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[[35, -12, -18, 5, 12, 12, 10, -7, -14, -6, 11, -20],\n [-12, 33, -9, 8, 6, 0, -8, -3, -2, -5, 20, 12],\n [-18, -9, -6, -8, -8, 25, 6, -9, -11, 12, 8, -21],\n [5, 8, -8, 9, -8, 6, 3, 0, -6, 6,... | 824 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, 6, -20, 33, 15, -27, -17, -9, 24, -9, 24, 23],\n [26, 32, -3, 10, 21, 13, 10, 11, 11, -4, 14, -5],\n [-8, -30, 29, 26, -34, -20, 10, -29, 35, 35, -24, -30],\n [-4, 12, 24, -8, -19, 15, -12, -20, -26, -22, 26, 1],\n [27, 26, -7, 11, 9, -1, -31, -14, -1,... | 808 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-6, 11, -7, -29, 27, -26, 15, 10, -10, -20, 35, 31],\n [0, 23, -14, 27, -12, 3, 27, -18, -10, -30, 2, 7],\n [0, 0, -22, 24, -8, 14, 22, 24, -1, 9, 34, 1],\n [0, 0, 0, -22, -22, -15, 9, -20, -25, 34, -33, -24],\n [0, 0, 0, 0, 23, 14, -9, 9, -18, -16, 2, 17]... | 434 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[4, -11, -1, 15, 16, -6, 19, -23, 0, -26, -23, -6],\n [12, -24, 0, -9, 4, 33, 7, 32, 21, 30, 14, -28],\n [-25, 18, -16, -35, -32, -15, -22, 7, -15, 27, 6, 35],\n [-23, -22, 10, 13, 26, ... | 32 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-9, 19, 6, 1, -20, 3, 4, -22, -24, 0, -19, -28],\n [19, -2, -14, -22, 10, -4, -26, 14, -6, -27, -2, 1],\n [6, -14, -21, -8, -20, 10, 12, -34, 16, 22, 6, 4],\n [1, -22, -8, 19, -18, 3, 0, -18, 7, -12, -10, 20],\n [-20, 10, -20, -18, -30, -2, -24, -31, -12,... | 440 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 17, -2, 0, -26, -7, 5, 5, 4, 29, -33, 24],\n [0, 29, 14, -29, -27, -9, -8, 34, -32, -5, -27, -24],\n [0, 0, 22, 32, 34, -1, -5, -15, -12, -34, 5, 17],\n [0, 0, 0, -33, 32, 7, -25, -... | 501 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-28, -31, -8, -26, -6, 12, 28, -34, 1, 28, 33, 1],\n [0, 19, -9, 7, 2, -26, -25, -5, -14, -32, -14, -11],\n [0, 0, -34, 27, 32, 27, -2, -33, 19, 7, -24, -11],\n [0, 0, 0, 21, -16, -15, 35, -11, -18, -33, -8, 35],\n [0, 0, 0, 0, -13, -14, 12, 4, -12, -11, ... | 662 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, -24, -24, 12, 22, -8, -9, 32, 4, -9, 3, -26],\n [0, -35, -22, 23, -2, 14, -30, -17, -9, 25, 0, -31],\n [0, 0, 24, 25, 27, -20, -27, -28, 4, 10, 21, 17],\n [0, 0, 0, -7, -1, -4, -30, 0, -25, -14, -2, 30],\n [0, 0, 0, 0, -31, 25, -3, -17, 8, -11, 0, 14],\n [0, ... | 3 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[13, -7, -11, 25, 18, 30, -13, -33, -13, -3, -28, -12],\n [5, 16, -30, 13, -17, -1, 4, 5, -27, 11, -18, 29],\n [20, -6, -28, -21, 4, -21, 20, -8, -27, -31, 10, 9],\n [2, 24, -35, -2, 27, -34, 1, 12, -10, -29, -9, 18],\n [23, 26, 11, 4, -5, 24, 11, 15, 6, 17... | 336 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[28, -23, -6, 22, 6, -7, -27, 34, 28, 22, -16, -18],\n [0, -32, 10, -31, -13, 20, -32, 4, 13, -1, -26, 16],\n [0, 0, 16, -22, 4, 18, -24, 29, 5, -33, 26, 17],\n [0, 0, 0, -27, 25, -3, -20, -3... | 832 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-21, 32, -13, -10, 4, -1, -2, -6, 6, 5, 8, -32],\n [32, -21, 2, -12, 8, -15, -10, -12, 28, 0, 0, -25],\n [-13, 2, 23, 4, -4, 12, -14, -1, 13, -18, 8, -2],\n [-10, -12, 4, 3, 8, 3, 0, 6, 17, ... | 8 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[16, -10, 11, -24, -4, 14, -8, -17, 0, -14, -4, 6],\n [-10, -23, 18, 6, 2, -20, 15, 34, -29, 4, 0, -26],\n [11, 18, -20, -2, -4, 13, -12, -6, -4, -24, 18, 13],\n [-24, 6, -2, 2, 8, 12, -2, 10... | 448 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, 12, 14, -25, 9, -8, 26, -16, -18, 2, 10, -3],\n [12, 0, -12, 3, 2, 6, 0, 2, 5, 4, 7, -2],\n [14, -12, -21, 32, 28, -5, -3, -6, 30, 19, 29, -14],\n [-25, 3, 32, -6, 12, -6, 12, -4, 29, -6, 9, -7],\n [9, 2, 28, 12, 9, -4, -16, 25, 