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[[-15, -7, -2, 13, 2, -13],\n [0, 9, -10, -4, -6, 10],\n [0, 0, -2, 4, -4, 12],\n [0, 0, 0, 8, -9, 7],\n [0, 0, 0, 0, -14, 4],\n [0, 0, 0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\bo... | 760 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-8, -7, 2, 10, 4, -9],\n [0, 2, 12, -5, 0, 11],\n [0, 0, -15, 3, -4, -1],\n [0, 0, 0, -10, -4, -2],\n [0, 0, 0, 0, 10, 1],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\box... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 8, 1, 12, -1, 8],\n [0, 9, 8, -4, -15, 10],\n [0, 0, 1, -4, 8, 7],\n [0, 0, 0, 12, -7, 1],\n [0, 0, 0, 0, -2, -4],\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: \... | 960 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, 0, -5, -7, -12, -4],\n [0, -12, -3, -10, 0, -9],\n [0, 0, 6, -15, 7, 14],\n [0, 0, 0, -2, -14, 2],\n [0, 0, 0, 0, -14, -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 ... | 616 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 2, -1, 10, -6, 0],\n [2, 8, 0, 3, -7, 4],\n [-1, 0, -2, 5, 0, -5],\n [10, 3, 5, 12, -15, -2],\n [-6, -7, 0, -15, 0, -7],\n [0, 4, -5, -2, -7, -6]]\n\nPresent the answer in LaTex fo... | 391 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, -3, -12, -12, -3, -8],\n [0, 8, -14, -3, -12, 11],\n [0, 0, 15, -5, 6, -8],\n [0, 0, 0, 12, 2, 13],\n [0, 0, 0, 0, -4, -4],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex for... | 480 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, 8, 8, -4, -11, -7],\n [0, -4, -11, -10, -3, 15],\n [0, 0, 12, -5, 9, 13],\n [0, 0, 0, -14, 15, -4],\n [0, 0, 0, 0, 3, -7],\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... | 96 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 3, -5, 1, -4, -15],\n [0, -5, 9, 10, 1, 15],\n [0, 0, 8, -8, 8, -2],\n [0, 0, 0, -2, -1, 2],\n [0, 0, 0, 0, 6, -1],\n [0, 0, 0, 0, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed... | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 8, 3, -10, 0, -8],\n [-14, -10, -13, 6, -15, -7],\n [-6, -6, -3, 10, -11, 13],\n [3, 12, -6, -11, -11, 6],\n [1, -4, 5, -9, -10, 3],\n [13, -1, 14, -15, 0, 15]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex for... | 840 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-4, -9, 7, 9, -8, 7],\n [-3, -8, -8, 10, -10, 13],\n [-13, -1, -9, -14, 12, 2],\n [-15, 0, 11, -4, -1, -8],\n [-8, 10, 2, 2, 7, -3],\n [-7, -4, 7, -9, -15, 12]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer... | 164 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-14, 14, 0, -11, 12, 1],\n [14, 10, 8, -11, 10, -2],\n [0, 8, -2, 8, 2, -1],\n [-11, -11, 8, -1, 10, 7],\n [12, 10, 2, 10, 0, 6],\n [1, -2, -1, 7, 6, -4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex f... | 336 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, -4, -10, 12, 12, 11],\n [0, 14, -11, 14, 11, 3],\n [0, 0, -3, -14, -9, -15],\n [0, 0, 0, -3, -2, -4],\n [0, 0, 0, 0, -12, 1],\n [0, 0, 0, 0, 0, 10]]\n\nPresent the answer in LaTex format... | 360 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -2, -2, -5, -2, 0],\n [-2, 10, 6, -4, 9, -1],\n [-2, 6, 9, 6, -4, 4],\n [-5, -4, 6, -15, 4, -8],\n [-2, 9, -4, 4, 5, 2],\n [0, -1, 