messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[32, 13, 18, 3, -4, -11, 20, 20, -6, 33, -22, 6],\n [-30, -10, -23, -19, -20, -22, -23, -24, 34, 20, 0, -20],\n [12, -5, 23, -12, -18, 4, 26, -33, -10, 11, 21, 12],\n [33, 13, 29, -9, 3... | 112 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, 13, -20, -22, -2, -9, 11, -6, 6, 12, -14, 14],\n [13, 21, 0, -6, -8, 15, -24, -18, -6, 4, 20, 2],\n [-20, 0, 19, -16, -20, 6, 14, 3, 8, 8, -18, 2],\n [-22, -6, -16, -29, -1, -9, -14, -24, 28, 22, 12, -8],\n [-2, -8, -20, -1, -5, 9, 29, -8, 30, 26, 8, 9],\n [-9... | 920 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-6, 3, 12, 2, 1, 6, 3, 12, -10, -5, -14, -6],\n [3, 18, -21, -12, -9, 9, 0, -12, 2, 6, 34, 21],\n [12, -21, 6, 13, 21, 10, -14, 18, 6, 12, -8, 9],\n [2, -12, 13, 9, 3, -8, 13, -12, -22, -6, -2, 14],\n [1, -9, 21, 3, -14, 11, 6, -2, 21, -6, 5, -6],\n [6, 9, 10, -8,... | 944 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[32, -18, -4, -32, 2, 28, -33, -35, -2, 24, -8, 17],\n [0, 34, -18, 6, -2, 11, -7, 14, -2, -8, 8, -2],\n [0, 0, 27, -35, 13, 27, 13, -4, -6, -31, 13, 23],\n [0, 0, 0, -32, 35, -15, 9, -2, -3,... | 26 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-33, 6, 1, -3, -24, 4, 2, 8, 11, 16, -10, 22],\n [6, 15, 4, -4, -18, -18, -14, 6, -5, -22, -28, -15],\n [1, 4, -23, -18, -35, -5, 13, -24, -15, 7, -4, 4],\n [-3, -4, -18, 23, -14, -14, 8, 22, -14, 22, -16, 3],\n [-24, -18, -35, -14, 13, 4, 7, -10, -5, -7, -21, 8],... | 96 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, 22, 16, 28, 21, -29, 21, -14, 0, -3, 29, 29],\n [0, 35, -18, -33, 7, -7, 34, -33, -4, -2, -21, 23],\n [0, 0, 17, -27, 17, 13, 1, 17, -19, 4, -4, 17],\n [0, 0, 0, 35, -19, -8, -7, 27, 20, -12, -27, -1],\n [0, 0, 0, 0, 32, 6, -8, -26, -8, -24, 5, 7],\n [... | 819 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-6, 29, 31, 13, 20, 1, 1, 35, 23, 30, 12, -22],\n [2, 28, 34, -30, -5, 18, -17, 1, -12, -30, 8, -20],\n [-15, 16, -9, -1, -7, 0, 12, 25, -34, -27, 11, 28],\n [-7, 7, 8, -18, -11, 26, -25, -6... | 760 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-5, -20, 2, 1, -10, 16, 12, 2, 6, -21, 8, 24],\n [-20, -30, -29, 18, 0, -3, 19, 2, 4, -26, 4, 20],\n [2, -29, 14, -2, 2, 4, 13, 6, -8, -21, 6, -24],\n [1, 18, -2, 20, 20, 2, -28, -4, -25, -14, 0, -4],\n [-10, 0, 2, 20, 14, 6, -4, -2, 8, 11, -4, 14],\n [16, -3, 4, ... | 240 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[7, -27, -26, -30, -2, -12, -18, -6, 22, 32, 35, 22],\n [0, 16, -8, 28, 14, 23, 8, -35, 4, -33, -2, 33],\n [0, 0, -7, 0, -25, 35, 32, 33, -1, -2, 25, 9],\n [0, 0, 0, 5, 20, -31, -9, -22, 33, 12, -25, -9],\n [0, 0, 0, 0, -17, -5, -22, 15, 25, -8, -28, -26],\n [0, 0,... | 400 