10, -10, -3, -15],\n [-... | 248 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-14, -10, 23, 10, -24, 12, -4, -4, -6, 0, 2, -1],\n [-10, -12, -5, 8, 31, -7, 8, -4, -6, -26, 14, 19],\n [23, -5, -33, -18, -16, 4, 7, 0, -12, 12, 4, -12],\n [10, 8, -18, 3, 29, -18, -12, 2, 2, -14, -12, -10],\n [-24, 31, -16, 29, 25, 0, 16, 18, 24, -9, 4... | 312 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[11, 7, 32, 7, -11, -14, 14, 28, -1, -18, -24, -11],\n [7, -16, 8, -8, -4, 15, -3, -11, -4, 10, 5, -5],\n [32, 8, -17, -26, -5, -16, 26, 0, -2, 8, -28, 6],\n [7, -8, -26, -24, -14, 8, -28, 14, 12, 8, 2, 13],\n [-11, -4, -5, -14, 3, -10, 14, 2, 18, 20, -2, 0... | 992 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-12, -26, -28, 0, 6, 9, -10, -9, 4, 24, -6, -9],\n [-26, 3, -4, 6, -6, -8, 30, 15, -2, 18, -6, 0],\n [-28, -4, 1, 0, -4, 20, -12, 21, 2, -15, -7, 0],\n [0, 6, 0, -26, 26, 14, 12, 2, -26, -23... | 592 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[34, 17, 6, 14, 4, -6, -11, 8, 6, -6, -4, -4],\n [17, 32, 12, 12, 16, -3, 13, 4, -19, 2, 0, 12],\n [6, 12, -31, 11, 6, -22, 8, 18, 5, -16, -3, 14],\n [14, 12, 11, 10, -5, -2, 9, 4, 5, 12, 4, ... | 128 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-23, -16, 12, 20, -8, -5, -16, 3, -30, 11, 6, 1],\n [-16, -30, -14, 31, -10, 10, 23, -14, -14, -24, -9, 24],\n [12, -14, -19, 16, 0, -4, -10, 22, 10, -10, 2, -2],\n [20, 31, 16, -10, -... | 232 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[4, -9, -29, 15, 22, -26, -7, 2, -16, -11, -20, -20],\n [0, -23, -29, -3, -2, -14, 31, -6, 7, -11, 4, 24],\n [0, 0, 28, -24, -33, -2, 28, 0, 23, -10, 1, 16],\n [0, 0, 0, 31, -4, 8, -6, 14, -14, -2, -20, -32],\n [0, 0, 0, 0, -26, 2, 1, -14, -14, 17, 30, 14],... | 599 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[25, -21, -12, 31, 27, -3, -29, 26, 31, -25, 4, -16],\n [0, 33, 27, -7, 13, 7, 22, 0, 26, -32, 22, -32],\n [0, 0, 16, 33, -19, 10, -4, -31, 1, -27, 8, 19],\n [0, 0, 0, -24, -12, -17, -9, 6, 20, -2, -22, -33],\n [0, 0, 0, 0, 34, -15, 15, -28, -11, -24, -15, 18],\n [... | 5 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-33, -33, 30, -2, 14, 33, 15, -1, 3, 14, -13, -25],\n [20, -10, -35, -5, 8, 19, 25, -13, 17, -19, 26, 20],\n [28, -29, 6, 10, -18, 27, 31, -3, -6, 3, 12, -15],\n [-1, 20, -7, -23, 7, -26, 24, -24, -23, 7, -2, 15],\n [-34, -19, 8, 2, -21, 1, 28, 14, -22, -1... | 928 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[35, -3, 22, 3, 18, -17, 24, -29, -26, 12, 15, 20],\n [-16, -10, 27, 28, -3, -28, -3, 15, 34, -2, -28, -3],\n [-14, -9, -9, -10, -1, 27, 1, -8, 15, -24, -10, 25],\n [8, -11, 15, -14, -7... | 208 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-31, -17, 2, 10, -15, 17, 12, 6, 8, -4, -8, -13],\n [-17, 18, 3, -14, 1, 12, 14, -19, 8, 32, -24, 18],\n [2, 3, 9, -24, -14, 4, -12, 0, 4, -14, 11, 12],\n [10, -14, -24, 23, -4, 4, 26, 2, -12, 2, 8, -7],\n [-15, 1, -14, -4, 12, -6, 2, -12, -18, -18, 10, 5... | 208 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-30, 2, 4, 11, 14, -10, 0, 18, 4, -12, 22, 0],\n [2, -3, 26, -6, 17, 14, 30, 8, 26, -12, -15, 24],\n [4, 26, -8, 24, -32, 10, 11, -17, 7, -2, 20, 12],\n [11, -6, 24, -26, 29, 5, 12, -14, -2, -8, -20, -16],\n [14, 17, -32, 29, -8, 16, 6, 22, -8, 18, 22, 0]... | 264 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[27, -5, -29, 14, -5, -35, -27, 22, 0, -28, 1, 19],\n [-6, -27, -19, 25, 1, 19, -11, -31, 1, 15, 25, 27],\n [-22, -20, -27, 27, 23, 1, 0, -5, -29, 22, -23, 25],\n [-13, -6, -26, 26, 11, 32, -30, -28, -34, -11, 6, 4],\n [-25, 12, 13, -29, -34, 24, 1, -2, -3,... | 152 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[19, 4, 8, -28, -2, -16, -9, 20, -6, 12, -10, 10],\n [4, 21, 13, -1, 