4, -8, 2, -15]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex f... | 148 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 5, -9, -14, -14, -6],\n [8, 2, -3, 13, -10, 5],\n [6, -3, -5, 14, -8, -8],\n [-12, 5, -8, 1, 7, -6],\n [13, 12, -12, 6, -8, -13],\n [-13, 6, -2, 5, 14, -8]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in La... | 829 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[9, 8, -10, 10, 4, 1],\n [4, 9, -14, 9, 2, 9],\n [-9, 6, 2, -1, 5, -8],\n [-1, -4, -14, -10, -15, 13],\n [-13, -7, 10, 11, -2, -14],\n [5, -13, 14, -6, 0, -2]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaT... | 986 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, -11, 1, -2, -3, -13],\n [-15, -8, 14, 7, 1, 4],\n [-2, 3, 0, 3, -9, 3],\n [0, 12, 7, 9, 3, -9],\n [12, -1, -4, 6, 9, 7],\n [-3, 14, 4, -4, -5, -3]]\n\nPresent the answer in LaTex format: ... | 672 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-4, -10, -5, -13, 4, -12],\n [0, -7, 2, 14, 3, -9],\n [0, 0, 2, -15, 0, 2],\n [0, 0, 0, 2, 1, 14],\n [0, 0, 0, 0, 10, 12],\n [0, 0, 0, 0, 0, -7]]\n\nPresent the answer in LaTex format: \\box... | 160 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, 9, 1, 3, -1, 12],\n [0, -11, 9, -9, 15, 12],\n [0, 0, 8, 0, -15, 10],\n [0, 0, 0, 15, -15, 8],\n [0, 0, 0, 0, 4, 7],\n [0, 0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed... | 720 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-15, 8, -12, -5, 4, 10],\n [0, 1, 8, 0, 3, -14],\n [0, 0, 4, -15, 7, 11],\n [0, 0, 0, -13, -4, 12],\n [0, 0, 0, 0, 11, -2],\n [0, 0, 0, 0, 0, -12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: ... | 40 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 0, -4, -12, -6, 0],\n [0, 1, 12, 15, 6, -6],\n [0, 0, -11, 0, -13, 10],\n [0, 0, 0, 13, 10, -13],\n [0, 0, 0, 0, 5, -7],\n [0, 0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format... | 575 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-9, 7, -9, 12, -13, 10],\n [0, 4, 7, 12, 3, -3],\n [0, 0, -6, 14, -6, 5],\n [0, 0, 0, 4, 15, -13],\n [0, 0, 0, 0, -10, -13],\n [0, 0, 0, 0, 0, -6]]\n\nPresent the answer in LaTex forma... | 840 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-7, 8, 5, 12, 2, 7],\n [8, 12, -8, -1, -2, -8],\n [5, -8, 4, 5, 11, 2],\n [12, -1, 5, -14, -4, 8],\n [2, -2, 11, -4, -6, -4],\n [7, -8, 2, 8, -4, -9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex forma... | 64 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, 13, 9, 1, -5, 9],\n [-8, 3, -8, 2, -4, 6],\n [4, -15, 5, 11, -12, 9],\n [-7, -5, 12, 0, -1, -10],\n [-3, 15, -3, 1, -12, 9],\n [7, 3, 5, -9, 9, 14]]\n\nPresent the answer in LaTex ... | 802 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, 0, 10, -2, 14, -11],\n [0, 9, -6, 3, 0, 0],\n [10, -6, -5, 2, 4, -5],\n [-2, 3, 2, 12, -2, -4],\n [14, 0, 4, -2, 6, 10],\n [-11, 0, -5, -4, 10, 9]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex form... | 982 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 0, -12, -12, 6, -13],\n [0, -11, -8, -3, 11, -3],\n [0, 0, -11, 8, 5, -8],\n [0, 0, 0, 3, 12, -4],\n [0, 0, 0, 0, -9, 10],\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{Y... | 310 