messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute |A| for the matrix A =\n[[10, -2, -4, 2, -12, 11],\n [0, 3, 13, -3, 9, 14],\n [0, 0, -5, 12, -10, -7],\n [0, 0, 0, -1, -5, -10],\n [0, 0, 0, 0, 9, -5],\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{You... | 850 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 8, -10, -4, 5, 1],\n [8, 3, -4, 0, 2, -4],\n [-10, -4, -10, 10, 7, 6],\n [-4, 0, 10, -11, -10, 2],\n [5, 2, 7, -10, -12, -8],\n [1, -4, 6, 2, -8, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxe... | 156 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 6, 9, -4, 8, -2],\n [6, 3, -12, -7, -10, 4],\n [9, -12, -14, 2, 9, 0],\n [-4, -7, 2, -9, 0, -3],\n [8, -10, 9, 0, -1, -3],\n [-2, 4, 0, -3, -3, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex... | 484 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[13, -2, -10, -4, 2, -8],\n [-2, 0, -6, 3, 0, 6],\n [-10, -6, -2, 8, -10, 8],\n [-4, 3, 8, 15, -2, -2],\n [2, 0, -10, -2, 3, 5],\n [-8, 6, 8, -2, 5, 6]]\n\nPresent the answer in LaTex format:... | 906 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, 9, -11, -10, 3, -15],\n [11, 0, 12, 2, 8, -3],\n [-15, -6, -9, -11, -3, 6],\n [0, 8, 4, 6, -2, -5],\n [3, 7, -14, 12, -8, -3],\n [-9, -4, 12, -8, 0, 2]]\n\nPresent the answer in La... | 746 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, -6, 5, -7, 14, 5],\n [-3, -6, -10, -5, -12, 10],\n [-2, 14, 15, 1, 4, -14],\n [-6, -13, -9, -9, -15, -8],\n [7, -15, -8, -2, -2, -14],\n [-8, 3, -6, -9, -3, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex for... | 377 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, -1, -2, -15, 1, -15],\n [7, 13, 5, 6, -3, 15],\n [14, -8, 14, -3, 0, -14],\n [-3, 2, -13, -3, 3, -3],\n [3, -12, 3, 2, 9, -10],\n [3, 9, 15, -12, -12, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer i... | 951 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 4, -5, 1, 13, 10],\n [0, -2, 0, 8, -6, 15],\n [0, 0, -6, 10, 4, 13],\n [0, 0, 0, -1, -7, -9],\n [0, 0, 0, 0, 4, 8],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\b... | 680 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, -5, 7, 5, 4, 3],\n [0, 4, -8, 10, -13, -6],\n [0, 0, -10, -1, 0, -11],\n [0, 0, 0, -14, -10, 11],\n [0, 0, 0, 0, -9, 15],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex form... | 520 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 2, -9, -15, 12, -15],\n [2, -12, 7, 4, 5, 4],\n [-12, 9, 15, -10, 12, -13],\n [-10, -3, 7, -9, 8, 13],\n [-12, -15, -10, 8, -11, -3],\n [3, -12, 8, -10, -3, 15]]\n\nPresent the answer in ... | 134 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 2, -10, -10, 2, -10],\n [0, 6, 12, -3, -2, 5],\n [0, 0, -1, -4, 5, 11],\n [0, 0, 0, -13, 2, 10],\n [0, 0, 0, 0, 2, 12],\n [0, 0, 0, 0, 0, -14]]\n\nPresent the answer in LaTex format: \\bo... | 896 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, -14, 14, 13, 5, -4],\n [-11, -4, 7, -15, 12, -14],\n [11, 0, 11, 6, -14, 0],\n [4, 10, 0, -10, -3, -4],\n [7, -6, -11, -8, -10, -11],\n [4, 6, -10, 6, 1, -10]]\n\nPresent the answer in L... | 160 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 0, -6, -4, -3, -7],\n [11, 5, -3, -10, -10, -5],\n [3, 11, -5, -6, 7, -1],\n [-3, 7, -8, -11, -14, 0],\n [15, -3, 3, -7, -1, -10],\n [-8, 8, -2, -11, 1, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: ... | 200 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-7, 10, 13, 5, -11, 6],\n [11, -10, -13, -10, -8, 12],\n [-10, 0, 12, 0, 11, 5],\n [-13, 1, 5, -10, 14, -10],\n [14, 6, 3, 15, 4, -1],\n [3, -14, -8, -9, 11, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answ... | 770 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 8, 0, 0, -8, -13],\n [4, -1, -15, -6, -14, -9],\n [15, -2, 0, 11, 12, -1],\n [-9, -3, 9, -6, -7, -7],\n [-10, 8, 9, -4, 14, 7],\n [4, 14, 4, 6, -2, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\b... | 189 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 11, -9, -8, -8, 14],\n [0, -14, -2, -6, 2, 2],\n [0, 0, 4, -11, 4, 15],\n [0, 0, 0, -6, 1, 14],\n [0, 0, 0, 0, 1, 12],\n [0, 0, 0, 0, 0, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\b... | 968 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[4, -12, -12, -13, -11, 9],\n [15, -5, -8, 10, -14, 12],\n [0, 9, 12, -6, 2, -9],\n [-11, 15, 13, -9, 5, 12],\n [-10, 8, -15, 13, -5, -3],\n [-4, -15, 5, -1, -15, -13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the... | 84 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-14, -13, 13, 8, -8, -5],\n [-4, -12, -7, 8, 1, 8],\n [0, 1, -1, 4, 10, 6],\n [-9, -6, 13, -12, 8, 8],\n [-2, -2, -2, 9, -2, 6],\n [4, 2, -1, 7, 10, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTe... | 215 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, -3, -4, 3, 3, 4],\n [0, 13, 13, 5, -13, -6],\n [0, 0, 13, -9, -7, -14],\n [0, 0, 0, -4, -10, 11],\n [0, 0, 0, 0, -7, 4],\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: ... | 896 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -10, 9, 1, 10, 6],\n [-3, -8, 8, -4, -1, 15],\n [3, 13, 5, 10, 4, 12],\n [1, -7, 5, 2, 12, -14],\n [-5, 7, 4, 1, 5, 2],\n [-1, -9, 0, 15, 9, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex forma... | 732 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 10, 0, -10, 0, 0],\n [10, -5, 0, 2, 7, -2],\n [0, 0, 0, -4, -11, 3],\n [-10, 2, -4, -8, 2, 0],\n [0, 7, -11, 2, 13, 2],\n [0, -2, 3, 0, 2, -2]]\n\nPresent the answer in LaTex format... | 664 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, -11, 0, -12, -5, -2],\n [13, -3, 11, 8, 11, -8],\n [5, 15, 4, -1, 2, -9],\n [5, 3, 9, -7, -5, 15],\n [11, -6, -2, 0, 11, -8],\n [-15, -4, -13, -14, 0, -12]]\n\nPresent the answer in LaTex... | 296 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-14, -4, 11, 8, 1, 4],\n [0, 14, -6, 4, -8, 2],\n [0, 0, 2, 13, -14, -4],\n [0, 0, 0, -6, -5, -2],\n [0, 0, 0, 0, 7, -6],\n [0, 0, 0, 0, 0, 6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\bo... | 784 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, 0, -4, -8, 6, -2],\n [0, 11, 10, 4, -8, 7],\n [-4, 10, 0, 6, -4, -2],\n [-8, 4, 6, -6, 8, 1],\n [6, -8, -4, 8, -13, 2],\n [-2, 7, -2, 1, 2, 0]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \... | 832 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -3, 3, -8, 2, -8],\n [-3, 5, 4, 0, 4, 1],\n [3, 4, -2, 0, 0, 10],\n [-8, 0, 0, 12, -6, -10],\n [2, 4, 0, -6, -2, -2],\n [-8, 1, 10, -10, -2, 