 6, 13, -1, -12, 13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answe... | 709 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -2, 6, -3, 2, 9],\n [-2, -10, 1, 3, 4, -14],\n [6, 1, 5, -3, -2, 4],\n [-3, 3, -3, 10, -7, -8],\n [2, 4, -2, -7, -11, -4],\n [9, -14, 4, -8, -4, -11]]\n\nPresent the answer in LaTex... | 787 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, -14, -2, -4, 4, 2],\n [12, 9, -4, 10, 9, -6],\n [10, 8, -4, -12, 6, 14],\n [-8, -13, -14, -11, -1, 10],\n [11, -6, -13, 4, 7, 6],\n [-15, -12, 6, 5, 12, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answe... | 156 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 6, -15, -1, 7, 12],\n [0, -12, -7, -15, 14, 0],\n [0, 0, 3, -6, 1, 12],\n [0, 0, 0, -9, 12, 6],\n [0, 0, 0, 0, -3, 3],\n [0, 0, 0, 0, 0, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 792 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -14, -3, 7, 6, 2],\n [0, 7, -5, -5, -14, 7],\n [0, 0, -8, 8, -6, -9],\n [0, 0, 0, -9, -2, -3],\n [0, 0, 0, 0, 7, 7],\n [0, 0, 0, 0, 0, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 640 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, -7, 14, 2, 4, -15],\n [-2, -5, -10, 7, -8, -1],\n [-8, 10, -4, -11, 11, 15],\n [0, -13, -10, 2, -9, -15],\n [14, -15, 3, 14, 0, -11],\n [2, 11, 4, 6, 4, 10]]\n\nPresent the answer in LaT... | 655 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 8, -8, -9, 5, 11],\n [0, -3, -6, 9, -15, -6],\n [0, 0, 6, -5, -3, -6],\n [0, 0, 0, 4, -11, 1],\n [0, 0, 0, 0, -15, -2],\n [0, 0, 0, 0, 0, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\... | 160 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[13, -7, 2, -3, 8, -13],\n [0, -3, -10, -7, -3, 2],\n [0, 0, -14, -5, -12, 14],\n [0, 0, 0, -1, -10, 0],\n [0, 0, 0, 0, 13, 15],\n [0, 0, 0, 0, 0, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format... | 314 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -4, -9, 5, -8, -6],\n [-4, 12, -3, -2, 0, -2],\n [-9, -3, -11, 3, 1, -6],\n [5, -2, 3, -13, 2, -9],\n [-8, 0, 1, 2, 7, 1],\n [-6, -2, -6, -9, 1, -12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\box... | 965 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, -3, -12, -2, 13, -9],\n [0, -2, -15, 4, -5, 2],\n [0, 0, -1, 3, -3, -8],\n [0, 0, 0, -2, -7, 7],\n [0, 0, 0, 0, -8, 5],\n [0, 0, 0, 0, 0, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 96 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, -8, -1, -10, 15, -12],\n [8, 0, 2, -13, 6, -3],\n [-15, 1, -10, -7, -15, 15],\n [13, -6, 14, 9, -5, -1],\n [-2, -14, -9, -10, 11, -1],\n [-2, 9, -7, -2, 13, 10]]\n\nPresent the answer in... | 729 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[15, 7, -7, -13, 7, -14],\n [2, 12, 5, 9, 14, -2],\n [4, 13, 5, 3, -3, -12],\n [-1, -14, 13, 14, 9, -5],\n [-8, 7, -15, 7, 5, -2],\n [1, 7, -14, 7, 7, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex fo... | 308 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -2, 1, -1, 5, 4],\n [-2, -12, 3, -3, 4, 4],\n [1, 3, 0, -2, -2, 2],\n [-1, -3, -2, -11, -4, -1],\n [5, 4, -2, -4, 5, -10],\n [4, 4, 2, -1, -10, 15]]\n\nPresent the answer in LaTex f... | 710 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, -7, -10, 6, 6, 2],\n [-7, -11, 6, -9, 14, 0],\n [-10, 6, 1, 12, 0, 2],\n [6, -9, 12, 6, -1, 7],\n [6, 14, 0, -1, -14, 6],\n [2, 0, 2, 7, 6, -8]]\n\nPresent the answer in LaTex for... | 388 