20, -21, -4, -14, -4, -1, -4, -4],\n [8, 13, 31, -9, -30, 18, 19, 30, -8, 3, 14, 8],\n [-28, -1, -9, 14, 4, -10, -13, -28, 16, -9, 22, 14],\n [-2, 20, -30, 4, -4, 24, 16, -8, 8, 1, -8, -20],\n [-1... | 400 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[20, -24, 11, 0, 31, 28, 5, 7, -31, 24, 32, -35],\n [-11, -9, -6, 26, -16, 12, 33, 19, -24, 24, 7, 16],\n [-11, 3, -25, 23, -2, -28, 34, -31, -22, -5, -4, 4],\n [-21, 7, 32, 16, -14, -6, 26, 5, -4, -5, 22, 6],\n [-12, 0, -18, 16, -9, 6, -12, -23, -8, -17, -17, -10]... | 176 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-30, 3, 27, -20, 26, -1, 22, -22, -14, 16, -1, -35],\n [26, 32, -31, 14, -14, 3, -21, 28, 9, -33, 18, 5],\n [19, -32, 22, 18, -21, -24, -31, -11, -4, 22, 23, -6],\n [-23, -17, 33, 5, 27, 31,... | 32 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-22, 27, 3, 16, -12, -26, 34, -3, -26, -14, 28, -31],\n [0, 32, -13, 19, -11, -30, -4, -25, -27, -20, -12, -15],\n [0, 0, -29, -25, -7, 34, -25, 35, -13, 4, 23, -31],\n [0, 0, 0, -14, 3, -34... | 420 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-13, -1, -31, 22, -14, 27, -23, -31, -26, 25, 32, -24],\n [0, -22, 3, -11, -23, -11, 31, -29, 4, -19, 8, -1],\n [0, 0, -18, 29, -23, -14, 8, 30, 12, 0, 2, -31],\n [0, 0, 0, -35, 13, 0, 26, 13, 14, -18, 18, -23],\n [0, 0, 0, 0, 30, 30, -20, 7, 26, 7, -22, ... | 848 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-8, -11, 1, -27, -1, -13, 19, 32, 19, -11, 25, 24],\n [-21, 33, 27, 1, -8, -6, -34, 10, -12, 17, -25, -28],\n [23, -7, 32, 20, -21, -21, 7, 26, -3, -29, 27, -25],\n [27, 7, 30, -21, -22, -4, -13, -14, 20, 5, 14, -13],\n [-27, -31, -1, 12, -32, 17, -1, 24, -9, -26,... | 344 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, -7, -10, -16, -13, 10, -32, 0, 9, 1, 14, -16],\n [-7, -14, -10, -25, -14, -9, 24, -20, -23, -2, 12, -11],\n [-10, -10, 33, -26, -24, 18, 4, 1, 2, 6, -10, -3],\n [-16, -25, -26, -15,... | 400 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-19, -10, 18, -21, 35, -5, -30, 32, -26, -25, 9, -18],\n [0, 16, 16, -7, -15, 23, 10, -17, -20, 14, 29, 15],\n [-25, 5, 1, 21, -13, 0, -18, -8, -2, -35, -32, 26],\n [-7, 19, -16, -18, 18, 8,... | 384 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-20, -12, 27, -8, -28, 1, 15, 4, -30, -2, 27, 0],\n [-4, 26, -33, 29, -17, -17, 16, 16, -30, -16, 24, -2],\n [1, 29, -25, 5, -17, -5, 30, -3, 15, 29, -24, -26],\n [5, -11, -32, 15, 11, -19, 22, -17, 33, -9, -8, 2],\n [22, 15, -31, 29, -10, 4, 15, 2, 32, -25, -2, 1... | 880 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-30, -18, 24, -24, -29, 19, 34, 25, -5, -2, -1, -19],\n [-32, -16, 25, -11, 3, 6, 1, -25, -23, -26, -16, 13],\n [22, 27, 16, -24, -16, 18, -28, 27, 17, -20, 25, 9],\n [-34, -1, -15, 28... | 752 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-32, -20, 32, -31, -14, 21, -35, 21, -17, 22, 13, 13],\n [0, -35, -4, 5, -32, 22, 34, 15, 28, -7, 29, 22],\n [0, 0, 28, 27, 25, 22, 19, 9, -17, 28, 27, 10],\n [0, 0, 0, 20, 1, -11, -31... | 960 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-33, -20, 15, 21, 32, 20, -7, 10, -16, -25, 33, 16],\n [0, 29, -10, -27, -1, -4, 34, -15, 33, 24, -16, -24],\n [0, 0, -32, 26, 7, 21, -16, 19, -25, -3, 13, -7],\n [0, 0, 0, 19, 24, -21, -23,... | 828 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[29, 16, -16, 8, -12, -17, -8, 0, -12, 17, -23, -27],\n [-33, 20, 22, 23, -29, 20, -30, -17, 10, 15, 27, -15],\n [-28, -14, -30, -17, 24, -20, -28, -4, -6, 15, -4, 0],\n [-22, 11, 15, -16, -7, 27, 15, 20, 32, 9, 18, 17],\n [10, -6, 17, 5, -14, -32, -32, -20... | 616 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[34, 23, -22, -20, -10, 12, -5, 6, -10, 0, -6, 6],\n [23, 7, 32, 0, 8, -6, 19, 