1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: ... | 480 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 10, 5, 15, -7, -3],\n [0, -3, 1, -8, -7, -7],\n [0, 0, 4, 14, 14, -9],\n [0, 0, 0, -11, 1, -8],\n [0, 0, 0, 0, 14, 15],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\bo... | 384 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 2, -12, -14, 8, 12],\n [0, -15, 9, -4, -3, -2],\n [0, 0, 12, -13, 12, 11],\n [0, 0, 0, -5, -8, -4],\n [0, 0, 0, 0, 5, 1],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\... | 500 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[7, -11, 8, 8, 13, 2],\n [-3, 15, -11, 10, 8, 3],\n [7, -13, 15, 6, 2, -10],\n [-10, 8, -11, 14, -15, 15],\n [-8, 12, 9, -15, 5, 12],\n [-10, 4, -2, -5, -14, 5]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in L... | 600 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 1, -2, -2, 3, 13],\n [0, -3, 2, 10, -1, 13],\n [0, 0, -9, 11, 3, 14],\n [0, 0, 0, -11, -14, -1],\n [0, 0, 0, 0, 4, -5],\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 ... | 136 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -1, -12, -11, 15, 13],\n [-1, 11, 1, 7, -8, 12],\n [9, 13, 3, 15, -7, -6],\n [-11, -6, 6, -15, 9, 9],\n [6, 8, -12, 5, -11, 7],\n [-9, 7, -11, 4, -8, 1]]\n\nPresent the answer in ... | 446 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, 8, -7, -11, 13, -10],\n [3, -4, -11, -11, 15, 14],\n [2, 10, -10, -7, -5, 15],\n [7, -2, 8, -14, 11, 13],\n [-2, 9, 3, -6, -11, 14],\n [7, -12, -9, 8, 15, -3]]\n\nPresent the answer... | 401 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 14, -6, -12, 0, -1],\n [0, -5, 3, 5, 8, -13],\n [0, 0, -2, 13, -11, 10],\n [0, 0, 0, -15, 13, 11],\n [0, 0, 0, 0, 5, -2],\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: ... | 500 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 8, -14, 4, 8, 7],\n [9, -11, 6, 15, 11, 8],\n [-1, -4, -2, 15, -5, 15],\n [5, 14, -7, 4, -8, -4],\n [14, -13, 5, -1, -8, 15],\n [10, 12, -9, 1, -4, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex ... | 110 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, -6, -4, -8, 11, -10],\n [8, 3, -15, -3, 6, 0],\n [2, -4, 15, 9, -11, 5],\n [-3, 10, -8, -10, -13, 9],\n [10, 4, 10, -12, -4, -3],\n [-14, 3, -12, 7, -3, 3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format:... | 539 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[13, -2, -11, 0, -8, -1],\n [-2, -7, -2, -9, -10, 8],\n [-11, -2, 0, 4, 8, 4],\n [0, -9, 4, -4, -5, 6],\n [-8, -10, 8, -5, 0, 10],\n [-1, 8, 4, 6, 10, -14]]\n\nPresent the answer in LaT... | 210 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 13, 7, 13, 15, -7],\n [-12, -14, 6, 6, -7, 15],\n [4, 8, -3, -2, 13, -13],\n [2, -7, -1, 6, 11, 8],\n [11, -6, 9, 1, -3, -15],\n [-5, -11, -7, -9, -9, -14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in L... | 146 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, -10, 2, 6, 2, 3],\n [0, 1, 12, -15, -7, -3],\n [0, 0, 10, 14, 15, 7],\n [0, 0, 0, 11, -6, 9],\n [0, 0, 0, 0, -3, -3],\n [0, 0, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\box... | 850 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 1, 1, 5, 7, -11],\n [15, -3, -13, 11, 7, 1],\n [-5, -15, 12, 2, 1, -7],\n [4, -9, -11, 