messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 4, 13, -1, -5, -8],\n [0, 5, -9, 10, 3, 7],\n [0, 0, 8, 5, -12, -8],\n [0, 0, 0, 5, -14, 8],\n [0, 0, 0, 0, 12, 5],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{... | 400 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -11, -15, -15, 3, 14],\n [-14, 5, -4, 10, -10, 7],\n [-12, 7, -5, 8, 11, 1],\n [15, -10, 8, -11, 4, -14],\n [-10, 6, -5, 15, 0, 0],\n [-15, -7, 12, 11, -10, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex form... | 510 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, -11, -14, -10, 5, -14],\n [-3, 14, -5, -5, 0, -5],\n [3, -1, 9, 7, 7, 0],\n [15, -5, 6, 0, -8, -12],\n [-8, -12, 8, 9, -13, -13],\n [11, 13, 2, 13, 10, 3]]\n\nPresent the answer in ... | 687 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 13, 14, 0, -8, 3],\n [2, -15, -2, 3, -1, 2],\n [-14, 6, 12, 1, 2, 14],\n [-10, 3, 15, -12, -15, -8],\n [13, 7, -9, -13, -6, -6],\n [3, -2, -14, 12, -15, 7]]\n\nPresent the answer in LaTe... | 836 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, 12, 2, -9, 13, -8],\n [0, 9, 7, -13, 8, 7],\n [0, 0, 13, -8, 6, 9],\n [0, 0, 0, 3, -15, 12],\n [0, 0, 0, 0, 8, -2],\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 format: \\... | 624 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, -6, 6, -15, 6, 10],\n [8, 11, 2, 2, -2, -1],\n [13, -4, -12, 11, -13, 4],\n [13, -4, -9, 13, -5, -15],\n [-10, -1, -1, 3, -5, 10],\n [7, 10, -14, -2, -14, 13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answ... | 931 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 3, 6, 0, -4, 0],\n [3, -1, 12, 7, 2, -6],\n [6, 12, -4, 6, -4, -3],\n [0, 7, 6, 12, 0, -1],\n [-4, 2, -4, 0, 8, -2],\n [0, -6, -3, -1, -2, 2]]\n\nPresent the answer in LaTex format: \\box... | 800 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, -3, 7, 12, 3, -8],\n [6, -11, 4, -8, 8, -4],\n [-15, 9, 14, 5, 4, -10],\n [6, 2, -8, -9, -15, 5],\n [0, -4, -10, 4, -14, 13],\n [-2, -12, -15, 7, 2, -3]]\n\nPresent the answer in LaTex f... | 64 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 1, -11, -9, 12, 4],\n [13, 4, -12, 12, -10, -9],\n [2, 15, -11, 4, 15, 14],\n [13, -13, -9, 11, 12, 6],\n [-2, -9, -11, 13, 6, -11],\n [14, 7, -14, 14, 11, 5]]\n\nPresent the answe... | 918 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -10, -1, 5, -6, 7],\n [0, 8, -9, -11, -15, -3],\n [0, 0, 2, -3, 5, 5],\n [0, 0, 0, -12, 1, -13],\n [0, 0, 0, 0, 5, 4],\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 forma... | 640 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[13, -3, 1, -13, -8, -2],\n [-13, 0, -3, 4, 8, 1],\n [-3, 13, -10, 1, -2, 1],\n [14, -8, -5, 4, 12, -15],\n [10, -9, 5, 5, 1, 14],\n [-6, -5, 6, 14, -7, -7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in ... | 736 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -12, 10, 11, -2, 6],\n [-5, 11, -6, 3, 2, -10],\n [11, 13, -1, 5, 14, -6],\n [-11, 10, 13, -11, -6, 12],\n [-11, -13, 7, -10, -12, 2],\n [12, -7, 1, 13, -3, 11]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the a... | 550 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -6, -6, -4, -8, 12],\n [-6, -8, -10, 6, 3, -10],\n [-6, -10, 9, -10, -15, 3],\n [-4, 6, -10, -8, -12, 2],\n [-8, 3, -15, -12, -13, -14],\n [12, -10, 3, 2, -14, -2]]\n\nPresent the ... | 888 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 2, 2, -9, 8, 10],\n [2, 2, 6, -5, -1, 4],\n [2, 6, -13, 6, -8, 4],\n [-9, -5, 6, -5, -4, -12],\n [8, -1, -8, -4, 2, -6],\n [10, 4, 4, -12, -6, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex ... | 996 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, 2, -7, 2, -2, -1],\n [2, 4, 12, -10, -2, 4],\n [-7, 12, 6, 0, 8, -10],\n [2, -10, 0, 8, 5, 0],\n [-2, -2, 8, 5, 3, -6],\n [-1, 4, -10, 0, -6, 1]]\n\nPresent the answer in LaTex format: \\... | 352 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[14, -12, 11, 12, 4, -5],\n [10, 15, -5, 11, 14, -5],\n [-14, 14, 1, -7, 12, 15],\n [12, -14, 13, 8, -1, 0],\n [9, -12, -8, -7, 10, 10],\n [-11, 0, -3, 14, -9, 10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer i... | 940 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, -6, -7, 10, 8, 0],\n [-6, 11, -9, 0, 8, -2],\n [-7, -9, -5, 0, 7, -6],\n [10, 0, 0, -4, 2, 0],\n [8, 8, 7, 2, 14, -12],\n [0, -2, -6, 0, -12, 14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 728 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-4, 0, 12, 14, 7, 1],\n [-15, 7, 15, 15, -6, 9],\n [7, -6, 5, 8, -14, -7],\n [6, -3, 9, 0, 2, 3],\n [-4, -8, 1, -1, -6, -1],\n [-1, 15, 7, -9, -3, 1]]\n\nPresent the answer in LaTex fo... | 528 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, 2, 1, 3, 14, 4],\n [2, 2, -2, -3, 5, 9],\n [1, -2, 7, -3, 0, -2],\n [3, -3, -3, 4, -1, 1],\n [14, 5, 0, -1, 14, -8],\n [4, 9, -2, 1, -8, -15]]\n\nPresent the answer in LaTex format: \\bo... | 447 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, 5, 14, 13, -15, 4],\n [-10, 13, -1, 10, 10, -2],\n [4, -1, -2, 9, 5, 8],\n [9, 10, -11, -10, 1, -5],\n [0, -4, -1, 7, -12, 11],\n [2, 5, 12, -13, 6, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex... | 720 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, -5, -1, -4, -13, 1],\n [-13, 3, 4, -12, -13, 10],\n [0, -4, -8, 8, 13, 13],\n [1, -9, -5, 2, -15, -13],\n [-12, -3, -10, 10, -2, -11],\n [0, -1, -1, 14, -12, -8]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex f... | 868 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[11, -6, 3, 8, 8, 11],\n [-6, 7, 6, -8, -2, -4],\n [3, 6, 1, -4, -10, -9],\n [8, -8, -4, 13, -6, -4],\n [8, -2, -10, -6, -4, -4],\n [11, -4, -9, -4, -4, -5]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in ... | 848 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-11, 6, 10, 10, 2, 10],\n [6, -6, 0, -5, -3, -4],\n [10, 0, 11, -1, -4, 6],\n [10, -5, -1, 13, -14, -2],\n [2, -3, -4, -14, 4, -11],\n [10, -4, 6, -2, -11, -9]]\n\nPresent the answer in LaTe... | 785 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 2, -4, -10, -11, 10],\n [0, -4, 11, 15, 10, -5],\n [0, 0, 2, -12, 1, -14],\n [0, 0, 0, -14, -4, 15],\n [0, 0, 0, 0, 9, 5],\n [0, 0, 0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format... | 360 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -15, -6, -5, 0, -2],\n [0, 8, 1, 9, 2, -4],\n [0, 0, 12, 10, -2, 0],\n [0, 0, 0, 9, 7, -5],\n [0, 0, 0, 0, 9, 2],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{You... | 792 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[2, -8, -4, -1, -3, -2],\n [-8, 15, 2, 2, -4, 4],\n [-4, 2, 7, 2, 6, -4],\n [-1, 2, 2, -2, -4, 6],\n [-3, -4, 6, -4, -15, 6],\n [-2, 4, -4, 6, 6, 6]]\n\nPresent the answer in LaTex format: \\... | 222 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-3, -2, -8, -4, 7, 7],\n [0, 5, 10, -8, 5, 9],\n [0, 0, -10, 7, 3, 7],\n [0, 0, 0, 14, -3, -5],\n [0, 0, 0, 0, 5, 9],\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 answer}... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 12, 7, -9, -8, -9],\n [0, 7, 13, -2, 10, 3],\n [0, 0, 15, 9, 15, 2],\n [0, 0, 0, 1, -3, -14],\n [0, 0, 0, 0, 12, -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 format: ... | 160 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 4, 10, -10, -2, 0],\n [4, 4, 0, -1, 12, 3],\n [10, 0, -7, 10, -6, 2],\n [-10, -1, 10, 3, -9, 2],\n [-2, 12, -6, -9, -15, -2],\n [0, 3, 2, 2, -2, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaT... | 890 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -15, 7, 7, 10, -3],\n [-9, -1, -4, 11, 10, -15],\n [-1, -12, -3, 7, 11, 9],\n [-11, 13, -14, 7, 10, -15],\n [0, 7, -10, 7, 0, -2],\n [13, 10, -13, -1, -13, 7]]\n\nPresent the answer in L... | 548 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, 12, 10, 0, 9, -1],\n [-3, -1, 11, -12, 0, 14],\n [-4, 14, -12, -13, 6, 1],\n [6, 2, 9, 2, 7, 12],\n [1, -4, 7, 5, 8, -12],\n [15, -4, 15, 10, 7, 6]]\n\nPresent the answer in LaTex f... | 878 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 2, -2, -6, -8, 2],\n [2, -6, 0, -6, 6, 8],\n [-2, 0, -8, -5, 0, 7],\n [-6, -6, -5, 14, 8, -4],\n [-8, 6, 0, 8, 9, 2],\n [2, 8, 7, -4, 2, -5]]\n\nPresent the answer in LaTex format: \\box... | 480 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -11, 8, 5, 2, -1],\n [-10, 9, 13, 3, -15, -15],\n [-3, -13, -6, 5, -13, -7],\n [-8, -13, 9, 15, -3, -10],\n [-3, 7, 4, 4, -4, -3],\n [-14, 5, 8, 7, 0, 7]]\n\nPresent the answer in LaTex ... | 798 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 2, -7, 5, -10, 0],\n [2, -7, 8, 2, 4, -5],\n [-7, 8, -6, -9, 2, -7],\n [5, 2, -9, -13, 0, 6],\n [-10, 4, 2, 0, -9, -4],\n [0, -5, -7, 6, -4, -13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Y... | 821 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, -3, 4, 0, -6, 2],\n [-3, -11, 2, -8, -4, 0],\n [4, 2, 15, 12, -14, -10],\n [0, -8, 12, -10, 8, 1],\n [-6, -4, -14, 8, 9, 13],\n [2, 0, -10, 1, 13, 10]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\bo... | 254 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, -6, -4, 1, -12, -14],\n [-5, -9, -14, 10, 2, 5],\n [-12, -8, 4, -2, -4, 6],\n [5, 11, 14, 2, -5, 15],\n [13, 12, 14, -8, -14, 9],\n [-1, -7, 3, 4, -8, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\... | 404 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[3, -2, -1, -4, -4, -2],\n [-2, 11, -3, -2, 6, 2],\n [-1, -3, -6, 8, -1, 3],\n [-4, -2, 8, -11, -3, -2],\n [-4, 6, -1, -3, 10, 0],\n [-2, 2, 3, -2, 0, -11]]\n\nPresent the answer in LaT... | 834 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[1, 