16, -20, -22, 17, -9],\n [-22, 32, 27, -25, 22, 28, 10, -4, -14, 16, 6, 2],\n [-20, 0, -25, 15, 16, -19, 6, 16, 17, 8, 19, -12],\n [-10, 8, 22, 16, -16, 5, -2, -1, -22, -21, 6, ... | 152 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-31, 1, -11, 10, -34, -1, 30, 20, -1, -31, 18, -24],\n [0, -10, 3, -6, 8, 34, 13, -26, 25, 32, 3, 9],\n [0, 0, -20, 25, 18, 15, -24, -30, 13, -28, 35, 14],\n [0, 0, 0, -33, 21, -17, -7, 25, 15, 28, -16, 6],\n [0, 0, 0, 0, 28, 2, 24, 17, 17, 20, -12, 1],\n ... | 999 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-32, 5, -10, -5, 24, 27, -35, 0, -24, 25, 27, -14],\n [0, -9, -3, -28, 25, 31, 18, -20, 14, 14, 16, 31],\n [0, 0, -31, -3, -32, -2, 8, 21, 33, -19, -2, 20],\n [0, 0, 0, -2, -4, -19, 13, -29, 5, -22, 22, 1],\n [0, 0, 0, 0, 18, 18, -29, 5, 11, 3, -33, 28],\... | 719 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-32, 32, -12, 22, 20, 31, 34, 24, 22, -34, -18, 18],\n [0, 26, 3, 9, 27, -22, 27, 12, 18, 28, -1, 28],\n [0, 0, -20, 33, 1, 0, 34, -22, 4, -7, -13, -4],\n [0, 0, 0, 21, -30, 23, 8, 34, -4, 1, 22, -28],\n [0, 0, 0, 0, 31, 30, -16, -12, -14, -3, -9, 10],\n ... | 168 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[18, 1, -7, -3, -8, 10, -5, -18, -31, 14, 0, -4],\n [1, -6, 8, 10, 17, 20, -6, -2, -6, 8, -26, -10],\n [-7, 8, -20, -6, 7, 28, -5, 13, -4, 4, 18, 15],\n [-3, 10, -6, -15, -3, -20, 4, -7, -12, -15, 26, -16],\n [-8, 17, 7, -3, -22, -12, 6, 13, -3, 16, -16, -8],\n [10... | 184 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-12, 29, -18, 16, 11, 11, -26, 0, 2, 1, -21, 12],\n [23, -26, -3, -33, 1, -13, 32, 6, -23, 35, 3, -8],\n [-3, 24, -35, -24, 15, 7, -12, -2, -7, -34, -4, -28],\n [-20, 25, -20, -6, 12, 10, -26, -21, -1, 10, -34, -20],\n [6, 24, 27, -19, 0, -20, -27, 28, -3,... | 648 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-30, -30, 10, 25, 20, -5, 10, 15, 25, 16, 5, 24],\n [-21, 8, 8, 8, -5, 15, -10, -32, 5, 33, -22, -19],\n [3, 20, -8, 33, -14, 20, -11, -19, 22, -21, 5, -31],\n [21, -28, 5, 18, 28, 0, -28, -5, 7, -12, -4, -32],\n [-29, -27, -14, -3, -22, -1, -18, -34, 16, ... | 152 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -4, -2, -4, 18, 34, -6, -5, -8, -11, 20, -14],\n [-4, 6, 31, -10, 26, -16, 25, -25, 13, 10, 27, -16],\n [-2, 31, -5, -5, -8, 8, -14, -5, -16, 18, 0, -23],\n [-4, -10, -5, 3, 1, -15, 9, 0, -19, 16, 14, 4],\n [18, 26, -8, 1, -14, 0, 6, -4, 10, 10, 21, 2],\n [34,... | 656 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-24, -4, 2, -26, 6, 26, -30, 16, 0, 1, 16, -7],\n [-4, 11, -24, 7, -8, 26, 2, 4, 11, -4, 13, -22],\n [2, -24, 33, -8, -18, 11, 32, 10, 14, 13, -26, -3],\n [-26, 7, -8, 28, -18, 2, -14, -24, 9, -4, 1, -4],\n [6, -8, -18, -18, 33, 8, -10, 22, -17, 30, 24, 2... | 168 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-34, -20, 22, -1, 31, 7, -18, 0, -14, -1, 24, -1],\n [23, 35, 9, 9, -6, 14, -13, 21, 7, 20, -24, 32],\n [17, -1, 17, -28, -10, -22, 28, -21, -29, -31, -26, 8],\n [35, 29, -19, 31, 18, 28, -18, 9, 19, -18, 2, -15],\n [-31, -32, 28, 35, -27, 8, 34, 26, 5, 10, -20, 2... | 432 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[22, 1, -7, -7, -7, 8, -22, -1, -9, -25, -31, -23],\n [0, -9, -10, 17, 28, 29, 7, 14, -14, 34, 25, -8],\n [0, 0, -18, 24, 15, 9, 14, -7, 6, 19, -14, -24],\n [0, 0, 0, -18, 3, 17, 14, 32, -6, ... | 2 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[31, 20, 11, -6, 14, 20, 4, -11, 17, 9, 30, -6],\n [20, 24, -1, -1, 21, -2, -4, 8, -10, 1, 11, 10],\n [11, -1, 8, -9, 31, 14, -30, -17, 10, 18, 4, -2],\n [-6, -1, -9, -3, 14, 30, -15, -24, -1, 20, 0, -9],\n [14, 21, 31, 14, -13, -6, 2, -28, 13, 0, 18, 16],\... | 552 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-15, -4, 