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-24, -7, -19, 2, 7, -28, -7, -1, -23, 19, -4, 3],\n [0, 33, -17, 19, -13, -27, 6, 11, -34, 20, 31, -23],\n [0, 0, -30, -5, -17, -12, 31, 33, -22, 29, -13, 14],\n [0, 0, 0, 34, 11, -11, -34, 18, 8, 27, 10, -7],\n [0, 0, 0, 0, 14, 35, -5, 8, -5, -7, 13, 5],\... | 78 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-33, 29, -30, -10, -12, -14, 0, -10, 17, 0, -7, 27],\n [0, -30, -26, 25, 34, -28, -10, -16, 30, 0, -2, -12],\n [0, 0, 6, 25, -35, -4, 17, -35, -17, -27, 30, -24],\n [0, 0, 0, -7, 35, -9, -35, 9, -32, 23, 30, -25],\n [0, 0, 0, 0, 12, -30, -29, 14, 16, 3, -5, 19],\n... | 641 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-24, 10, -8, 12, 9, -1, -6, 1, -7, -18, -14, 0],\n [10, -3, -29, 30, 2, 8, 10, 6, -4, -17, 27, -28],\n [-8, -29, -1, 11, 13, 24, -7, 18, -6, -22, 22, 30],\n [12, 30, 11, 16, -18, -16, 4, 4, -18, -15, 10, 6],\n [9, 2, 13, -18, -4, 0, -4, 2, -14, 4, 28, 0],\n [-1, 8... | 800 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[26, 34, -21, -25, -35, -30, 18, 9, 24, -15, 33, 13],\n [-34, 10, 1, -13, 17, -29, -23, 9, -1, -9, 15, 7],\n [2, 29, -14, 1, 34, 4, -29, -35, 26, 12, 1, 6],\n [-20, 3, -17, 20, -13, 8, 19, -21, 26, 5, 4, 22],\n [-12, -27, 10, 33, 32, 27, 35, -6, 14, 28, -26... | 240 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[18, 6, 6, -11, 32, -22, 0, 8, 20, -1, -5, -8],\n [6, 18, -26, -14, 12, -1, 11, -24, -3, 11, 24, 0],\n [6, -26, 11, 17, -6, -4, -24, 3, 18, -18, 12, 12],\n [-11, -14, 17, 28, -7, -4, 17, -5, ... | 832 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[20, 16, 24, 18, -4, 13, -3, -27, 33, 28, -27, 30],\n [6, 35, 5, -6, -17, -1, 19, -8, 24, 13, -4, 35],\n [3, -28, -11, 25, 2, 11, -13, -15, 11, -14, -21, -8],\n [-17, 14, 21, 26, 23, -28, 14, 34, 21, 30, 13, 18],\n [-12, 12, -8, 25, 4, -11, 20, -21, 30, 8, ... | 536 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[28, 10, 26, -17, -3, 17, -9, -33, -16, 35, 10, -20],\n [0, 13, 29, -16, -21, -4, 0, 0, -31, -34, 23, 4],\n [0, 0, 35, 21, -16, -28, 33, -21, 26, 9, -22, 29],\n [0, 0, 0, 11, 22, -4, 23, 12, -28, -22, 7, -26],\n [0, 0, 0, 0, 15, -18, -12, 10, -26, -10, -29, -4],\n ... | 829 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[17, -6, 5, 18, 13, -1, 14, -7, 22, -3, 28, -10],\n [0, -32, -11, 9, -12, -28, -34, 8, -6, 30, 28, 14],\n [0, 0, -24, -18, 0, -34, 19, -10, 25, 20, 9, 7],\n [0, 0, 0, 15, -19, -19, -30, 6, -27, -28, -30, -27],\n [0, 0, 0, 0, 31, -3, -15, 9, -28, 23, -22, -31],\n [0... | 805 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[13, 7, -10, 34, -14, -9, -19, 12, 29, 20, -17, -31],\n [0, -35, -16, 21, -2, 33, -11, 14, -13, 11, -27, -27],\n [0, 0, 26, -7, 19, -2, 24, -4, 21, 8, -28, 14],\n [0, 0, 0, 26, 10, 20, 7, 20, 