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[15, -3, -2, 4, 2, 2],\n [-3, 2, -4, -2, 2, -6],\n [-2, -4, -2, -5, -6, 8],\n [4, -2, -5, -14, 0, 4],\n [2, 2, -6, 0, -7, 2],\n [2, -6, 8, 4, 2, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex for... | 456 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -13, 0, 2, 9, -5],\n [0, -12, -15, 11, -13, -6],\n [0, 0, 9, 3, -5, 2],\n [0, 0, 0, 2, -14, 0],\n [0, 0, 0, 0, -7, -8],\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... | 584 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-14, -8, -7, -4, 6, 13],\n [-8, -15, 0, -12, 12, 4],\n [-7, 0, 5, -4, 3, -8],\n [-4, -12, -4, -3, 15, 4],\n [6, 12, 3, 15, 0, -8],\n [13, 4, -8, 4, -8, -3]]\n\nPresent the answer in LaTex fo... | 339 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, -3, 8, 4, -13, -12],\n [-4, -11, 1, -12, 4, -15],\n [-2, 14, -9, 14, 7, 11],\n [-8, 11, 13, 9, 9, -12],\n [-14, 3, -4, -15, 7, 7],\n [-13, 15, 6, 0, 3, 8]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer ... | 510 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-13, 10, -9, 0, 14, -2],\n [0, -11, -14, 12, 7, 14],\n [0, 0, 1, -8, 4, -6],\n [0, 0, 0, 1, -9, -8],\n [0, 0, 0, 0, 12, 4],\n [0, 0, 0, 0, 0, -13]]\n\nPresent the answer in LaTex forma... | 692 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-12, -7, -8, 12, 2, 7],\n [0, -7, -13, -15, -11, -14],\n [0, 0, -2, 1, 10, -12],\n [0, 0, 0, 5, 9, -13],\n [0, 0, 0, 0, -3, 11],\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... | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -2, -8, -6, 14, -3],\n [-2, 9, 6, 0, -4, -2],\n [-8, 6, -6, 0, -6, 4],\n [-6, 0, 0, -10, -1, 2],\n [14, -4, -6, -1, -12, -4],\n [-3, -2, 4, 2, -4, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex ... | 434 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, 1, -5, 8, 8, 8],\n [1, 0, 2, 2, 4, -12],\n [-5, 2, -3, 2, 1, -2],\n [8, 2, 2, -1, -2, 0],\n [8, 4, 1, -2, -5, -2],\n [8, -12, -2, 0, -2, 0]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 960 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-3, 8, -2, -7, 4, 9],\n [8, 6, 7, -12, -8, 4],\n [-2, 7, 9, 9, 7, -12],\n [-7, -12, 9, -11, 9, 14],\n [4, -8, 7, 9, 6, -3],\n [9, 4, -12, 14, -3, 1]]\n\nPresent the answer in LaTex for... | 792 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, 4, 8, 0, -5, -2],\n [4, 13, -4, -2, -5, -4],\n [8, -4, -6, 0, 5, 2],\n [0, -2, 0, 4, -6, -11],\n [-5, -5, 5, -6, 11, 0],\n [-2, -4, 2, -11, 0, 3]]\n\nPresent the answer in LaTex for... | 715 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -7, 4, 0, 2, -7],\n [-7, 7, 3, 4, -2, -7],\n [4, 3, 3, -7, 6, -4],\n [0, 4, -7, 7, 9, 0],\n [2, -2, 6, 9, 5, -1],\n [-7, -7, -4, 0, -1, -10]]\n\nPresent the answer in LaTex format... | 911 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[14, 0, 12, 9, -12, 6],\n [-4, 11, 6, 8, -10, -3],\n [-1, 10, 9, 7, -2, 5],\n [-12, -8, 0, 5, 6, 4],\n [-14, 8, -2, 14, -2, 7],\n [9, -6, 9, -4, 7, 7]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{Y... | 422 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-2, 6, -1, -7, -9, 2],\n [0, -7, -1, 6, -3, 10],\n [0, 0, 15, 10, 4, 9],\n [0, 0, 0, 12, 2, -4],\n [0, 0, 0, 0, 4, -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: \\bo... | 40 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-15, -8, 12, -15, 6, -4],\n [-7, 9, -6, -7, 6, 6],\n [1, 10, 13, -10, 1, 6],\n [-2, 5, 10, -15, 5, -1],\n [4, 6, 11, 7, -2, 15],\n [-6, 7, -8, 5, 4, 13]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaT... | 515 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-11, -8, 8, -2, -2, 2],\n [-8, 14, -2, 2, 9, -8],\n [8, -2, -10, -3, 1, -6],\n [-2, 2, -3, 1, -1, -6],\n [-2, 9, 1, -1, 14, 11],\n [2, -8, -6, -6, 11, 3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex f... | 545 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[15, 3, -14, 7, 7, -4],\n [0, 14, 2, 9, -8, 12],\n [0, 0, 13, 1, -7, 12],\n [0, 0, 0, 14, 0, -3],\n [0, 0, 0, 0, -3, -11],\n [0, 0, 0, 0, 0, -2]]\n\nPresent the answer in LaTex format: ... | 320 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, 13, -1, 9, -12, -9],\n [0, 3, -4, -8, 1, 3],\n [0, 0, -4, -2, -5, 1],\n [0, 0, 0, 2, -4, -10],\n [0, 0, 0, 0, 9, -4],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \... | 648 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, 11, 2, -4, 11, 1],\n [11, 3, -4, 0, 6, 2],\n [2, -4, 6, 5, -5, 0],\n [-4, 0, 5, -4, 4, 2],\n [11, 6, -5, 4, -2, -6],\n [1, 2, 0, 2, -6, -9]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex forma... | 725 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-14, -5, 4, 6, -5, -4],\n [-5, -7, 1, 4, -8, 6],\n [4, 1, 7, 8, 8, -4],\n [6, 4, 8, -1, 0, 4],\n [-5, -8, 8, 0, -5, 0],\n [-4, 6, -4, 4, 0, -3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTex format... | 487 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, 9, -3, -1, -8, -7],\n [0, 3, -7, -13, 10, 6],\n [0, 0, 8, 15, -3, -10],\n [0, 0, 0, -13, -10, -14],\n [0, 0, 0, 0, -6, 3],\n [0, 0, 0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\... | 768 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[7, 6, -1, 6, -2, -11],\n [6, -6, 8, -12, -2, 12],\n [-1, 8, -12, 12, -4, 0],\n [6, -12, 12, -13, 4, -8],\n [-2, -2, -4, 4, -10, -12],\n [-11, 12, 0, -8, -12, 7]]\n\nPresent the answer in LaT... | 856 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[11, 4, -10, -12, -9, -7],\n [0, -4, 8, 4, -8, 7],\n [0, 0, 3, -6, -7, 14],\n [0, 0, 0, 8, 0, 14],\n [0, 0, 0, 0, 5, 8],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\b... | 320 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -15, -13, -8, 13, 8],\n [-11, 14, -4, 6, -10, 14],\n [-6, -6, -9, 7, 13, 9],\n [11, -8, -14, -4, -6, 4],\n [-3, 9, -12, 5, 5, -15],\n [11, 12, 8, 9, -1, -10]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in... | 778 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 6, 11, -13, -9, 10],\n [0, -1, 2, -5, 2, 4],\n [0, 0, 10, 6, 14, -6],\n [0, 0, 0, 3, 11, 13],\n [0, 0, 0, 0, 6, 9],\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 answ... | 980 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-15, -10, -2, 4, -1, 2],\n [-10, 10, -4, -10, 4, -6],\n [-2, -4, -7, 0, -2, -10],\n [4, -10, 0, 13, -6, 1],\n [-1, 4, -2, -6, -2, -6],\n [2, -6, -10, 1, -6, 2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format:... | 86 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[1, -14, -12, -12, 