14, 0, -9],\n [-3, -3, -1, 7, 1, 1],\n [11, 3, -6, -14, -2, 7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in L... | 240 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -1, 3, -6, -7, -6],\n [4, 7, -12, 3, -6, 1],\n [14, -4, 9, 13, 11, -15],\n [-5, -3, -15, 15, -15, 14],\n [5, 0, -9, 7, -6, 0],\n [-15, 6, -7, -10, -1, -12]]\n\nPresent the answer in LaTe... | 658 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 11, 8, 6, -9, 8],\n [-1, 1, -1, -6, 12, -12],\n [6, 1, -12, 6, 7, 13],\n [6, -5, -12, -4, 13, 7],\n [-6, -2, 2, -10, -11, -14],\n [9, -3, 7, -2, -13, 15]]\n\nPresent the answer in L... | 420 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 3, 6, -4, 2, -4],\n [3, 9, 12, -6, -1, 5],\n [6, 12, 13, -5, -8, -9],\n [-4, -6, -5, -3, 1, -2],\n [2, -1, -8, 1, 4, 12],\n [-4, 5, -9, -2, 12, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex for... | 237 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 1, 2, -2, 1, -2],\n [1, 5, 6, -14, 1, -10],\n [2, 6, -1, -5, 6, -4],\n [-2, -14, -5, -10, -2, 10],\n [1, 1, 6, -2, -14, 0],\n [-2, -10, -4, 10, 0, 3]]\n\nPresent the answer in LaTe... | 895 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 8, 4, -12, 6, 12],\n [8, -6, -6, 2, 2, -3],\n [4, -6, 11, -6, 2, 1],\n [-12, 2, -6, 8, -10, -8],\n [6, 2, 2, -10, 13, 2],\n [12, -3, 1, -8, 2, 15]]\n\nPresent the answer in LaTex format:... | 728 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 2, -9, -6, 7, 4],\n [-2, 4, 4, -5, -14, -3],\n [-3, -7, 1, -1, 8, 6],\n [15, 13, 10, 7, 12, 5],\n [6, 6, 13, 0, 9, -6],\n [13, 4, 12, 11, -4, 13]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format... | 696 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 7, -5, -3, -15, 3],\n [12, 5, -12, -11, 7, 9],\n [1, -11, 3, -13, -5, -14],\n [6, -2, -10, 3, -15, -9],\n [-14, 8, 3, -15, 10, -7],\n [5, 1, -6, 11, -10, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in ... | 182 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-13, -13, -14, -9, -8, -8],\n [-13, 1, 6, 1, 2, 0],\n [-14, 6, 11, -4, -3, 4],\n [-9, 1, -4, -9, -5, 3],\n [-8, 2, -3, -5, -3, 2],\n [-8, 0, 4, 3, 2, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex f... | 102 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 3, -2, -6, -2, 3],\n [3, 14, 4, 5, 7, 10],\n [-2, 4, 4, 2, -10, -6],\n [-6, 5, 2, 4, -2, 0],\n [-2, 7, -10, -2, 15, 6],\n [3, 10, -6, 0, 6, -7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format... | 292 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 0, 4, -13, 11, -11],\n [0, 11, 12, -14, -14, -12],\n [0, 0, 14, 7, 6, 10],\n [0, 0, 0, 3, -4, 0],\n [0, 0, 0, 0, -6, 9],\n [0, 0, 0, 0, 0, 13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex for... | 36 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -1, 2, -3, 9, -8],\n [0, 4, 2, -3, -2, -1],\n [0, 0, -9, -15, -1, 13],\n [0, 0, 0, 10, 14, -13],\n [0, 0, 0, 0, -10, -12],\n [0, 0, 0, 0, 0, -6]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format:... | 400 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, -14, -11, -2, -8, 13],\n [-4, -9, -10, -3, 6, -4],\n [1, 0, -15, -9, -13, -10],\n [12, 5, -13, 6, -13, -8],\n [-2, 15, 7, -7, -11, 12],\n [-1, 1, 11, -6, 15, 11]]\n\nPresent