10, -11, 6, -1, -3],\n [0, -15, -5, 7, -15, -5],\n [0, 0, 5, 14, 10, 0],\n [0, 0, 0, 10, 0, -15],\n [0, 0, 0, 0, -10, -2],\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... | 500 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-7, -8, 12, -6, 1, 7],\n [0, 13, 10, -10, -2, 6],\n [0, 0, 10, -9, -4, -13],\n [0, 0, 0, 7, 0, -9],\n [0, 0, 0, 0, 5, -7],\n [0, 0, 0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\box... | 850 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -14, 9, -3, -14, 3],\n [0, -14, -13, -10, -13, 15],\n [0, 0, 11, -10, 7, 0],\n [0, 0, 0, 2, -9, -7],\n [0, 0, 0, 0, -5, 9],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex for... | 920 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, -8, 10, 4, -13, -4],\n [0, -4, -14, 8, -2, 6],\n [0, 0, -11, -7, 5, -5],\n [0, 0, 0, 1, -14, 8],\n [0, 0, 0, 0, -2, -11],\n [0, 0, 0, 0, 0, 7]]\n\nPresent the answer in LaTex forma... | 224 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 11, 9, -3, 7, 5],\n [-3, 15, -11, 0, 10, -5],\n [6, -11, -3, 12, -5, 9],\n [3, -13, -1, -9, -9, -10],\n [-13, 14, -3, -9, -11, 7],\n [2, 6, 14, -8, 1, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaT... | 641 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, -9, 2, -2, 0, -4],\n [-9, 9, -6, 6, -6, 5],\n [2, -6, -6, 0, -6, -8],\n [-2, 6, 0, 4, -8, 8],\n [0, -6, -6, -8, 15, 0],\n [-4, 5, -8, 8, 0, -11]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{You... | 912 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, 5, 1, 6, 13, 9],\n [0, 7, 6, -11, -12, -12],\n [0, 0, 5, -3, 6, -11],\n [0, 0, 0, 7, -9, 4],\n [0, 0, 0, 0, 1, 5],\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 format: \\... | 800 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[13, 12, -8, 8, -13, 9],\n [3, -15, -14, -1, 6, 12],\n [-6, 2, 6, -2, 1, 11],\n [-3, -15, -11, 10, -3, 11],\n [9, -2, 8, -13, -1, 3],\n [15, 1, 14, -13, 0, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: ... | 601 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[2, 2, 4, -7, 8, -14],\n [-8, 4, -14, -5, 10, -9],\n [-10, 14, -6, -11, -5, -15],\n [-14, 8, -15, 3, -14, 5],\n [4, 13, 7, 5, 8, -12],\n [15, -4, 6, 4, 2, -15]]\n\nPresent the answer in... | 923 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 14, -8, 13, 13, -15],\n [-14, 14, -1, 4, 12, 2],\n [-5, 9, -6, 8, 8, -12],\n [-11, -12, -3, 9, -3, 2],\n [13, 11, 8, -14, 0, -15],\n [10, 3, -7, 12, -13, 9]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format:... | 165 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, -4, 6, 10, 6, 3],\n [-4, 4, 1, 2, 2, -9],\n [6, 1, 8, -2, 6, -6],\n [10, 2, -2, -6, 2, 13],\n [6, 2, 6, 2, -15, -5],\n [3, -9, -6, 13, -5, 14]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your... | 23 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 13, 7, 11, 6, -6],\n [9, -3, 0, -7, -14, 7],\n [-11, 13, 6, 1, 7, 6],\n [-12, 1, -7, 4, -14, 8],\n [2, 5, 11, 6, -5, -3],\n [-8, 11, -15, 1, -4, -12]]\n\nPresent the answer in LaTe... | 98 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 7, 12, -2, 6, -6],\n [0, 15, -11, 7, 11, -10],\n [0, 0, -3, 13, -3, 3],\n [0, 0, 0, -15, -8, 6],\n [0, 0, 