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[[7, 6, -3, 11, 5, 3],\n [0, 13, -6, -3, -6, 14],\n [0, 0, 10, -8, -3, -10],\n [0, 0, 0, 12, -2, 2],\n [0, 0, 0, 0, 12, -9],\n [0, 0, 0, 0, 0, 2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\b... | 80 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[0, -9, 5, 9, -3, -1],\n [8, -13, 3, 10, -4, -4],\n [-5, 6, 3, 7, 3, 1],\n [-9, -8, 5, -13, -10, 4],\n [0, 5, -8, 4, 2, -8],\n [-12, -15, -3, -4, -8, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex fo... | 428 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, -3, 5, 4, 5, -15],\n [0, 2, -8, -4, 10, -7],\n [0, 0, 14, 0, 6, 5],\n [0, 0, 0, -12, 8, -10],\n [0, 0, 0, 0, -11, 6],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex format: ... | 32 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, 3, 9, 7, -12, 14],\n [-2, 3, -4, 2, 6, -13],\n [-15, 2, 3, -11, 13, 12],\n [-12, 7, -11, 10, -9, -11],\n [-8, -13, -10, 10, 3, 3],\n [5, -7, 9, 12, 6, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaT... | 25 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[13, 0, -8, -4, 10, -3],\n [0, 3, 2, 5, 10, -4],\n [-8, 2, -7, -4, 10, 0],\n [-4, 5, -4, -3, -10, -6],\n [10, 10, 10, -10, -11, -2],\n [-3, -4, 0, -6, -2, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaT... | 678 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, 6, -4, 0, -1, -6],\n [6, 13, -8, -11, 5, -1],\n [-4, -8, -14, 0, 6, 10],\n [0, -11, 0, 12, -6, 10],\n [-1, 5, 6, -6, -1, -2],\n [-6, -1, 10, 10, -2, -9]]\n\nPresent the answer in L... | 458 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 10, -1, -1, -15, -4],\n [-4, 7, -9, -1, -12, -7],\n [-6, 2, -8, 11, -7, -11],\n [1, -1, 4, -6, -15, -10],\n [-1, 2, -8, 0, 15, -13],\n [0, 7, 2, 11, 12, -11]]\n\nPresent the answer... | 919 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -6, -7, 0, -6, 8],\n [-6, -9, 2, -12, 6, -2],\n [-7, 2, 8, -10, 3, 2],\n [0, -12, -10, -3, 0, 4],\n [-6, 6, 3, 0, 4, 2],\n [8, -2, 2, 4, 2, -5]]\n\nPresent the answer in LaTex form... | 642 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 1, 1, 5, -7, 0],\n [1, 0, 8, -2, -5, -5],\n [1, 8, 5, -2, 2, -10],\n [5, -2, -2, -9, 4, 0],\n [-7, -5, 2, 4, -13, 3],\n [0, -5, -10, 0, 3, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: ... | 268 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 8, -4, 4, 8, 5],\n [8, -2, -8, -8, -2, -1],\n [-4, -8, 10, 2, -6, 2],\n [4, -8, 2, 5, 2, -9],\n [8, -2, -6, 2, 11, 1],\n [5, -1, 2, -9, 1, -5]]\n\nPresent the answer in LaTex format: \\b... | 96 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 2, 5, 4, 5, 4],\n [2, 0, -7, 2, -1, 6],\n [5, -7, 0, 0, 8, 12],\n [4, 2, 0, 1, 4, 2],\n [5, -1, 8, 4, 13, 2],\n [4, 6, 12, 2, 2, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 895 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, 6, -12, 8, -10, 0],\n [-5, -8, -7, 13, 1, -14],\n [10, 3, 9, -9, 14, 11],\n [8, -6, 4, 0, 11, -4],\n [15, 0, -11, -10, -2, -11],\n [-9, 0, 4, 9, 14, 2]]\n\nPresent the answer in L... | 923 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 2, 10, 2, 0, 6],\n [2, 10, 0, 3, -6, -6],\n [10, 0, -3, 6, 4, -8],\n [2, 3, 6, 2, 2, 8],\n [0, -6, 4, 2, 3, 0],\n [6, -6, -8, 8, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your... | 817 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 3, -8, 0, -15, 1],\n [0, -6, 14, 13, -5, -5],\n [0, 0, 9, -14, -13, 4],\n [0, 0, 0, 3, -13, -12],\n [0, 0, 0, 0, 6, 14],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\b... | 372 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -3, -12, 14, 8, -13],\n [-10, 3, -3, -2, 4, 9],\n [-10, 13, -6, -10, -15, -15],\n [4, 9, -5, 4, 12, -8],\n [-5, 15, -4, -4, 0, 12],\n [10, -3, 2, -3, 9, -5]]\n\nPresent the answer in LaT... | 885 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, 0, 8, 3, 0, -6],\n [0, 10, 6, 9, -14, 4],\n [8, 6, 8, -4, 12, 0],\n [3, 9, -4, 0, 1, -1],\n [0, -14, 12, 1, 15, -14],\n [-6, 4, 0, -1, -14, 8]]\n\nPresent the answer in LaTex forma... | 912 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, 7, -3, 3, 15, 5],\n [4, -12, -3, -12, -5, 10],\n [12, -14, -13, -7, 5, 14],\n [4, 7, 11, 7, -7, 5],\n [3, 6, 1, -11, -5, -6],\n [-9, 15, 2, 6, 9, 5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaT... | 740 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, -12, 5, 3, 7, 4],\n [0, 6, -12, -3, -10, 10],\n [0, 0, 14, 10, 4, 15],\n [0, 0, 0, 7, -14, -13],\n [0, 0, 0, 0, -8, -3],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex forma... | 152 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, 1, -4, 0, 12, 13],\n [0, -5, -9, -5, -5, -11],\n [0, 0, 2, -4, 11, -2],\n [0, 0, 0, -8, -15, -1],\n [0, 0, 0, 0, 11, 5],\n [0, 0, 0, 0, 0, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex fo... | 480 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -2, 14, 15, 8, 6],\n [2, 10, -2, 3, -1, -3],\n [-8, 1, 2, 0, -15, -10],\n [9, -11, -5, 0, 5, -3],\n [11, -8, 9, 9, 6, -7],\n [-13, 11, -13, -7, -7, -10]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in ... | 39 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, 4, 10, 12, -8, -12],\n [0, -13, -9, 6, 6, -15],\n [0, 0, 2, -10, -10, -15],\n [0, 0, 0, -8, 15, -13],\n [0, 0, 0, 0, -3, -1],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex forma... | 304 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -5, -12, 1, -14, -3],\n [0, 13, 3, 8, 2, -15],\n [0, 0, 13, -15, 7, 5],\n [0, 0, 0, -8, -6, -13],\n [0, 0, 0, 0, 2, -3],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format... | 16 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[0, 4, 4, 2, 5, -4],\n [4, 6, 0, 0, 11, 2],\n [4, 0, 7, 1, 4, -5],\n [2, 0, 1, 8, 10, 3],\n [5, 11, 4, 10, 1, -4],\n [-4, 2, -5, 3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxe... | 550 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 3, 5, -15, -6, 4],\n [0, 3, -12, 7, -3, 8],\n [0, 0, -12, 5, -8, -3],\n [0, 0, 0, 7, 12, 14],\n [0, 0, 0, 0, 15, -3],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{... | 960 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -10, -14, 8, -13, -14],\n [0, 14, 1, 11, 14, -7],\n [0, 0, -1, -6, 5, -13],\n [0, 0, 0, 5, 3, -14],\n [0, 0, 0, 0, -12, -4],\n [0, 0, 0, 0, 0, 9]]\n\nPresent the answer in LaTex for... | 800 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[14, 8, 9, -5, 10, -11],\n [0, -15, 8, 