2, -10, -4, -20, -22, 2, 12, -27, 26, 24],\n [-4, 28, 12, -10, 12, 2, -19, -8, 4, 2, 9, 28],\n [2, 12, -8, 12, -4, 16, -26, 25, -8, -1, 10, -27],\n [-10, -10, 12, 20, 6, -11, 0, -6,... | 384 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[4, -29, 34, 7, 31, -8, 0, -11, -3, 12, 22, 1],\n [-3, 18, -23, -35, 16, -23, 17, -21, 19, -25, 9, 32],\n [23, 8, -14, 32, -25, -6, 18, -20, 25, 2, 1, -17],\n [-25, -13, -35, 24, 31, 21, -21, 29, -13, -31, -18, -14],\n [33, -2, 7, 33, 32, -21, 0, 16, 20, 5, -27, 19... | 824 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[17, 6, -20, -8, 14, -8, 6, 8, -20, -20, 20, 12],\n [6, 26, 6, 4, -6, 1, -9, 8, 13, 2, 16, -1],\n [-20, 6, 17, -8, -28, 28, -10, -2, 0, -2, -10, 1],\n [-8, 4, -8, -24, -15, 10, -6, -2, 2, 25,... | 104 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-30, 19, 11, 29, -35, -22, -24, -26, -33, 0, 17, -26],\n [0, 12, 7, -30, 4, -24, -18, 2, -4, 20, -31, 18],\n [0, 0, -11, -11, -22, -29, -16, -30, -3, 17, -4, 16],\n [0, 0, 0, 12, 11, 21, -18... | 405 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[19, -12, 2, -32, 34, -20, 17, 10, 33, -7, 0, 22],\n [0, 7, -3, -32, -24, -31, 21, -14, 8, -29, -20, -12],\n [0, 0, -24, 3, 11, 24, 11, 27, 19, -32, -2, -11],\n [0, 0, 0, -32, -21, 19, 0, 7, 34, 28, -27, 27],\n [0, 0, 0, 0, -9, -29, -10, 26, 14, -29, 11, -... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-25, -1, 10, 9, 5, -5, -8, 13, 33, -25, -10, -27],\n [0, 9, -6, -25, 1, -10, 23, 35, 21, -17, 11, -8],\n [0, 0, 16, -2, -12, -3, -34, 5, 24, 17, -23, -20],\n [0, 0, 0, 35, -33, -14, -27, -29, 11, 30, 35, -10],\n [0, 0, 0, 0, -26, -7, 32, -35, -18, -12, -25... | 0 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-26, -10, -1, 6, 19, -6, -14, -24, 14, 8, -4, 2],\n [-10, 12, -12, -32, 1, 10, 6, 21, -1, -24, -4, 26],\n [-1, -12, -34, 15, -20, -20, 12, -12, 4, 16, -16, -14],\n [6, -32, 15, -20, -4, -7, -14, 0, -2, -6, -7, 23],\n [19, 1, -20, -4, 13, -9, -4, 14, -4, 1... | 200 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-22, -10, -28, 28, -33, 15, 18, -8, 21, 15, 24, 9],\n [0, -16, -34, -31, 32, -27, 23, -18, 21, -3, -23, 19],\n [0, 0, -26, -22, 19, 6, 11, 24, -9, 33, -5, 1],\n [0, 0, 0, -13, 20, 7, 30, 19,... | 820 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, -6, -31, 31, -21, -14, -8, -8, 14, 7, -8, 4],\n [-6, -17, -4, 0, 16, 8, -13, 15, 19, 2, 32, -20],\n [-31, -4, -8, -7, -6, -2, -14, -1, -25, -6, 8, 12],\n [31, 0, -7, 34, -12, -19, -6, -22, -8, -22, 18, 2],\n [-21, 16, -6, -12, 3, -18, -4, 24, -10, -20,... | 632 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-20, 12, 6, -15, 19, 19, -24, -9, 7, 5, 11, -7],\n [0, 32, 10, -7, 34, 10, 4, -28, 29, 31, 4, -35],\n [0, 0, 20, 27, -25, 31, 32, 3, 6, -30, 22, 0],\n [0, 0, 0, 22, -29, -17, -11, 12, ... | 982 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[16, -9, -1, -10, 4, -4, 12, -9, 8, 13, 1, -20],\n [-9, -12, 1, -4, -1, 12, 2, -16, 26, -28, 0, -2],\n [-1, 1, -18, -4, 4, -9, -30, -6, 19, -2, -30, 0],\n [-10, -4, -4, 15, 14, 14, -22, -19, -20, -16, 19, -8],\n [4, -1, 4, 14, 35, -5, 0, 8, 2, 14, 2, 20],\... | 704 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-22, -2, -11, 8, 26, -15, 20, -3, 12, 16, 4, -12],\n [-2, -25, -22, 0, 22, -4, -10, -8, -20, 6, -10, 4],\n [-11, -22, 10, 0, 2, 12, -15, -20, 32, -22, -10, 4],\n [8, 0, 0, -15, -14, -8, -25, -24, 8, 0, -7, 12],\n [26, 22, 2, -14, 0, -18, 14, -2, 4, 4, 6, ... | 320 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-16, 27, 0, 18, 32, -28, 18, -28, -15, -20, 8, 8],\n [29, 29, 18, 0, -32, 11, -4, -6, -2, -34, 23, -18],\n [2, -13, 19, 20, -7, 6, 9, -30, 33, 35, 14, 19],\n [-29, 2, 19, 21, -29, 2, 16, 14,... | 264 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 