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -2, 0, 0, 1, -6],\n [-2, -7, 5, -8, 7, 2],\n [0, 5, 11, -6, 14, 4],\n [0, -8, -6, 5, -9, 0],\n [1, 7, 14, -9, 13, -2],\n [-6, 2, 4, 0, -2, 8]]\n\nPresent the answer in LaTex format: \\bo... | 616 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -13, 11, 2, 14, -4],\n [-4, 2, 2, -11, -12, 9],\n [-3, -3, -8, 5, 5, -8],\n [-8, 5, 14, 8, 5, 15],\n [-6, -15, 0, -3, -15, 8],\n [-12, -5, 11, 5, 5, -8]]\n\nPresent the answer in LaTex fo... | 360 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -13, -14, 9, -6, 5],\n [0, -13, 9, -8, -2, -7],\n [0, 0, 1, 8, 1, -8],\n [0, 0, 0, 5, 0, 11],\n [0, 0, 0, 0, -6, 2],\n [0, 0, 0, 0, 0, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 20 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -7, 2, 7, -2, 0],\n [-7, 7, 12, -4, 4, 0],\n [2, 12, -15, 2, -4, -10],\n [7, -4, 2, 8, -2, -2],\n [-2, 4, -4, -2, 7, 2],\n [0, 0, -10, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\... | 903 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -2, 0, -4, 12, 2],\n [-2, -1, 1, 2, -12, -1],\n [0, 1, 1, 8, -7, -6],\n [-4, 2, 8, 15, 4, 3],\n [12, -12, -7, 4, 15, 0],\n [2, -1, -6, 3, 0, -14]]\n\nPresent the answer in LaTex format: \... | 980 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 2, -13, -5, -10, -3],\n [0, 6, 5, 7, 8, -2],\n [0, 0, 5, 15, 14, 7],\n [0, 0, 0, 13, -1, -1],\n [0, 0, 0, 0, -5, -14],\n [0, 0, 0, 0, 0, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\b... | 300 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[14, 8, -5, 2, 6, -3],\n [8, 9, 4, 6, 11, -4],\n [-5, 4, -1, 2, -3, 8],\n [2, 6, 2, 10, 5, -5],\n [6, 11, -3, 5, -7, -4],\n [-3, -4, 8, -5, -4, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \... | 957 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 3, 1, 0, -2, 4],\n [3, 0, -9, -12, 2, 8],\n [1, -9, 6, -10, 6, -3],\n [0, -12, -10, 11, 8, -2],\n [-2, 2, 6, 8, 9, 0],\n [4, 8, -3, -2, 0, 5]]\n\nPresent the answer in LaTex format: \\b... | 84 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 5, 1, -12, 7, 2],\n [6, 5, -5, 9, -2, -5],\n [-10, 8, 15, 3, -1, -3],\n [-12, 4, 7, 1, -3, -9],\n [-5, 2, 0, -13, 4, 4],\n [-15, 10, 9, 5, -4, -11]]\n\nPresent the answer in LaTex ... | 942 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[13, 11, 9, -3, -12, -6],\n [0, -1, 15, 1, 0, -5],\n [0, 0, 7, -10, 10, 14],\n [0, 0, 0, 10, 1, -4],\n [0, 0, 0, 0, -6, 15],\n [0, 0, 0, 0, 0, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex form... | 160 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 2, -4, -5, 0, -5],\n [2, 1, -2, -5, -4, -8],\n [-4, -2, 10, -10, -3, 6],\n [-5, -5, -10, -9, 0, -3],\n [0, -4, -3, 0, -1, -2],\n [-5, -8, 6, -3, -2, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer i... | 427 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 11, 15, 15, -13, 13],\n [0, 8, -9, -10, -3, 0],\n [0, 0, -15, 5, -12, -4],\n [0, 0, 0, 14, -3, 8],\n [0, 0, 0, 0, 9, 12],\n [0, 0, 0, 0, 0, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex for... | 360 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 6, -5, -3, -8, -7],\n [0, 14, -5, -9, -5, -11],\n [0, 0, 13, -7, -7, 10],\n [0, 0, 0, -1, 3, -1],\n [0, 0, 0, 0, 1, -3],\n [0, 0, 0, 0, 0, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex form... | 370 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -4, 10, -8, 3, 7],\n [-15, -9, -8, -10, -5, -1],\n [12, 13, -15, -8, -9, -6],\n [15, 8, 11, 