0, 0, -10, 0],\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... | 500 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 9, 8, 9, 0, 4],\n [0, -10, -11, 5, -12, -14],\n [12, -10, -7, 12, 1, -2],\n [-9, 6, 3, -15, 13, 4],\n [15, 14, 9, -1, 2, -13],\n [2, 14, -14, -6, -5, 11]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTe... | 272 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[12, 4, 1, 0, -10, 3],\n [4, 4, -2, -2, 7, 5],\n [1, -2, -7, 5, 4, 1],\n [0, -2, 5, -15, -8, 0],\n [-10, 7, 4, -8, 0, 8],\n [3, 5, 1, 0, 8, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\box... | 45 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[2, 0, -4, 4, -3, -8],\n [11, 13, 14, 10, 6, -15],\n [10, 5, -9, -1, 13, 6],\n [-3, -3, 12, -7, 8, -1],\n [-12, -3, 11, -4, -11, -9],\n [-8, -11, -7, -2, 10, -4]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format... | 830 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 13, -12, 4, 7, 10],\n [0, -6, -3, -14, -13, 3],\n [-10, 3, 11, 5, 4, 3],\n [-8, -2, -6, -13, -10, 13],\n [-1, 7, 7, 2, -2, 3],\n [12, 10, -6, -1, -12, 7]]\n\nPresent the answer in L... | 736 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-14, -13, -9, 7, 0, 15],\n [0, 3, 12, 1, 12, 3],\n [0, 0, 4, -3, -3, -5],\n [0, 0, 0, 1, 6, 2],\n [0, 0, 0, 0, 6, 7],\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: \\... | 48 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -15, -4, -14, 11, 12],\n [0, 6, 1, 10, -13, -9],\n [0, 0, 4, -4, -13, 1],\n [0, 0, 0, 6, -10, 9],\n [0, 0, 0, 0, -3, 11],\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{Yo... | 984 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-14, -4, 12, -14, 10, 0],\n [0, -13, -6, 3, -8, -9],\n [0, 0, 13, 12, -11, 0],\n [0, 0, 0, 8, 5, -14],\n [0, 0, 0, 0, -4, -4],\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 fo... | 304 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, 0, -2, 1, -2, 1],\n [0, -8, -7, -2, -6, 2],\n [-2, -7, -9, -2, -6, 2],\n [1, -2, -2, -4, 2, -2],\n [-2, -6, -6, 2, -13, -4],\n [1, 2, 2, -2, -4, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTe... | 140 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 10, -2, 2, -4, -6],\n [10, 11, 0, -2, -3, 8],\n [-2, 0, -2, 2, 10, 4],\n [2, -2, 2, 10, 0, -6],\n [-4, -3, 10, 0, -10, 2],\n [-6, 8, 4, -6, 2, 13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Y... | 592 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 14, 13, 4, -15, -7],\n [-4, -12, 12, 6, -3, -9],\n [-8, 12, -3, -5, -7, 9],\n [8, 0, -6, -5, 15, -4],\n [12, 15, -2, 3, -4, 2],\n [5, 1, -13, -15, 13, 3]]\n\nPresent the answer in L... | 431 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[8, -2, 1, 9, 3, -15],\n [0, -3, -2, 11, -10, 11],\n [0, 0, 14, -2, -13, 7],\n [0, 0, 0, 3, 12, 7],\n [0, 0, 0, 0, 11, 9],\n [0, 0, 0, 0, 0, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\b... | 792 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, -5, -3, 0, 15, 2],\n [15, 1, 1, 13, -5, 4],\n [-6, 13, 0, -14, 1, 6],\n [14, 4, -6, -3, -4, -1],\n [-9, 11, 6, 5, 10, 12],\n [-3, -4, -4, 12, -14, -11]]\n\nPresent the answer in LaTex fo... | 617 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 