6, 6, -6, -21, 18, -12, -5, 18, 7, 6, -4],\n [6, 11, -26, -12, -18, -12, 3, -20, 9, -23, 2, -6],\n [6, -26, 9, 8, -3, -18, 7, 12, 24, 6, -6, -20],\n [-6, -12, 8, -35, -16, -17, -22, -21,... | 592 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[18, 19, 4, -26, 8, -10, 0, 11, -2, 13, -5, 28],\n [19, 11, -15, 22, 0, -28, -18, -21, 15, 12, -14, -10],\n [4, -15, 33, -20, 25, 16, 2, 10, -16, 10, 8, 8],\n [-26, 22, -20, 7, -6, 14, -10, -... | 392 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-31, -28, 19, -8, 31, -5, 16, -30, -20, -27, 31, -14],\n [0, 28, 27, -22, 28, -29, -6, -23, 3, 3, -29, 25],\n [0, 0, 17, 20, 18, -14, 30, 32, -17, -6, -21, 14],\n [0, 0, 0, -21, 13, 11... | 84 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-25, -17, -21, 2, -30, -3, 3, -10, 21, -22, -3, -14],\n [-14, 27, 1, 14, -27, -1, 33, -7, -25, -11, -1, -3],\n [33, -22, 17, -34, 3, 4, 21, -19, -7, 4, 1, 35],\n [0, 28, 13, -20, -34, ... | 264 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-26, 35, -33, -3, 16, 17, -25, 17, -20, 32, -5, 16],\n [0, 29, -1, 33, 30, -31, -23, 0, -4, -25, 32, -1],\n [0, 0, -3, 24, 9, 16, 33, -2, 22, 27, 29, -9],\n [0, 0, 0, 17, -28, -22, -23, 2, 0, -33, 4, 23],\n [0, 0, 0, 0, 22, 26, -12, -21, 28, -4, -9, -14],\... | 631 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-17, -18, 29, -8, 2, -18, -15, 7, 18, 14, 7, 12],\n [-18, -1, 16, 6, -1, 15, 6, 4, 22, -8, 24, -15],\n [29, 16, -28, -8, 30, 0, -14, 5, -4, -4, -14, 26],\n [-8, 6, -8, 16, -19, 8, -8, 25, 2, 4, -3, -11],\n [2, -1, 30, -19, 15, -12, 16, 7, -14, 2, 2, 7],\n... | 776 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[31, -4, 18, -16, -3, -26, -13, 11, 12, -17, -4, -1],\n [0, 14, -9, 7, 7, -25, -29, -23, -2, -12, -6, -12],\n [0, 0, -25, 2, -16, 29, -22, 34, 8, -3, -32, -21],\n [0, 0, 0, 23, 18, 12, 27, -20, -9, 19, 20, 8],\n [0, 0, 0, 0, 28, -25, -35, -30, 23, -29, -15... | 992 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-16, 34, 3, -21, -7, 10, 21, 34, -28, 26, -5, -29],\n [8, -30, 24, 13, 32, 6, -32, 16, 14, -9, 19, -11],\n [-25, 29, 7, -11, -21, -35, 10, 25, 32, -7, 18, 2],\n [26, -11, 9, -27, -3, -10, 27, -33, -19, -5, -33, -17],\n [-4, -3, -29, 4, -16, 7, 25, -21, 28, -12, 12... | 40 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[20, 4, -10, 31, -4, 28, 4, 14, -2, -8, -24, 16],\n [4, -2, 12, -2, 4, -11, -20, 2, -18, 7, -24, 0],\n [-10, 12, 30, 14, 11, 15, 6, 0, 0, -9, 8, 0],\n [31, -2, 14, 13, -28, -6, 14, 10, -10, -16, 2, 14],\n [-4, 4, 11, -28, 32, 22, -20, 8, 17, -4, -5, 24],\n [28, -11... | 440 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-29, 16, 30, 4, -5, 25, 2, -9, -6, 7, 19, 6],\n [16, -17, 8, -18, -3, -21, 0, -16, 2, -23, -4, 0],\n [30, 8, -32, 12, 20, 29, 13, -18, 12, -8, -16, -2],\n [4, -18, 12, 9, 13, 2, -18, -6, -10, -24, 8, 10],\n [-5, -3, 20, 13, -8, -20, -2, 12, 2, -2, 4, 2],\n... | 928 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -10, -20, -13, 11, -10, 18, -24, 26, 12, -4, 3],\n [-10, 21, -4, 8, -8, -14, 27, -3, 13, 2, -9, 20],\n [-20, -4, 25, 0, -32, -4, -6, 2, -4, -20, -15, 2],\n [-13, 8, 0, 32, 28, 3, 9, -4, -18, 6, 15, 9],\n [11, -8, -32, 28, -26, -2, -2, 12, 12, -23, 31, ... | 896 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-13, -2, 16, -6, 16, -9, -26, 29, -32, -31, -14, -33],\n [-26, 26, -7, -23, 26, -18, 13, -16, 24, -24, -33, 9],\n [34, 20, 2, 2, -25, -15, -32, 33, 29, 34, 15, -31],\n [5, -4, 3, 9, -11, 4, -19, 28, 27, 29, 35, 6],\n [0, -14, 30, -1, -6, -26, -4, 12, -2, -29, -8, ... | 728 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-9, -14, 8, -7, -15, 5, -21, -3, 0, -4, -16, -21],\n [-1, -22, -9, 1, 35, 30, 32, 11, -35, -32, 29, 8],\n [-7, 2, 21, -15, -6, 