the an... | 89 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 10, 6, 0, 5, 10],\n [10, 8, 6, 1, 0, -2],\n [6, 6, -6, 0, 4, 4],\n [0, 1, 0, 2, 0, -4],\n [5, 0, 4, 0, -14, 0],\n [10, -2, 4, -4, 0, -2]]\n\nPresent the answer in LaTex format: \\b... | 180 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -2, 10, -2, -6, 12],\n [8, -9, 0, -12, -9, -1],\n [1, -13, 0, -14, -9, 9],\n [0, 5, -7, -4, 13, 8],\n [-15, -2, -5, 2, 6, -11],\n [-1, 11, -9, 9, -2, 4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in ... | 912 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -12, -13, -4, 2, 8],\n [0, -5, 8, -5, -4, 3],\n [0, 0, -10, 5, -8, -1],\n [0, 0, 0, -6, 12, -1],\n [0, 0, 0, 0, -11, -4],\n [0, 0, 0, 0, 0, 13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex fo... | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 14, -11, -6, 8, -3],\n [13, 3, -9, 14, 0, 13],\n [-10, -6, 11, -6, 10, -5],\n [6, -6, 9, -2, -1, -9],\n [-3, -5, -9, -5, -2, 1],\n [0, -15, -7, -7, 12, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format:... | 524 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -13, 12, 4, 13, -3],\n [7, 7, 3, 0, -12, -13],\n [-1, -1, 2, 6, -9, 4],\n [-11, -8, 9, 7, -6, 14],\n [-15, -5, 14, -13, 11, 5],\n [-13, -1, 1, 2, -8, 7]]\n\nPresent the answer in LaTex f... | 70 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, -6, -13, 4, -2, -3],\n [0, -3, 4, 8, 9, 7],\n [0, 0, 9, 0, 7, 7],\n [0, 0, 0, 12, -4, 3],\n [0, 0, 0, 0, 6, 2],\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: \\boxed{Y... | 320 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 10, -14, -15, 0, -11],\n [0, 15, 9, -9, 14, -7],\n [0, 0, 11, 4, -1, -9],\n [0, 0, 0, 5, 13, 9],\n [0, 0, 0, 0, -13, 12],\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 fo... | 950 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -6, -8, 4, -1, -15],\n [11, -1, 8, 1, -3, -4],\n [-13, 7, 3, 13, 8, -11],\n [-13, 5, -11, 8, 12, -7],\n [-10, 0, -6, 0, -13, 2],\n [-5, 3, 9, 7, -1, -5]]\n\nPresent the answer in LaTex f... | 246 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[11, 9, 13, 15, 6, 8],\n [0, 11, -7, -13, 7, -7],\n [0, 0, 7, 5, 8, 0],\n [0, 0, 0, -3, 15, 10],\n [0, 0, 0, 0, -8, 3],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Yo... | 296 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, -1, -11, -11, -12, 14],\n [4, 5, 10, -7, 14, 11],\n [-4, 0, 6, -8, -7, -4],\n [14, 4, 12, 13, -9, 5],\n [-12, 12, 7, -13, -15, -9],\n [-7, -14, -9, -6, -14, -3]]\n\nPresent the answer in ... | 166 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, -15, 15, -7, 7, 4],\n [0, -8, -4, -9, 12, 2],\n [0, 0, -9, -2, 10, -15],\n [0, 0, 0, -11, -11, -2],\n [0, 0, 0, 0, 3, -11],\n [0, 0, 0, 0, 0, 14]]\n\nPresent the answer in LaTex format: ... | 264 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 14, -2, 8, 8, -13],\n [0, -4, 4, -2, 14, -11],\n [0, 0, 5, 0, -9, -13],\n [0, 0, 0, 11, -12, 4],\n [0, 0, 0, 0, -15, -13],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex form... | 400 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -4, 7, -2, -2, -2],\n [-4, 10, 4, -2, -2, -4],\n [7, 4, -7, 4, -6, 4],\n [-2, -2, 4, 3, -3, 2],\n [-2, -2, -6, -3, 12, 6],\n [-2, -4, 4, 2, 6, 