9, -4, 1],\n [9, 6, 2, 13, 13, -14],\n [4, -3, 8, 14, 6, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in ... | 192 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 6, -10, 11, 8, 8],\n [3, -2, 11, 5, 6, 0],\n [13, -1, -7, -10, 0, 11],\n [-5, -8, 13, -5, -11, -13],\n [-5, 5, 6, -6, -5, 4],\n [4, -3, 15, 5, 10, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex... | 408 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 3, 3, 2, -4, -6],\n [3, -4, 5, -6, 0, 4],\n [3, 5, -12, 2, -4, -6],\n [2, -6, 2, -10, 4, 0],\n [-4, 0, -4, 4, 9, 0],\n [-6, 4, -6, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\box... | 936 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -14, 3, -6, 13, -12],\n [-9, -2, 4, 11, 12, -13],\n [-12, 14, 8, 10, -12, -4],\n [-10, 5, -9, 7, -11, -6],\n [-12, -8, 13, -13, 0, 6],\n [-5, -5, -11, -12, 15, -8]]\n\nPresent the answer ... | 414 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 0, -10, 6, 11, 10],\n [0, -3, -7, -5, -3, -13],\n [0, 0, -2, 0, -10, 1],\n [0, 0, 0, 2, -2, 4],\n [0, 0, 0, 0, -9, -15],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex form... | 812 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, 15, -4, 2, 4, -4],\n [0, 2, 9, -13, -11, -5],\n [0, 0, 5, -1, 7, 2],\n [0, 0, 0, 13, -10, -4],\n [0, 0, 0, 0, 4, 6],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\... | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, -4, 4, 0, -4, 10],\n [-4, -8, -2, -8, 4, -7],\n [4, -2, -4, -3, -10, -2],\n [0, -8, -3, 9, 6, 0],\n [-4, 4, -10, 6, 11, -2],\n [10, -7, -2, 0, -2, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\bo... | 903 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 12, -15, 0, -5, -12],\n [0, 11, -7, 11, 3, 3],\n [0, 0, -14, -4, 1, -13],\n [0, 0, 0, -3, 9, 1],\n [0, 0, 0, 0, -1, 11],\n [0, 0, 0, 0, 0, -11]]\n\nPresent the answer in LaTex forma... | 246 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -6, -9, -14, 4, -5],\n [8, 0, -11, 11, 0, -3],\n [-9, -3, -3, 15, -9, 10],\n [13, -7, 9, 12, 15, -3],\n [7, -10, 11, 2, 14, 12],\n [-5, 0, 14, -3, -10, -3]]\n\nPresent the answer in LaTe... | 762 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 9, 3, 13, 5, 9],\n [0, -8, -12, -5, -2, -4],\n [0, 0, 10, 3, 1, 7],\n [0, 0, 0, 10, 1, 3],\n [0, 0, 0, 0, 13, -13],\n [0, 0, 0, 0, 0, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 400 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, -2, 3, 2, 2, -2],\n [-2, 5, -1, -7, -6, 2],\n [3, -1, 12, -8, -3, -2],\n [2, -7, -8, 12, 0, 2],\n [2, -6, -3, 0, -13, -4],\n [-2, 2, -2, 2, -4, -11]]\n\nPresent the answer in LaTex... | 422 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[10, -5, 11, 0, -2, 8],\n [-6, -2, 2, -14, -10, 12],\n [5, -8, 14, -9, 0, -2],\n [-4, -12, 9, 5, -5, 0],\n [-7, -1, -9, 11, -4, 10],\n [6, 4, 6, 6, 14, 4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\box... | 784 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -15, -2, 12, -9, -10],\n [10, -7, 4, -6, -4, 1],\n [0, 3, 9, 5, 8, 14],\n [15, -8, 2, -12, 2, 5],\n [-3, -8, 4, 7, -14, 0],\n [-2, -11, 13, 7, 12, 1]]\n\nPresent the answer in LaTex form... | 605 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, -2, -6, 10, -6, 10],\n [-2, 3, -4, 5, 3, -6],\n [-6, -4, 5, -6, 2, 0],\n [10, 5, -6, 6, 0, 4],\n [-6, 3, 2, 0, -6, -6],\n [10, -6, 0, 4, -6, 8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format:... | 620 