15, 1, -10, -32, -35, 4, 25],\n [-16, -26, -23, -16, -28, -23, 4, 15, -11, 13, -20, -35],\n [10, -32, -16, -27, 3, -22, 16, 11, -28, -24,... | 136 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[25, 19, 7, -34, -4, -23, 33, -8, 9, -31, 15, -28],\n [30, 1, -16, 28, -13, -25, 15, -21, 35, -4, 5, -19],\n [30, 23, 35, -27, -11, -34, -12, -34, 15, -20, 26, 22],\n [2, -20, -18, 22, -24, 30, -5, 9, 28, 6, 18, 10],\n [6, 12, 2, 22, 27, 7, -7, 2, -35, -9,... | 288 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[23, 30, 33, 33, 30, 24, 32, -24, -19, -26, -23, 3],\n [0, 30, -26, -22, -22, 9, -12, 31, -34, 21, -9, 30],\n [0, 0, -29, -21, -26, -30, 16, 22, 12, -15, 29, 25],\n [0, 0, 0, 26, 1, 25, 28, 0, 26, 15, 6, -6],\n [0, 0, 0, 0, 35, 30, -3, 17, -20, 22, 31, -33]... | 32 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[27, 18, 27, -4, 22, -4, -6, -3, -1, 20, -18, 24],\n [18, 23, -26, -14, -11, -14, 11, 15, 4, -3, -2, 23],\n [27, -26, -35, -30, 4, 8, -22, -4, -4, -8, 14, -6],\n [-4, -14, -30, -2, 4, -12, -4, 2, -24, 15, 26, -16],\n [22, -11, 4, 4, -7, -5, 1, 10, -2, 22, -25, -20]... | 160 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-30, 18, -25, -28, 4, -15, 17, 19, 35, 1, -6, 25],\n [0, -34, -5, -16, -25, -29, 0, 26, 22, 0, 22, 19],\n [0, 0, -31, -16, 31, -25, -17, 12, -21, -22, -13, 15],\n [0, 0, 0, -10, 21, 24, -1, 25, -23, 17, 32, -17],\n [0, 0, 0, 0, -21, 14, -18, -7, 17, 29, -... | 949 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, 25, 24, -22, 32, 18, -14, 0, 10, 35, 4, 13],\n [-27, -3, -12, 9, -12, 2, -16, -10, -17, -18, -35, -23],\n [10, -21, -32, 21, -13, -26, -3, 27, 7, 12, -25, -16],\n [24, -25, -25, 12, 2, -5, 3, -2, -11, 24, -15, 7],\n [10, 18, 23, -24, -17, -14, -35, -34, 11, 6, ... | 88 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 20, 25, 6, 34, 28, -27, -18, 3, 19, -5, -20],\n [2, 14, 4, 20, -24, 23, 12, -5, 1, -3, 32, 10],\n [2, 30, -29, -5, 28, 4, 14, 27, 19, -33, 23, 29],\n [-23, 17, 27, -14, -24, -32, -9, 2, -4, 18, -31, -16],\n [-17, 27, 21, -32, -13, -13, 28, -28, 9, 1, -... | 232 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[25, 28, -26, -18, 7, 33, -15, -22, 23, 17, -25, 16],\n [0, 21, -32, 23, 33, -28, -5, -26, -22, -21, 6, 5],\n [0, 0, 33, 5, 33, -9, 13, -18, -33, 6, 0, -20],\n [0, 0, 0, 33, -8, -33, 35... | 1 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-24, -1, -2, 6, -8, -3, 19, 14, 4, -2, 30, 0],\n [-1, -34, -16, -2, 1, 9, -15, -8, 1, 0, 22, -30],\n [-2, -16, 6, -1, 25, -18, 8, 12, 18, -12, 12, 3],\n [6, -2, -1, 0, -18, -6, 6, -5, -3, -20, 26, -31],\n [-8, 1, 25, -18, -25, 20, 2, -8, -4, 8, -10, 30],\n [-3, 9,... | 296 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[34, -31, -22, -3, -17, -20, 1, 6, -9, -11, 26, -15],\n [0, 11, 18, 11, 12, 33, -29, -2, -21, -18, -16, -8],\n [0, 0, -35, -24, 14, -16, -26, 25, -10, -12, 34, 8],\n [0, 0, 0, 31, 7, 22, -8, -16, -13, 13, -17, -9],\n [0, 0, 0, 0, -10, 28, -18, -1, -16, -22,... | 602 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[2, 6, -18, -31, 15, -31, -6, -19, -5, 8, -26, -34],\n [-28, -17, 12, -9, -29, 31, -15, -15, -13, 11, 1, -29],\n [-6, 31, 0, 27, -4, 30, 10, -19, -33, -2, 4, 30],\n [4, 21, 27, 2, -32, -28, -15, -21, 26, -22, -15, 0],\n [13, 11, -9, -29, 9, -3, 20, 4, 35, ... | 320 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[10, 27, 13, 30, 25, 18, -6, -15, -18, 15, 18, 25],\n [0, 11, -9, -5, 3, 15, 12, 33, -22, -30, -21, -3],\n [0, 0, 14, -7, 34, -10, 12, 9, -11, 7, 30, -9],\n [0, 0, 0, 31, -16, -9, -4, -13, 13... | 117 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-19, 12, 2, 0, -8, 8, 24, 14, 7, -24, 20, -18],\n [12, 27, 4, -22, 5, 17, -14, 17, 16, 19, -12, -14],\n [2, 4, 3, -20, -19, 