11, 6],\n [9, 5, -8, -13, 12, -11],\n [3, 13, -12, -14, 12, -12],\n [-14, -4, -11, 12, 5, 7],\n [-9, 7, 9, 6, -8, -9],\n [-6, 0, -2, -1, -8, -13]]\n\nPresent the answ... | 302 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, -6, 2, 13, -13, -6],\n [0, -9, 13, -3, 7, -7],\n [0, 0, -15, 3, -6, -4],\n [0, 0, 0, 7, 6, 0],\n [0, 0, 0, 0, -3, -15],\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 a... | 360 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -14, -10, 11, -12, -5],\n [-7, -9, -4, 7, -8, -8],\n [9, -4, 12, 15, -8, 5],\n [15, 8, -10, -6, -3, -6],\n [-15, -14, 6, 14, -6, 8],\n [6, -13, 7, 15, 10, 6]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format... | 8 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, 6, -2, -4, -15, 2],\n [6, 13, -8, -4, 4, -9],\n [-2, -8, -9, -1, -8, -6],\n [-4, -4, -1, 2, 2, 0],\n [-15, 4, -8, 2, -3, 0],\n [2, -9, -6, 0, 0, -2]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxe... | 579 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-1, 5, 4, 2, -10, 6],\n [5, -4, 10, -3, -2, -2],\n [4, 10, -6, 4, -4, -5],\n [2, -3, 4, 7, 1, -4],\n [-10, -2, -4, 1, -2, 10],\n [6, -2, -5, -4, 10, 7]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex for... | 521 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-2, -4, 5, -7, -2, 4],\n [0, -11, 2, 15, 4, -13],\n [0, 0, -8, -10, -15, -2],\n [0, 0, 0, 9, 13, -6],\n [0, 0, 0, 0, -3, 12],\n [0, 0, 0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\b... | 8 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -9, 2, 0, 6, -12],\n [6, -11, 2, -4, -3, -10],\n [3, -4, 11, 15, 9, 15],\n [13, 4, -4, 15, -9, 7],\n [3, -10, -12, -9, 12, 14],\n [15, 10, -4, -5, 11, -5]]\n\nPresent the answer in LaTex ... | 706 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[0, 4, 6, 1, 8, -9],\n [2, 14, -15, -3, 3, 4],\n [-14, -6, -2, -1, 2, -12],\n [-14, 9, 15, -12, 2, 6],\n [8, 10, 11, 2, -4, 0],\n [-11, -9, 10, -11, 13, -1]]\n\nPresent the answer in LaTex fo... | 83 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, -7, 12, 4, 15, 10],\n [-3, 6, 2, -5, -15, 3],\n [4, 7, -1, -10, -15, -13],\n [9, 11, -9, 3, 9, 4],\n [-5, -8, 15, -15, -10, 2],\n [-6, 6, -3, -14, -1, -4]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer ... | 64 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-8, -8, 1, -10, 2, 8],\n [0, 11, -14, 15, 15, 3],\n [0, 0, 9, 6, 11, 8],\n [0, 0, 0, 3, -13, 1],\n [0, 0, 0, 0, -10, -11],\n [0, 0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format:... | 720 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[9, 15, 12, 0, -6, 1],\n [0, 9, 6, 12, 10, -9],\n [0, 0, 10, 5, 15, 13],\n [0, 0, 0, -6, 10, -4],\n [0, 0, 0, 0, -4, 9],\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... | 920 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-5, 0, 2, 4, -1, -4],\n [0, -14, -6, -1, 6, 0],\n [2, -6, -3, 0, 10, -5],\n [4, -1, 0, -6, -8, 8],\n [-1, 6, 10, -8, -15, 6],\n [-4, 0, -5, 8, 6, -11]]\n\nPresent the answer in LaTex format:... | 60 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -7, 1, 8, -8, -7],\n [0, -11, -15, -15, -7, -14],\n [0, 0, 1, 0, 0, 8],\n [0, 0, 0, 1, -14, -7],\n [0, 0, 0, 0, 1, 5],\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... | 