3]]\n\nPresent the answer in LaTex format: ... | 736 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, -3, 4, 4, -14, -6],\n [0, 12, 4, -11, 4, 14],\n [0, 0, -14, -12, 14, 0],\n [0, 0, 0, 1, -1, -3],\n [0, 0, 0, 0, 4, -15],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format:... | 904 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[14, 0, 7, 2, 10, 1],\n [0, 4, -3, 8, 13, 6],\n [0, 0, 1, 11, -11, 6],\n [0, 0, 0, -13, -8, -4],\n [0, 0, 0, 0, 12, 9],\n [0, 0, 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: \... | 736 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 1, -10, -9, -2, 11],\n [14, -8, -4, 12, 2, -2],\n [-15, -12, 1, 2, 3, -12],\n [12, 12, -10, -8, 9, -1],\n [4, -15, 14, -11, 0, 5],\n [9, -10, 5, -6, -6, -11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answ... | 424 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, 9, -15, 2, 10, 5],\n [5, 6, 14, 8, 12, 1],\n [-6, 12, -7, 4, -8, 12],\n [-1, -3, 12, 5, 1, 14],\n [-7, 8, 5, 14, 15, -5],\n [14, -12, 8, 9, -9, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex form... | 220 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -8, -7, 0, -11, 7],\n [0, -15, 11, 8, 3, 1],\n [0, 0, -3, -8, 11, -13],\n [0, 0, 0, 5, 11, -8],\n [0, 0, 0, 0, 4, 8],\n [0, 0, 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... | 500 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[9, 6, 15, -2, -12, -8],\n [0, -2, 13, 10, 2, 7],\n [0, 0, -1, 4, 4, 10],\n [0, 0, 0, -1, 7, -1],\n [0, 0, 0, 0, -12, 2],\n [0, 0, 0, 0, 0, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format:... | 272 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, 8, -4, 6, -2, -1],\n [8, 2, 4, 4, -1, 4],\n [-4, 4, 2, -2, -9, -3],\n [6, 4, -2, 10, 6, 6],\n [-2, -1, -9, 6, 6, 2],\n [-1, 4, -3, 6, 2, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 434 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-14, -1, -4, 0, 10, 0],\n [0, 3, -13, 12, 13, 6],\n [4, -12, -15, 6, -8, 8],\n [-1, 8, 5, 10, 6, -11],\n [4, -4, 4, 4, -12, 14],\n [15, 6, -1, -10, -11, 12]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\... | 288 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -11, 1, -6, 5, 1],\n [-7, -3, -6, 13, 15, -8],\n [-9, -14, -14, 14, -12, -7],\n [14, 9, -2, 8, -5, 15],\n [5, 14, -9, 12, 9, 3],\n [-12, -14, 9, 7, 6, 5]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\... | 294 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -2, 0, -5, 10, -4],\n [-2, 9, -3, -6, 6, -2],\n [0, -3, -12, 4, -9, 2],\n [-5, -6, 4, 4, 0, 2],\n [10, 6, -9, 0, -13, 3],\n [-4, -2, 2, 2, 3, -1]]\n\nPresent the answer in LaTex fo... | 79 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-14, 4, 1, 3, 4, 0],\n [0, 3, 5, 1, 13, -12],\n [0, 0, 5, -13, 14, 6],\n [0, 0, 0, 5, 4, -11],\n [0, 0, 0, 0, 14, 11],\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 answer... | 400 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[3, 2, -6, 0, -4, 6],\n [2, 2, 12, -2, 0, 0],\n [-6, 12, 8, 6, -2, 2],\n [0, -2, 6, 13, 8, -4],\n [-4, 0, -2, 8, 0, 0],\n [6, 0, 2, -4, 0, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 104 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, 11, 13, -5, -9, 13],\n [-7, -2, -11, 2, 14, 