14, 2, -24, 7, 12, 26, -6],\n [0, -22, -20, -29, -14, -32, -17, 22, 12, -4, 1, 16],\n [-8, 5, -19, -14, 4, 4, 3, -22, -2, -8, 20, 0... | 272 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -21, 13, 25, 8, 25, -2, -8, -13, -3, -8, 22],\n [-21, 26, -25, 16, 7, -4, -1, 11, 8, -14, -5, -32],\n [13, -25, -17, -10, 0, -13, -25, -9, 6, -10, 9, 5],\n [25, 16, -10, 35, -9, -11, -8, -8, 1, 4, 7, 8],\n [8, 7, 0, -9, -29, 6, -8, -6, 10, 4, 16, 10],\n [25, -... | 744 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, -32, 3, -4, -22, 20, 21, 13, 19, -31, 29, 11],\n [21, 21, 26, 17, -10, 8, 32, 30, 12, 24, -28, 17],\n [-24, -19, -24, 10, -8, 34, -1, -31, 22, -3, 3, -35],\n [-33, 11, 18, -8, -11, -23, -1, -34, 12, -12, -13, 1],\n [24, 26, -10, 9, -30, 15, -11, -26, 1... | 720 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[32, 7, -1, -30, 10, -13, -29, 22, -15, -26, -4, 24],\n [-26, -10, 3, -1, -11, 31, -21, 13, -7, 18, 0, 26],\n [22, 19, 12, 0, -32, -16, -4, -7, -10, 32, -16, -15],\n [17, -29, 33, -4, -10, -18, -30, 13, 13, -23, -13, 21],\n [3, -21, 2, 31, -21, 32, 9, -6, 2... | 936 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[16, -8, 24, 17, 7, -21, -27, -3, -22, -15, -34, 14],\n [0, -12, -17, -13, -2, 12, 3, 18, 34, -15, 7, 11],\n [0, 0, 16, -10, 19, 18, -24, 18, -35, 9, 22, -8],\n [0, 0, 0, 14, -21, 16, 4, -28, 34, -35, 23, -5],\n [0, 0, 0, 0, -34, 30, -33, 7, 19, 24, 8, -3],\n [0, 0... | 520 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -3, -12, -25, -29, -34, -14, 7, 10, 26, 26, 14],\n [32, -10, 12, 10, -1, -28, 1, 33, -14, 3, 13, -29],\n [16, 35, -31, -2, -27, -14, 24, 22, -32, 9, -5, -34],\n [19, -16, 26, 18, -3, 35, -20, -2, 13, -10, -26, 28],\n [31, -7, -15, -19, 21, -4, -15, 29, -15, -3... | 456 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-2, -17, -14, 6, -12, 12, 25, 26, 4, 9, 28, 18],\n [-17, 32, 8, -32, 24, -16, 7, 8, 10, -12, 0, 0],\n [-14, 8, 33, -12, -18, -29, -16, 16, 15, -22, -15, 26],\n [6, -32, -12, -20, 13, -... | 144 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, -22, -7, -18, 4, -28, 2, -28, 30, -23, 18, 30],\n [19, 25, 18, 3, 9, 0, -10, 22, -19, 4, 13, 29],\n [-11, -27, 18, 22, -12, 8, 6, 12, 25, 32, -13, 0],\n [-12, -26, -26, 35, 12, 13, -29, -32, 32, 18, 8, 7],\n [17, 4, 23, 19, 3, 15, 11, 27, 19, -16, -29, -11],\n... | 496 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[28, -16, 18, -2, 8, 21, 13, 32, 8, 2, -32, 4],\n [-16, -34, 17, 8, 8, 8, 10, -8, 2, 7, -14, 20],\n [18, 17, -2, 29, -8, -9, 12, 14, -9, 6, 8, 6],\n [-2, 8, 29, 35, -10, -2, 0, -6, -17,... | 56 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-20, -24, 19, 21, -4, -9, 11, 21, 4, 32, -21, 19],\n [-3, -17, 23, -32, 3, 21, -26, -7, 17, 0, 6, -17],\n [-7, 33, -2, -22, 7, -29, -16, 22, -28, -8, -25, 5],\n [-21, -22, 25, 5, 17, -... | 232 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[5, 30, -7, -33, -27, 3, 29, -22, 17, 14, 8, 17],\n [-4, -3, -2, 5, 15, 28, -20, -8, 35, -33, 18, -12],\n [26, 21, -34, -12, -11, 15, 25, -18, -25, -21, 25, -29],\n [-16, -2, 35, 0, -2, 28, -... | 720 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-25, 12, 0, -18, 0, -6, 6, 5, 32, -22, 26, 24],\n [12, 27, -17, -18, 30, 19, 24, 0, -4, -20, 17, 14],\n [0, -17, 2, -17, 10, -2, 16, -12, 2, 14, 25, -5],\n [-18, -18, -17, 7, 15, 16, -6, -9,... | 896 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[8, -26, -25, -5, 19, -29, 19, -19, -4, 4, 0, -25],\n [0, 31, -5, -12, 29, -13, -30, -14, 0, -22, 4, -19],\n [0, 0, 35, -5, -6, 18, -29, 20, -23, -30, -8, 33],\n [0, 0, 0, 19, -10, -22, -15, -34, 5, 13, -30, -7],\n [0, 0, 0, 0, 33, -2, -19, 33, -7, -30, 2,... | 401 | MATH |
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