76 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 1, 6, -6, 9, 11],\n [2, -8, -2, 14, -15, -2],\n [12, 6, -11, 0, 0, 14],\n [-4, 14, -5, 10, -3, 1],\n [4, 7, -2, -3, -5, -4],\n [-14, 3, 3, 14, -12, 1]]\n\nPresent the answer in LaTe... | 768 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[1, -2, 1, -15, -4, -7],\n [0, -2, 11, -6, 7, 6],\n [0, 0, 5, 5, -12, 12],\n [0, 0, 0, -6, 1, -11],\n [0, 0, 0, 0, 5, 0],\n [0, 0, 0, 0, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed... | 900 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, -3, 0, 1, 4, 10],\n [-3, 1, 2, -2, 8, -3],\n [0, 2, -14, 6, -3, 2],\n [1, -2, 6, -11, -2, 4],\n [4, 8, -3, -2, 10, -6],\n [10, -3, 2, 4, -6, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format:... | 797 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-2, 5, 3, -2, 0, 8],\n [0, 15, 14, 8, 1, -6],\n [0, 0, -2, -8, -6, -8],\n [0, 0, 0, -9, -1, 1],\n [0, 0, 0, 0, -7, -11],\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 format... | 80 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, 4, -8, -12, -11, -13],\n [0, 3, 2, 10, 11, -5],\n [0, 0, -5, 3, -3, -6],\n [0, 0, 0, -3, 0, 10],\n [0, 0, 0, 0, -8, 8],\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... | 80 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-6, 6, -1, 6, 10, 2],\n [6, 2, -4, 2, -2, -6],\n [-1, -4, -15, -8, -2, 2],\n [6, 2, -8, -12, -3, 2],\n [10, -2, -2, -3, -8, 12],\n [2, -6, 2, 2, 12, -14]]\n\nPresent the answer in LaTe... | 256 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-7, 8, 2, 2, 8, 3],\n [8, -11, 0, -4, 2, 1],\n [2, 0, 10, -5, -5, -3],\n [2, -4, -5, 8, 10, 4],\n [8, 2, -5, 10, -14, 0],\n [3, 1, -3, 4, 0, 5]]\n\nPresent the answer in LaTex format: ... | 570 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[14, 12, 14, 2, 11, -11],\n [-15, -10, 12, 3, -15, -13],\n [3, 14, 7, -12, 7, -10],\n [6, -1, -3, -11, -7, 2],\n [11, 7, -3, -7, 4, 15],\n [-15, 11, 11, 12, -3, -4]]\n\nPresent the answer in ... | 614 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[1, 8, 4, -7, -12, -1],\n [0, -13, 4, 7, -2, 10],\n [0, 0, -14, -12, -9, -12],\n [0, 0, 0, -7, 11, -13],\n [0, 0, 0, 0, 3, -15],\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... | 686 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, -5, -1, 14, 12, -7],\n [0, -3, 14, 8, 11, 12],\n [0, 0, 11, 13, 3, -11],\n [0, 0, 0, -2, -12, -11],\n [0, 0, 0, 0, 10, -12],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex fo... | 600 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, 7, 11, 6, 0, -15],\n [0, 9, -2, -1, -6, 6],\n [0, 0, -11, 2, -8, 6],\n [0, 0, 0, 8, 6, -4],\n [0, 0, 0, 0, -1, 4],\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: \\boxe... | 288 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[7, -7, 13, -11, 9, -13],\n [0, -11, -1, 10, -6, -11],\n [0, 0, -6, 4, 6, 12],\n [0, 0, 0, -4, -11, 9],\n [0, 0, 0, 0, -14, 1],\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 f... | 24 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -8, 4, -6, -2, -12],\n [-8, -14, -6, -8, 2, 0],\n [4, -6, 11, 2, -6, 12],\n [-6, -8, 2, 7, 8, -5],\n [-2, 2, -6, 8, -13, 2],\n [-12, 0, 12, -5, 