9, -14, 7, 10, 14],\n [4, -3, 13, -13, -5, 0],\n [-15, 3, -5, -7, -2, 15],\n [-7, -9, 0, -13, 13, 3],\n [-12, -9, 7, 12, -4, 14],\n [2, 12, 15, -11, 7, 7]]\n\nPresent the answer in ... | 48 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 8, 13, 6, -14, -9],\n [0, -7, -11, -1, 2, -12],\n [0, 0, 10, -9, 10, -8],\n [0, 0, 0, 5, 12, 7],\n [0, 0, 0, 0, 1, -11],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format... | 200 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -8, 2, -13, 8, 8],\n [0, -8, -6, -14, -4, 7],\n [0, 0, 5, 7, 8, -13],\n [0, 0, 0, 13, 5, -11],\n [0, 0, 0, 0, -2, 0],\n [0, 0, 0, 0, 0, -1]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\bo... | 880 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 5, 12, -9, 10, -13],\n [0, -10, 5, -7, -6, -12],\n [0, 0, -7, 8, 6, 1],\n [0, 0, 0, -4, 11, -15],\n [0, 0, 0, 0, 3, -10],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\b... | 240 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 6, 0, -4, 0, 1],\n [6, -4, 8, -3, -15, 2],\n [0, 8, -1, -2, 6, -8],\n [-4, -3, -2, 5, -2, 4],\n [0, -15, 6, -2, -7, 2],\n [1, 2, -8, 4, 2, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \... | 666 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 5, 15, -4, 12, -15],\n [0, 1, -7, 7, 3, 9],\n [0, 0, -9, -7, 6, 10],\n [0, 0, 0, -2, -1, -1],\n [0, 0, 0, 0, -8, 15],\n [0, 0, 0, 0, 0, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\bo... | 776 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-15, -7, -10, 4, 10, 14],\n [0, -7, -11, -2, -11, -8],\n [0, 0, -3, -8, -5, 12],\n [0, 0, 0, 3, -10, 6],\n [0, 0, 0, 0, 9, 12],\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{Y... | 930 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[12, -7, -3, 13, -12, -7],\n [0, -2, 3, -4, 5, 10],\n [0, 0, -13, 10, 9, 6],\n [0, 0, 0, 4, 8, 7],\n [0, 0, 0, 0, 3, 14],\n [0, 0, 0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed... | 24 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, 12, 11, -1, 2, 0],\n [0, 5, 1, -8, -15, 13],\n [0, 0, 11, -13, 0, 12],\n [0, 0, 0, -7, 0, 15],\n [0, 0, 0, 0, -9, 2],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed... | 650 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[14, 9, -3, 0, -9, 0],\n [0, -2, 1, -4, 13, 8],\n [0, 0, -3, 8, 4, -1],\n [0, 0, 0, 6, -14, 12],\n [0, 0, 0, 0, 14, 10],\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 format: ... | 672 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -12, 4, -10, -2, 1],\n [-12, -13, -4, 8, 3, 3],\n [4, -4, 3, -3, -2, 6],\n [-10, 8, -3, -9, 0, -5],\n [-2, 3, -2, 0, -2, 6],\n [1, 3, 6, -5, 6, 1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{... | 387 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, 5, 11, 3, 7, 3],\n [2, 3, -5, -13, -8, 4],\n [3, -6, 0, -11, 4, -7],\n [-8, -5, 0, -9, -1, 8],\n [13, 5, 4, 7, 1, -10],\n [-1, -8, -9, -14, 14, -3]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{... | 138 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 10, 0, -2, -7, 2],\n [10, 0, -1, 0, 6, -2],\n [0, -1, -2, -2, 3, -3],\n [-2, 0, -2, 5, 4, 1],\n [-7, 6, 3, 4, 12, -10],\n [2, -2, -3, 1, -10, 10]]\n\nPresent