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[13, -13, -4, 15, 14, -4],\n [0, -9, -2, -15, 3, 7],\n [0, 0, -3, 6, 9, -9],\n [0, 0, 0, -6, 1, 15],\n [0, 0, 0, 0, 12, 4],\n [0, 0, 0, 0, 0, -5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 360 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[14, -6, -2, 2, 0, -11],\n [-6, 15, 10, 2, 8, 4],\n [-2, 10, 13, 6, -6, -2],\n [2, 2, 6, -8, 6, 10],\n [0, 8, -6, 6, -6, 8],\n [-11, 4, -2, 10, 8, -11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex... | 604 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, 7, 15, -9, -14, -12],\n [13, 1, -13, -15, -14, 3],\n [9, 7, -1, -15, 9, -10],\n [7, -7, -3, 0, 7, 1],\n [11, 1, -11, 8, 3, 2],\n [11, -3, -1, -2, -1, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in... | 154 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 11, 6, -1, 10, 1],\n [0, -5, -8, -2, -14, -2],\n [0, 0, -2, 9, 13, -10],\n [0, 0, 0, 7, 2, 9],\n [0, 0, 0, 0, -12, 15],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: ... | 160 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-10, 11, 6, -7, 15, 3],\n [0, 8, 2, 6, 2, -4],\n [0, 0, 15, -8, 0, 12],\n [0, 0, 0, -12, -2, 4],\n [0, 0, 0, 0, -7, -10],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed... | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 4, -7, 2, 1, 8],\n [4, -2, -2, 8, -6, 0],\n [-7, -2, -7, 7, -10, 3],\n [2, 8, 7, 14, 7, 2],\n [1, -6, -10, 7, 14, 0],\n [8, 0, 3, 2, 0, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 102 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 12, 5, 5, 4, -5],\n [12, 5, 6, -3, 7, -10],\n [5, 6, -2, -6, 4, 4],\n [5, -3, -6, -14, -12, -2],\n [4, 7, 4, -12, -8, 4],\n [-5, -10, 4, -2, 4, -13]]\n\nPresent the answer in LaTex forma... | 40 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 10, 10, 2, 8, 1],\n [10, 10, 0, -12, 2, 7],\n [10, 0, -5, -5, 2, 2],\n [2, -12, -5, -3, 8, -14],\n [8, 2, 2, 8, 5, 7],\n [1, 7, 2, -14, 7, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: ... | 24 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -2, 5, -7, -2, 8],\n [-2, 2, 12, -7, -2, 2],\n [5, 12, -15, -8, -4, 10],\n [-7, -7, -8, -12, 7, -10],\n [-2, -2, -4, 7, -3, -4],\n [8, 2, 10, -10, -4, -12]]\n\nPresent the answer in LaTex... | 72 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 4, 0, 15, -12, -2],\n [0, 1, 3, -1, 12, 7],\n [0, 0, -10, -13, 7, 12],\n [0, 0, 0, 8, -15, 5],\n [0, 0, 0, 0, -14, -15],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format... | 400 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -6, 2, 4, 2, 2],\n [-6, 0, 1, 12, 2, 1],\n [2, 1, 9, -2, 2, 4],\n [4, 12, -2, 11, 3, -6],\n [2, 2, 2, 3, -8, 2],\n [2, 1, 4, -6, 2, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 8 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 4, 3, -6, -4, 13],\n [4, 9, 4, 2, 0, 2],\n [3, 4, 7, -5, -9, 13],\n [-6, 2, -5, -7, -2, 3],\n [-4, 0, -9, -2, 14, -2],\n [13, 2, 13, 3, -2, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex for... | 287 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -5, -10, 10, 12, 6],\n [0, -3, 8, -3, -4, -14],\n [0, 0, -15, -8, 8, -3],\n [0, 0, 0, -5, 9, 14],\n [0, 0, 0, 0, 14, 10],\n [0, 0, 0, 0, 0, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{You... | 400 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -10, 3, -7, -14, 15],\n [0, 8, 1, 0, 12, -14],\n [0, 0, 6, 2, 12, -11],\n [0, 0, 0, 3, 13, 12],\n [0, 0, 0, 0, 