2, -7]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in ... | 8 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[10, 12, -4, 8, -6, -1],\n [8, 2, 9, -10, 8, -9],\n [1, -11, 1, 7, -6, -10],\n [-6, 1, -7, 10, 2, -9],\n [7, 1, 4, 1, 10, 7],\n [-2, 3, -11, -2, -10, 9]]\n\nPresent the answer in LaTex ... | 24 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[9, 3, -4, 13, -9, 2],\n [0, -2, 14, -11, -12, -10],\n [0, 0, -7, -15, 2, 0],\n [0, 0, 0, -1, 12, 10],\n [0, 0, 0, 0, -1, 8],\n [0, 0, 0, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\bo... | 756 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[6, -7, 3, 2, 5, -10],\n [-7, 2, 0, 4, -8, 6],\n [3, 0, 12, 8, -10, 0],\n [2, 4, 8, -14, 3, 12],\n [5, -8, -10, 3, 11, 6],\n [-10, 6, 0, 12, 6, -13]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{You... | 410 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-9, -5, -8, 1, -5, -14],\n [-5, 6, 12, -6, 8, -9],\n [6, -8, 12, -5, 8, -13],\n [3, -3, 2, 5, 11, -12],\n [-10, -14, -4, 6, -7, -2],\n [-15, 8, 1, -14, 1, 4]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaT... | 576 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-15, 13, -4, 4, -2, 5],\n [13, -15, 0, -4, -2, -8],\n [-4, 0, -12, -2, -6, 5],\n [4, -4, -2, 13, 2, -8],\n [-2, -2, -6, 2, -9, 4],\n [5, -8, 5, -8, 4, 6]]\n\nPresent the answer in LaTe... | 276 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 7, -3, 12, 2, -1],\n [0, -11, -1, 8, 6, 8],\n [0, 0, -4, -3, 10, 5],\n [0, 0, 0, 2, 9, 9],\n [0, 0, 0, 0, 3, -7],\n [0, 0, 0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Y... | 512 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-4, -14, -1, 7, -3, -4],\n [13, -10, 10, 0, 12, 11],\n [-4, 8, -4, -1, 8, -8],\n [-15, 0, -4, -14, -11, 3],\n [15, -15, 12, 9, 9, 8],\n [-15, -14, -3, 1, -11, -3]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer i... | 256 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-10, 5, -13, 1, -10, 13],\n [1, 11, -2, -1, 9, -5],\n [-15, 7, 3, 0, -12, -4],\n [6, -7, 9, 2, 4, -14],\n [-1, -15, 1, -11, 10, -4],\n [-13, 1, -9, 13, 2, -15]]\n\nPresent the answer i... | 568 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-1, -12, 0, 4, 6, 6],\n [-12, 8, -2, -12, -6, 0],\n [0, -2, 2, 12, 0, 0],\n [4, -12, 12, -12, 3, -6],\n [6, -6, 0, 3, 5, 0],\n [6, 0, 0, -6, 0, -1]]\nRound to the nearest integer, then take the result modulo 1000.\n\nPresent the answer in LaTex format: \\boxed{You... | 4 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, -3, 15, -9, 12, -10],\n [-2, 9, -6, 12, 15, -12],\n [0, -10, -6, 0, -8, 1],\n [-9, 8, 13, 8, 11, -9],\n [1, 12, -3, -8, -5, 11],\n [13, -9, -2, 7, 11, -2]]\n\nPresent the answer in LaTex ... | 584 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-10, -2, 2, 3, -2, 3],\n [-2, -1, 10, 0, 3, -2],\n [2, 10, -13, -5, 12, -3],\n [3, 0, -5, 3, 6, -2],\n [-2, 3, 12, 6, 9, -4],\n [3, -2, -3, -2, -4, -14]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex fo... | 350 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-8, -4, 0, -5, 11, 7],\n [0, 15, 10, 2, 3, 5],\n [0, 0, 6, -14, -9, -4],\n [0, 0, 0, -4, 15, 13],\n [0, 0, 0, 0, -6, 10],\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... | 