the answer in LaTex for... | 505 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, 4, 3, -4, -2, 0],\n [4, 2, 0, -6, -7, 8],\n [3, 0, -7, 6, -6, -4],\n [-4, -6, 6, -5, -4, 5],\n [-2, -7, -6, -4, 6, -3],\n [0, 8, -4, 5, -3, 1]]\n\nPresent the answer in LaTex format: \\b... | 40 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, -10, 0, 4, 8, -13],\n [0, 3, 3, 8, -12, -15],\n [0, 0, 14, 10, 13, -3],\n [0, 0, 0, 3, 6, 8],\n [0, 0, 0, 0, 1, -6],\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 answe... | 32 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -7, -6, 7, 4, 4],\n [0, -10, -12, -11, -7, -4],\n [0, 0, 5, -11, 13, -5],\n [0, 0, 0, -2, 12, -8],\n [0, 0, 0, 0, 3, -4],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex forma... | 400 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -2, -1, 0, -14, 14],\n [0, 2, 15, -4, 0, -3],\n [0, 0, 2, -13, 7, -6],\n [0, 0, 0, 3, -12, 13],\n [0, 0, 0, 0, -8, 11],\n [0, 0, 0, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\bo... | 608 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -6, -6, -2, -14, -12],\n [0, 2, -3, 3, -11, 4],\n [0, 0, -5, 14, 14, 10],\n [0, 0, 0, 7, 12, -6],\n [0, 0, 0, 0, -5, 3],\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{You... | 500 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 11, 4, -12, 12, -2],\n [0, -12, -10, 14, -7, 5],\n [0, 0, 10, 14, 15, -8],\n [0, 0, 0, 11, 10, 9],\n [0, 0, 0, 0, 3, 11],\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... | 560 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -9, -6, 5, 7, 14],\n [0, 13, -6, -3, -1, 7],\n [0, 0, 15, -12, 4, 1],\n [0, 0, 0, 5, -14, -12],\n [0, 0, 0, 0, -10, -9],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format... | 250 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, 12, -1, -2, 5, -5],\n [8, 15, -12, -13, -14, 4],\n [11, -6, 14, -3, 4, 13],\n [10, 5, 13, 7, 9, 2],\n [5, 0, -5, -6, -7, -4],\n [14, 13, 3, -15, 2, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\... | 783 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -3, 6, -8, -1, 1],\n [-11, 4, -12, -5, 2, -6],\n [1, 14, -1, -10, 7, 5],\n [0, -1, -8, -7, -5, 11],\n [-14, 11, -3, -12, 11, -7],\n [-11, 3, 6, 15, -13, 14]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer... | 466 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[3, -12, 4, 1, 3, -13],\n [0, -2, 1, -3, -7, 11],\n [0, 0, 1, 0, 2, -14],\n [0, 0, 0, 11, 1, -13],\n [0, 0, 0, 0, -14, -14],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\box... | 620 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -6, 15, 7, -1, 14],\n [0, -3, 12, -12, 2, 8],\n [0, 0, -14, -14, -12, -13],\n [0, 0, 0, -14, 0, -5],\n [0, 0, 0, 0, 7, -14],\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{Y... | 784 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, -2, 2, -7, 0, 1],\n [-2, -9, 0, 1, 0, -5],\n [2, 0, -2, -2, -2, -2],\n [-7, 1, -2, 1, 2, -6],\n [0, 0, -2, 2, -8, 8],\n [1, -5, -2, -6, 8, 9]]\n\nPresent the answer in LaTex format: \\bo... | 488 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -3, 5, -8, 15, -3],\n [-1, 4, 4, -3, 7, 11],\n [-11, 6, 6, 12, -10, 14],\n [10, -11, -3, 13, -11, 9],\n [-3, 8, 15, 4, 7, -8],\n [12, -7, 5, 3, 15, 13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\bo... | 866 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, 8, 8, 6, -2, -2],\n [8, 9, -1, -6, -8, 2],\n [8, -1, 8, 1, -12, 3],\n [6, -6, 1, -12, -4, -3],\n [-2, -8, -12, -4, 1, 2],\n [-2, 2, 3, -3, 2, 11]]\n\nPresent the answer in LaTex fo... | 288 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -9, 12, 1, -13, -5],\n [15, -10, 15, -10, -1, -9],\n [-5, 14, 11, 1, 7, 2],\n [6, 13, 8, 13, 5, 10],\n [3, 11, -8, 8, 4, -8],\n [5, 13, -5, 5, -13, 15]]\n\nPresent the answer in La... | 820 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[15, -14, 8, 14, 3, 1],\n [0, 1, -6, 2, 7, 12],\n [0, 0, 12, 11, 2, 4],\n [0, 0, 0, -13, -1, 4],\n [0, 0, 0, 0, 7, -2],\n [0, 0, 0, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 420 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-8, 0, -11, 2, 4, -2],\n [-14, 7, 7, 14, 15, -13],\n [-2, 13, -9, -1, 1, -15],\n [-7, 6, 13, -2, 0, 12],\n [5, -3, -10, 6, -15, 5],\n [9, -12, -13, 1, 14, 15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in La... | 234 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[10, -1, -9, 3, 4, 6],\n [14, -5, 7, -2, -3, 4],\n [10, 11, 9, -7, -7, 0],\n [-4, -6, -10, 2, -14, 11],\n [4, -7, 3, -10, -14, -1],\n [1, 0, 12, 5, -8, -6]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in L... | 636 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, -8, 8, -9, 5, 2],\n [-2, -1, -6, 10, 5, -4],\n [-9, 12, 12, -9, -5, -3],\n [-1, 2, -9, -10, 7, -5],\n [-8, 4, -15, -8, -8, 3],\n [-13, -11, 14, -13, -1, -2]]\n\nPresent the answer ... | 964 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, -10, -2, -13, 0, -15],\n [0, 14, 15, 15, -2, 3],\n [0, 0, -7, -9, -2, -11],\n [0, 0, 0, 5, -9, -7],\n [0, 0, 0, 0, -10, 2],\n [0, 0, 0, 0, 0, 8]]? 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[[15, 0, 3, -6, -10, 0],\n [0, -3, -7, -9, -12, 3],\n [0, 0, 3, 12, 3, -4],\n [0, 0, 0, -12, 9, 12],\n [0, 0, 0, 0, 14, -11],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format:... | 80 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-5, 2, 0, -2, 2, -2],\n [2, -1, 10, 10, -8, 0],\n [0, 10, 0, 4, 4, 4],\n [-2, 10, 4, -7, -2, 6],\n [2, -8, 4, -2, 4, 4],\n [-2, 0, 4, 6, 4, 0]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format:... | 600 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-3, 6, -12, -12, 5, -2],\n [0, -11, 0, -2, 14, -2],\n [0, 0, 8, 9, 13, -2],\n [0, 0, 0, 1, -2, -6],\n [0, 0, 0, 0, -1, -1],\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: \\... | 152 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-11, 0, 8, -11, 8, 7],\n [-4, -12, 15, 7, -10, 3],\n [-7, -4, 10, -1, 0, -3],\n [9, 14, 5, 8, -9, 9],\n [7, 4, -12, -5, -8, -10],\n [9, 14, -6, 14, -9, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in ... | 828 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-12, -13, 8, -9, -12, -3],\n [0, 1, 11, -9, 1, 10],\n [0, 0, -5, 14, -13, -5],\n [0, 0, 0, -12, -2, -15],\n [0, 0, 0, 0, -1, 15],\n [0, 0, 0, 0, 0, 15]]\n\nPresent the answer in LaTex ... | 800 | MATH |
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