10, 4, -8],\n [0, 0, -8, 13, -7, 15],\n [0, 0, 0, 1, 10, -3],\n [0, 0, 0, 0, 15, -14],\n [0, 0, 0, 0, 0, -14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex fo... | 200 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, 2, -2, -3, -5, 6],\n [2, 14, 4, 10, -2, 6],\n [-2, 4, 4, -2, 4, 0],\n [-3, 10, -2, -4, 0, -7],\n [-5, -2, 4, 0, 9, 2],\n [6, 6, 0, -7, 2, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\b... | 840 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -4, 12, -6, 5, -12],\n [-4, -10, 3, -2, -5, 2],\n [12, 3, 11, -8, 2, 0],\n [-6, -2, -8, 4, 0, 2],\n [5, -5, 2, 0, 3, 6],\n [-12, 2, 0, 2, 6, -7]]\n\nPresent the answer in LaTex form... | 216 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, -1, 2, 0, -10, -2],\n [-1, -13, 7, -8, -6, 2],\n [2, 7, -3, 8, -12, -1],\n [0, -8, 8, -9, 10, 6],\n [-10, -6, -12, 10, -1, 5],\n [-2, 2, -1, 6, 5, -5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex ... | 178 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 0, -3, -11, 14, -2],\n [0, 15, -14, 7, -11, 14],\n [0, 0, 6, 0, -10, 14],\n [0, 0, 0, -10, -13, 14],\n [0, 0, 0, 0, 11, -12],\n [0, 0, 0, 0, 0, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex form... | 800 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, -10, 14, -7, 3, 10],\n [0, -8, -9, -7, -14, -5],\n [0, 0, -11, 0, -15, 7],\n [0, 0, 0, 2, -6, 11],\n [0, 0, 0, 0, 5, -6],\n [0, 0, 0, 0, 0, 11]]\n\nPresent the answer in LaTex forma... | 360 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -1, 0, 4, -1, -6],\n [-1, 5, -4, 0, -4, 0],\n [0, -4, 1, -6, -2, -7],\n [4, 0, -6, -4, -4, -4],\n [-1, -4, -2, -4, -1, -9],\n [-6, 0, -7, -4, -9, -4]]\n\nPresent the answer in LaTex... | 228 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, -4, -2, -12, -7, -10],\n [-4, 9, 6, 6, -3, 10],\n [-2, 6, 4, 2, -9, 8],\n [-12, 6, 2, -15, -2, -2],\n [-7, -3, -9, -2, -13, -4],\n [-10, 10, 8, -2, -4, 4]]\n\nPresent the answer in LaTex ... | 660 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, 0, 7, -15, 7, 7],\n [13, -6, 8, 10, -6, 14],\n [-12, -11, -6, -1, -4, -13],\n [-4, -13, -2, -6, 1, 13],\n [13, -12, 13, -14, 7, 4],\n [8, 0, -7, -6, -2, 9]]\n\nPresent the answer in LaT... | 892 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -12, 2, 15, 3, -13],\n [-14, 3, 5, -15, 15, -10],\n [-8, 9, -8, 5, -9, -8],\n [-2, 1, 5, 4, 2, -9],\n [10, -3, -1, 10, -15, -3],\n [8, 0, 5, 7, -7, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex... | 822 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -9, 1, 1, 14, 7],\n [-9, -8, 0, 0, -4, 8],\n [1, 0, 0, -4, -6, 0],\n [1, 0, -4, 0, 6, -4],\n [14, -4, -6, 6, -4, -4],\n [7, 8, 0, -4, -4, -9]]\n\nPresent the answer in LaTex format: \\bo... | 928 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-13, 1, 7, 3, -3, -12],\n [-12, -13, 1, 11, 10, 0],\n [6, 14, 8, -9, -13, -11],\n [-2, 10, 8, -10, -2, -6],\n [11, 4, -7, -4, -6, 13],\n [9, -7, -11, 4, -13, 8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format... | 322 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 8, 10, 0, -12, 6],\n [8, 3, 4, -5, -6, -4],\n [10, 4, 5, -14, 10, -6],\n [0, -5, -14, 13, -7, -8],\n [-12, -6, 10, -7, -3, 2],\n [6, -4, -6, -8, 2, -13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\b... | 718 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -2, -12, 2, -7, -13],\n [-5, -15, -7, 0, 12, -5],\n [10, 15, 5, -11, -7, 12],\n [-3, -8, -9, 6, 3, 13],\n [12, 13, 4, -6, -7, 0],\n [8, -5, 0, 11, -12, -13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format... | 738 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 0, 12, 13, -1, -4],\n [-7, -10, -5, -3, 4, 1],\n [-5, 9, -4, -9, -4, 11],\n [-6, 8, 7, -7, 3, -9],\n [-2, -9, 3, 6, 4, 8],\n [-13, 2, 13, -5, 6, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex for... | 272 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, 7, 2, -6, 0, 0],\n [7, 9, 0, 2, 3, -8],\n [2, 0, -8, 12, 8, 4],\n [-6, 2, 12, -6, 6, -8],\n [0, 3, 8, 6, 5, 6],\n [0, -8, 4, -8, 6, 14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: \\... | 528 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[3, 10, 8, 4, 13, -10],\n [0, 2, -14, -8, -9, -9],\n [0, 0, 3, -15, 14, -15],\n [0, 0, 0, -12, -5, -12],\n [0, 0, 0, 0, 3, -6],\n [0, 0, 0, 0, 0, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex f... | 296 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, 7, -15, -2, 8, 9],\n [0, 14, -6, 12, -1, 14],\n [0, 0, 15, 9, -6, -4],\n [0, 0, 0, 13, 1, 4],\n [0, 0, 0, 0, 1, 1],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\b... | 430 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 1, 9, -15, -8, -5],\n [0, -5, -10, 8, -12, -8],\n [0, 0, -4, -15, 0, 12],\n [0, 0, 0, -10, -1, -12],\n [0, 0, 0, 0, 2, -8],\n [0, 0, 0, 0, 0, -10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[15, 0, 0, -6, 2, 4],\n [0, -2, 12, 4, -8, -4],\n [0, 12, 8, 2, -14, -2],\n [-6, 4, 2, 2, 0, -4],\n [2, -8, -14, 0, -5, 10],\n [4, -4, -2, -4, 10, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format... | 896 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 0, -4, -2, 0, 6],\n [0, -1, -3, 0, 0, -1],\n [-4, -3, -9, 3, 0, -10],\n [-2, 0, 3, -11, -10, -8],\n [0, 0, 0, -10, -9, -8],\n [6, -1, -10, -8, -8, 7]]\n\nPresent the answer in LaTe... | 838 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, 1, 5, -3, -9, -11],\n [-11, 4, 4, 13, -4, 1],\n [-7, -4, -14, 1, -9, -3],\n [9, 0, 1, 13, -7, 14],\n [-4, 6, 4, 6, 14, -2],\n [14, -1, 6, 0, -4, 6]]\n\nPresent the answer in LaTex ... | 598 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 10, 7, -4, 8, -5],\n [10, 8, 2, 2, 2, 0],\n [7, 2, -2, 0, -3, -3],\n [-4, 2, 0, -3, 2, -10],\n [8, 2, -3, 2, 0, 0],\n [-5, 0, -3, -10, 0, 14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex for... | 776 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -7, -10, -14, -14, -5],\n [10, -11, 8, 0, 3, -5],\n [-6, 12, -1, 2, 3, -8],\n [13, -8, 8, 7, 1, -1],\n [14, 15, 11, 8, -4, 15],\n [14, -11, 7, 9, 1, 1]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in ... | 986 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, -4, -10, -6, 2, -6],\n [0, 4, 2, 6, -6, -8],\n [0, 0, -12, -5, 3, 9],\n [0, 0, 0, 2, 3, 9],\n [0, 0, 0, 0, 6, 0],\n [0, 0, 0, 0, 0, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\box... | 640 | MATH |
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