400 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 11, 15, 5, -13, -8],\n [-1, -4, 5, 7, -7, 1],\n [-13, -13, 15, -15, 13, -4],\n [11, -3, -9, -3, 13, -14],\n [-13, 11, 4, -3, -10, -9],\n [-5, 13, 6, -15, 11, -1]]\n\nPresent the answer i... | 776 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-1, 0, -6, -4, 1, -2],\n [0, 3, 6, -6, 2, -2],\n [-6, 6, 9, 4, 10, -5],\n [-4, -6, 4, -11, 10, -11],\n [1, 2, 10, 10, -1, 3],\n [-2, -2, -5, -11, 3, 3]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the answer in LaTe... | 611 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[2, 0, -12, 12, -8, -8],\n [0, 1, 2, -14, 0, 0],\n [-12, 2, -6, -4, -3, -8],\n [12, -14, -4, -4, 1, -6],\n [-8, 0, -3, 1, 8, -4],\n [-8, 0, -8, -6, -4, 15]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex ... | 876 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-9, 14, 13, -2, -12, -8],\n [0, 3, 2, -3, 6, 13],\n [0, 0, -8, 4, -9, 15],\n [0, 0, 0, -4, 2, -6],\n [0, 0, 0, 0, 1, -3],\n [0, 0, 0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed... | 88 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 10, 3, 1, -11, -12],\n [0, -11, -9, 12, -3, 12],\n [0, 0, -13, -11, 13, 0],\n [0, 0, 0, 2, -1, -4],\n [0, 0, 0, 0, 9, -12],\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... | 72 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, 9, -3, 14, -4, 13],\n [0, 1, -7, -13, 0, 13],\n [0, 0, -11, 4, 5, -7],\n [0, 0, 0, 7, 2, 15],\n [0, 0, 0, 0, 6, -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: ... | 736 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 9, -6, -5, 7, -4],\n [0, 6, 6, -11, 5, -15],\n [0, 0, -11, -12, 11, 15],\n [0, 0, 0, 6, 12, 13],\n [0, 0, 0, 0, -3, -15],\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... | 960 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-3, -11, -6, -1, -10, -8],\n [0, 14, 10, 13, 8, -10],\n [0, 0, 9, 8, -15, 14],\n [0, 0, 0, 14, 0, 0],\n [0, 0, 0, 0, 12, -2],\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... | 488 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 4, 10, -3, -14, 1],\n [2, 8, -1, -7, 8, 3],\n [-3, -1, 14, -13, 2, -10],\n [-6, 2, 2, 0, -1, 2],\n [-13, -11, -12, 0, -10, 8],\n [-2, 10, -8, -8, 4, -6]]\n\nPresent the answer in L... | 978 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[13, -11, 8, 15, 0, -1],\n [0, 6, -4, 2, -14, 6],\n [0, 0, 11, 6, -15, 7],\n [0, 0, 0, 3, 13, 4],\n [0, 0, 0, 0, 1, 2],\n [0, 0, 0, 0, 0, 12]]? Round to the nearest integer, then express your answer modulo 1000.\n\nPresent the answer in LaTex format: \\boxe... | 888 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[5, -12, -9, 5, 6, 10],\n [0, 7, 7, 8, 4, -12],\n [0, 0, -10, 10, 11, -12],\n [0, 0, 0, -5, -9, 6],\n [0, 0, 0, 0, -3, 2],\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{Your an... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -4, -14, -11, 10, -7],\n [-13, -6, 11, 12, -11, -7],\n [-6, -10, -6, 0, -4, -13],\n [4, 15, -7, 15, -7, -4],\n [0, -14, 0, 6, -6, -9],\n [-2, -8, 11, 15, 1, 2]]\nRound to the nearest integer, then give your answer as det(A) mod 1000.\n\nPresent the ans... | 380 | MATH |
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