30, -19, -10, 34],\n [0, 0, 0, 0, 14, 11, -9, 28, -35, -31, -21, 0],\n [0... | 998 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[23, -13, 19, 17, -17, -1, 7, 0, -7, 29, 18, 34],\n [15, 27, 15, -16, -35, -1, 22, 8, 28, -20, 28, -7],\n [-7, -30, 25, -2, 3, -16, 2, -18, -3, -33, 6, 16],\n [30, 7, -33, 20, 30, -20, 16, 19, -33, 10, 32, 14],\n [-8, 5, 21, 11, -18, -25, -16, 20, 15, 3, 13... | 896 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-1, 10, 13, -7, 26, -12, -3, 20, 29, 9, 8, -21],\n [10, 30, -26, -24, -21, 20, -26, -4, 16, 0, 14, -26],\n [13, -26, -31, 13, 22, 10, -21, 10, -22, -2, 10, 7],\n [-7, -24, 13, -30, 8, 4, -27... | 608 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-30, 2, -17, -15, 29, -14, 11, 11, 19, -34, -7, -12],\n [0, -13, 3, -20, 4, 27, 11, -25, 12, 5, 15, 22],\n [0, 0, 23, -4, 29, 19, -10, 35, -29, -32, 28, -24],\n [0, 0, 0, 17, -1, -20, 17, 25... | 19 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[17, 27, -26, -25, 4, 6, -2, 34, -1, -18, -29, -1],\n [0, 21, 11, -2, 15, 1, -33, 1, -12, 30, -35, -7],\n [0, 0, -23, -16, -2, 35, -20, 21, 31, -32, 15, 16],\n [0, 0, 0, 18, -35, 14, 5, -26, 6, 27, 3, 18],\n [0, 0, 0, 0, 34, 25, 25, 24, -12, -30, 18, 24],\n... | 966 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-34, -14, -26, 30, 12, -5, 12, 14, -8, 18, 4, 16],\n [-14, -15, -9, 3, -12, -26, -4, -14, 1, 8, 12, -14],\n [-26, -9, 6, 4, -1, 4, -3, -14, -30, -20, 22, 2],\n [30, 3, 4, -8, -8, 30, 1... | 640 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, 26, 16, -21, -7, 13, -10, -29, 33, -3, 27, 34],\n [0, -5, -8, -28, 2, -33, 22, 18, -3, 26, 6, -8],\n [0, 0, 24, 7, 9, -23, 8, -33, -27, 2, -35, -29],\n [0, 0, 0, -18, -6, -29, 11, 16, 19, -32, 32, 28],\n [0, 0, 0, 0, 4, 21, 18, -10, -16, 22, -13, 9],\n [0, 0,... | 0 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[6, 12, -22, -17, -28, 5, 15, 21, 19, 27, -29, 6],\n [-30, 27, -25, -35, 17, 8, -30, 21, 5, -33, 35, 20],\n [-2, 10, 32, -31, -13, -7, -5, -19, 7, 25, -30, -16],\n [15, -33, -2, 34, -20... | 904 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[31, -22, 6, 16, 19, 16, 7, 12, 35, 19, 5, 19],\n [0, 31, -22, -21, -9, -8, 29, -1, 9, -3, 23, -23],\n [0, 0, -32, -19, -25, -18, 35, -26, -2, 7, 9, 22],\n [0, 0, 0, 13, -30, 27, 5, 7, -1, 18, 19, -18],\n [0, 0, 0, 0, 31, -33, -18, 20, -3, -16, 2, -18],\n [0, 0, 0,... | 196 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-25, 31, -5, 31, -18, -10, 25, 0, -33, -23, -14, -20],\n [0, -23, 6, -17, -33, -26, 16, 17, -18, -26, -35, 17],\n [0, 0, -22, -9, -21, -24, 10, 23, -13, -6, 22, 27],\n [0, 0, 0, 21, -1... | 4 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[17, 5, -1, -24, -16, 16, 27, 21, -20, -17, 26, 20],\n [0, -23, -30, 25, 31, 19, -31, 21, -17, -22, 10, -34],\n [0, 0, 28, 9, 18, 31, -33, 10, -18, 4, -20, 17],\n [0, 0, 0, -30, -32, 6, -16, ... | 371 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-35, 28, 3, 9, -11, -13, 1, 11, 30, 18, 7, 32],\n [0, 25, -15, -15, -33, -17, 6, 2, 24, 0, 16, 17],\n [0, 0, -8, 13, 6, 10, -21, 4, 15, 22, -32, -17],\n [0, 0, 0, 4, -24, -23, -31, 1, -30, 2... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-28, -4, 20, 0, 17, -18, 24, 14, 8, 12, 10, 29],\n [-4, 2, -8, -16, -17, 20, 14, 6, -24, -1, 7, 16],\n [20, -8, 22, -23, -8, -8, 14, 4, -26, 30, 20, -13],\n [0, -16, -23, 21, -7, 6, -14, -18, -6, -2, -10, 2],\n [17, -17, -8, -7, -23, 20, 6, 6, -28, -8, -19... | 152 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[0, -20, -4, 27, 9, 34, 4, -6, 5, -15, 35, -23],\n [20, 12, -23, 0, -31, 3, -31, -15, 8, -5, -10, -8],\n [-2, 29, -28, -28, 15, 23, -13, 13, -7, 27, -21, 14],\n [-10, 15, 19, 9, 13, 26, 16, 22, 17, 27, 9, 7],\n [16, -33, -24, 6, -32, -4, 16, 8, -35, 26, 27... | 488 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-29, -13, 20, -4, 3, 8, 5, 10, -10, 29, 0, -10],\n [-13, 4, 1, 32, 14, -14, -13, 4, 34, 14, -5, 0],\n [20, 1, -3, -6, -22, -14, 18, -4, 4, -22, -6, 4],\n [-4, 32, -6, -28, 8, -13, -6, ... | 448 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[22, -25, 19, 30, -34, -1, -9, -32, -23, 32, -35, -15],\n [26, -35, -20, -4, -17, 1, -30, 8, 19, -1, -20, -1],\n [21, -27, 5, 32, 17, 22, 7, 29, 33, -13, -4, -23],\n [0, 16, -31, -25, 21, -21, 30, -26, 22, -4, -23, 30],\n [3, -3, -13, -18, -31, -34, 4, -19, -17, -2... | 448 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[25, -16, 18, 32, -2, -7, 4, -14, -2, 16, -14, 28],\n [-16, -22, -28, 2, 12, -13, 5, 0, 21, -18, 0, -4],\n [18, -28, 18, 18, 14, 10, 3, 2, 4, -20, 4, 16],\n [32, 2, 18, -16, 18, 12, -27, -20, -31, -5, -10, 17],\n [-2, 12, 14, 18, -8, 6, -28, 5, 18, 4, -10, ... | 696 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[8, 10, -34, 3, -15, -14, 31, 10, -4, 7, -9, 5],\n [-5, -21, -11, 30, 19, -25, -18, -22, 0, 7, -24, -27],\n [14, 7, -11, 24, -27, 34, -24, 7, 15, 25, -26, -4],\n [4, -18, -22, 3, -35, 2... | 432 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[12, 26, -12, -12, -10, -22, 16, -26, -2, 9, 15, -5],\n [-14, -17, 28, -30, -28, -16, 10, -9, -1, -26, 2, 22],\n [-10, -33, -7, 9, 10, -24, -13, -27, -21, -3, -21, -12],\n [-22, 4, -22, -32, 4, -25, 23, -3, -33, 25, -35, 18],\n [29, 17, 18, 2, -14, 20, 9, ... | 328 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-10, 21, -2, -1, -22, -16, 4, -4, -3, 10, -18, 1],\n [21, -19, 9, -10, -27, -14, 30, 24, 16, -6, -19, -28],\n [-2, 9, -11, 6, -9, -7, 6, -8, 22, -1, 4, 14],\n [-1, -10, 6, 3, 5, -9, -22, -12, 14, 4, 