8],\n [15, 9, 7, 12, -3, -11],\n [-8, -1, 6, 12, -12, -15],\n [-10, 8, 3, -4, -9, -3],\n [12, -9, -7, -15, 5, 8]]\n\nPresent the answer in LaT... | 628 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 5, -6, 7, -4, 0],\n [5, 0, 4, 2, 0, 10],\n [-6, 4, 6, 8, -10, 5],\n [7, 2, 8, 10, -10, -12],\n [-4, 0, -10, -10, -2, -4],\n [0, 10, 5, -12, -4, -2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex... | 392 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 9, -3, -3, -7, -10],\n [0, 9, 14, -11, 9, 5],\n [0, 0, -12, -14, -14, 15],\n [0, 0, 0, -2, 3, 1],\n [0, 0, 0, 0, 13, -9],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\bo... | 232 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 4, 1, 9, 3, 14],\n [1, 9, 11, 11, -2, 15],\n [-3, 10, -2, 10, 0, 5],\n [12, -1, 14, 9, 3, 6],\n [-5, -4, -5, 12, 7, -11],\n [12, -8, 10, -10, 0, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTe... | 660 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, -10, -9, 10, 11, -8],\n [11, 15, -13, 8, -1, 6],\n [-10, -5, 14, -13, 0, -10],\n [-5, 13, -8, 13, 7, -6],\n [15, -6, 7, -13, 10, -2],\n [3, 5, 12, 5, -7, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answ... | 523 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[12, -3, -6, 2, 5, -6],\n [-3, -2, 0, -10, -3, -4],\n [-6, 0, 0, 0, 0, 4],\n [2, -10, 0, -9, 9, 12],\n [5, -3, 0, 9, -11, -8],\n [-6, -4, 4, 12, -8, 12]]\n\nPresent the answer in LaTex ... | 288 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 0, 2, -3, -4, -6],\n [0, 15, 4, 2, 0, 4],\n [2, 4, -7, 2, -14, 6],\n [-3, 2, 2, -4, 8, 4],\n [-4, 0, -14, 8, -13, -12],\n [-6, 4, 6, 4, -12, 13]]\n\nPresent the answer in LaTex format: \... | 843 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-15, -13, -15, -1, 2, 4],\n [-13, 13, -1, 11, 6, 12],\n [12, -11, 5, -6, -9, 7],\n [9, -8, -13, 2, 1, 15],\n [0, 10, 6, 13, -3, -12],\n [-13, -5, 11, -14, 2, 11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex forma... | 282 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -2, 5, 8, 0, 4],\n [-2, -6, 4, 10, -2, 6],\n [5, 4, -6, -1, 7, 6],\n [8, 10, -1, -3, 0, -8],\n [0, -2, 7, 0, -7, 2],\n [4, 6, 6, -8, 2, -7]]\n\nPresent the answer in LaTex format: \... | 818 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[13, 4, -3, 1, -8, -2],\n [4, 9, 6, 4, 6, 3],\n [-3, 6, 1, 1, -4, -4],\n [1, 4, 1, -1, -6, -5],\n [-8, 6, -4, -6, 14, 2],\n [-2, 3, -4, -5, 2, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex forma... | 544 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-14, 12, -10, 0, 8, -9],\n [0, 3, -4, 2, -6, -9],\n [0, 0, 1, 1, -12, 5],\n [0, 0, 0, 6, 10, 7],\n [0, 0, 0, 0, -12, 13],\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... | 24 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -13, 2, 10, -9, 12],\n [0, 9, 2, 4, -8, -5],\n [0, 0, -9, -1, -6, -4],\n [0, 0, 0, -1, 5, 5],\n [0, 0, 0, 0, 9, -7],\n [0, 0, 0, 0, 0, -8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format: ... | 336 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 15, 10, -11, 13, -12],\n [-10, -5, 14, 12, -11, 13],\n [6, -2, 14, -6, -5, -13],\n [15, 7, -8, 5, -11, 12],\n [4, 15, 10, 5, 12, -6],\n [11, -8, 5, -7, 13, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the