6, -10],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\box... | 632 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -9, 6, -13, 10, -3],\n [0, 15, -2, 1, -1, -4],\n [0, 0, -14, 9, -10, 8],\n [0, 0, 0, -6, -9, -2],\n [0, 0, 0, 0, -2, -4],\n [0, 0, 0, 0, 0, 14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -14, 11, -1, 11, 3],\n [-5, -6, -5, -9, -10, -6],\n [-7, 10, -11, -10, 13, 15],\n [-3, 12, -8, -14, -2, 15],\n [7, 2, -1, 8, 2, 11],\n [5, 5, 13, -7, 8, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format... | 352 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 2, -3, 0, -10, 3],\n [2, -7, 4, -3, -8, -8],\n [-3, 4, -8, -2, -4, 2],\n [0, -3, -2, 1, 7, -5],\n [-10, -8, -4, 7, -6, 2],\n [3, -8, 2, -5, 2, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex form... | 470 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 7, 12, -15, -2, -10],\n [-2, -15, -8, 7, 8, 14],\n [12, -13, 12, -9, 7, 1],\n [14, -2, 11, -9, 13, 9],\n [13, 6, -5, 14, -4, -7],\n [-7, 1, 15, 0, 14, -15]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer ... | 367 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -1, 6, 2, 5, 7],\n [-9, 3, -11, -13, -5, -14],\n [-9, 11, 6, 4, -15, 15],\n [-8, -15, 6, -1, -5, -7],\n [5, -1, -12, -13, -3, -9],\n [14, 14, 6, -10, 15, -7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex forma... | 440 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -1, 13, -7, 11, -6],\n [0, -12, 6, -3, -12, -12],\n [0, 0, 2, -5, 11, -9],\n [0, 0, 0, -1, 9, -13],\n [0, 0, 0, 0, 6, 14],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\b... | 912 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, -3, 1, 2, 2, 8],\n [-3, 15, 3, 4, 8, 12],\n [1, 3, -11, -10, -12, 6],\n [2, 4, -10, -9, -12, 6],\n [2, 8, -12, -12, -15, 2],\n [8, 12, 6, 6, 2, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex for... | 168 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, -9, -10, 3, 5, 6],\n [8, 6, -3, 2, -9, -1],\n [-13, 15, 2, 14, -4, -10],\n [-14, 13, 1, 7, -2, 8],\n [4, 13, 14, -2, 5, 1],\n [3, -4, 9, -4, -2, 12]]\n\nPresent the answer in LaTe... | 784 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -7, 2, -8, 2, 12],\n [1, 15, 14, 10, 2, -2],\n [8, -7, 12, 12, 4, 12],\n [-4, 8, -7, -10, 10, -6],\n [-4, -5, 0, -2, -4, 12],\n [5, -5, 9, -3, 6, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex for... | 184 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 13, -2, 6, -4, 0],\n [13, 2, 0, -2, 9, 10],\n [-2, 0, 3, 2, 2, -4],\n [6, -2, 2, -7, 3, 3],\n [-4, 9, 2, 3, 14, 2],\n [0, 10, -4, 3, 2, 5]]\n\nPresent the answer in LaTex format: \... | 237 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -1, 2, 3, 2, -3],\n [-1, 1, 10, -8, -5, 0],\n [2, 10, -4, 5, -13, 6],\n [3, -8, 5, 11, 4, 13],\n [2, -5, -13, 4, -4, 8],\n [-3, 0, 6, 13, 8, 9]]\n\nPresent the answer in LaTex format: \\b... | 205 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, 11, -4, -4, 1, 13],\n [13, -10, 13, 11, 4, 4],\n [-2, 12, 1, -3, -7, 13],\n [9, -7, -12, 7, -13, 1],\n [3, 11, 15, 0, 0, 4],\n [-4, 8, 0, -9, -12, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in La... | 796 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -6, -7, -9, -4, 8],\n [3, -13, -4, -4, 5, 9],\n [-9, 1, 4, -12, 1, -4],\n [-12, 10, 12, -10, -14, 6],\n [-9, -15, 11, 8, 11, 12],\n [8, -12, -13, -4, -1, 12]]\n\nPresent the answer ... | 244 | MATH |
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