an... | 671 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, -12, -2, 3, 15, -12],\n [-12, -10, 6, -6, 0, -2],\n [-2, 6, -15, 6, 13, 4],\n [3, -6, 6, -7, 4, -6],\n [15, 0, 13, 4, 2, -4],\n [-12, -2, 4, -6, -4, 10]]\n\nPresent the answer in LaTex f... | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[13, -12, 13, -13, -15, 14],\n [-12, -7, -15, 0, 7, -13],\n [8, -10, -3, 1, -1, 10],\n [5, 14, -4, 13, -8, 11],\n [15, 0, -13, 12, 12, -12],\n [-9, -1, -5, 0, 6, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex fo... | 151 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, 0, 12, -8, -2, 13],\n [1, 13, -12, -9, 1, 12],\n [8, 0, -2, 0, 11, -14],\n [8, -1, -5, -3, -12, 8],\n [-15, -1, -4, 5, -7, -9],\n [-13, 0, -12, 10, 7, -2]]\n\nPresent the answer in LaTex... | 442 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 13, -14, -8, 5, 14],\n [0, 8, -4, -2, 12, -2],\n [0, 0, -14, -2, 7, 9],\n [0, 0, 0, -7, 13, -8],\n [0, 0, 0, 0, -1, 9],\n [0, 0, 0, 0, 0, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex form... | 40 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, 3, -2, 11, -12, 11],\n [14, -5, 0, 7, 10, 14],\n [-14, -14, -7, 6, 11, 15],\n [15, 7, 5, 13, 5, 15],\n [-12, -8, 7, 10, 2, -1],\n [-14, 6, 12, -5, 1, -9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \... | 25 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 5, 2, -6, -3, -8],\n [5, 12, 2, 4, -5, 0],\n [2, 2, -2, -1, -6, 4],\n [-6, 4, -1, 8, -5, -4],\n [-3, -5, -6, -5, -6, 2],\n [-8, 0, 4, -4, 2, -11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex ... | 769 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -15, -5, 5, -10, -8],\n [-9, -10, 2, -4, -8, 8],\n [11, 5, 3, 12, 11, 8],\n [-11, 3, -7, 9, -4, -1],\n [7, -3, 8, -3, 5, 5],\n [-11, 15, -14, 3, -8, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\b... | 521 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -3, 5, -7, 5, -7],\n [6, 6, -5, 15, -10, 7],\n [-4, 11, -12, -12, 9, 15],\n [12, 7, 11, 10, 6, 1],\n [-9, -10, 12, 4, 13, -8],\n [-9, -8, -7, -15, -13, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \... | 211 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 13, -7, 8, 4, 5],\n [0, 1, 14, -10, -13, 11],\n [0, 0, 1, -10, -8, -2],\n [0, 0, 0, -1, -8, -5],\n [0, 0, 0, 0, -3, 15],\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: ... | 820 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[6, 0, 0, -1, 2, 10],\n [0, -5, -1, 7, -6, 2],\n [0, -1, -2, -2, -2, -8],\n [-1, 7, -2, -2, 6, 10],\n [2, -6, -2, 6, -3, -2],\n [10, 2, -8, 10, -2, -2]]\n\nPresent the answer in LaTex format:... | 526 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, 12, -11, 7, 4, -11],\n [-9, 1, 15, -4, -1, -13],\n [1, -2, -1, -1, -1, 3],\n [-5, 2, 5, -6, 5, 10],\n [-7, 8, -13, -15, 5, -5],\n [0, -13, 5, -7, -5, 14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTe... | 364 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 2, -6, 4, 5, 5],\n [2, -5, -7, 10, -7, -3],\n [-6, -7, -11, 1, 12, 1],\n [4, 10, 1, 1, 1, 0],\n [5, -7, 12, 1, -7, 3],\n [5, -3, 1, 0, 3, 3]]\n\nPresent the answer in LaTex format: \\box... | 29 | MATH |
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