18, -6],\n [-22, -27, -9, 5, -29, 21, -22, -22, 5, 8, 0,... | 536 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[29, -23, 7, 16, -21, 33, -20, -11, 8, 22, 18, -3],\n [0, 5, -11, 30, 23, -6, -12, 22, -33, 8, 2, 14],\n [0, 0, 30, 23, -20, -7, -18, -12, -30, 4, -22, -13],\n [0, 0, 0, 14, 12, -1, -2, 28, 14, 5, -9, 34],\n [0, 0, 0, 0, -25, 1, -6, 9, -27, -29, -30, -22],\n [0, 0,... | 994 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-10, -20, -11, -25, 3, 15, -27, -17, 30, -5, 2, 8],\n [5, 25, 24, -18, 34, -18, -28, 19, 27, 9, -17, 17],\n [1, -4, 16, 9, -17, -32, -14, 23, -25, -33, 10, -16],\n [-9, -22, -12, 9, -29, 19, 18, 29, -26, 5, 14, -17],\n [24, 2, 18, 33, -1, -9, -29, -17, -5, -20, -1... | 56 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[0, -9, 17, -4, 22, -23, 6, 16, 7, 16, -24, 12],\n [-9, 2, 14, 26, -28, 15, -7, -8, -8, -20, 8, 22],\n [17, 14, -20, 2, 24, 8, 4, -10, 4, 2, 6, -16],\n [-4, 26, 2, -25, -5, 1, 9, -11, 4, 29, 2, -30],\n [22, -28, 24, -5, 6, 30, -12, -5, -26, 1, 28, -7],\n [-23, 15, ... | 632 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-31, -29, 34, -32, 4, 8, -32, 8, -3, -12, 9, 35],\n [0, 15, -31, -19, -4, 10, -26, -18, -35, 14, -17, 6],\n [0, 0, 6, -12, -23, -35, -13, -15, 21, -25, 8, -8],\n [0, 0, 0, 27, -35, 8, 11, 35, 35, 17, -19, 31],\n [0, 0, 0, 0, -31, -5, -3, -34, -32, -23, -28, -31],\... | 2 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[6, -6, 20, 29, -19, 22, -4, -22, -19, -2, -29, -3],\n [-14, -9, -26, -3, -16, 22, -4, 16, -20, -27, 12, -15],\n [-22, 32, 17, -21, -21, -24, -10, -31, 18, 18, 17, -21],\n [-8, -25, -20, 4, 31, 13, -33, -29, 28, -9, 15, -20],\n [9, 8, 32, -3, -27, 18, -15, ... | 800 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[17, -32, -28, 3, -23, 13, 24, 25, -1, 23, 13, 32],\n [-12, 35, 6, 8, -21, -13, 27, -1, 15, 28, 12, -23],\n [18, -27, 5, -24, 17, 20, 1, 31, -3, 19, 20, 4],\n [24, -25, 10, 2, 31, -33, ... | 360 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[25, -17, 35, -22, 3, 6, 29, 22, -13, -27, 29, -27],\n [-4, 4, 28, -25, 30, -10, 22, -9, -1, -4, -25, 13],\n [6, -27, -5, -25, -26, -5, -10, -28, -26, -12, -6, 2],\n [29, -21, 2, -27, 22, -21, -4, -18, -16, -25, -8, 21],\n [3, -5, 32, 34, 24, 7, 20, -30, 34... | 696 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-11, 32, -18, -31, 11, -8, -8, -19, 12, -27, 23, 22],\n [0, 34, 23, 3, -5, 15, 19, -5, -26, 20, -32, 25],\n [0, 0, 22, 26, -35, -10, 3, 30, -12, 14, -3, -32],\n [0, 0, 0, -18, -20, -26, 29, -11, 5, -19, -35, -14],\n [0, 0, 0, 0, 25, -11, 1, -7, 19, -5, 2, -9],\n [... | 991 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-27, -2, -6, 19, -17, 5, -19, 1, 18, -33, 15, -31],\n [33, 24, 6, 3, 35, 23, 10, 5, -11, -21, 17, 4],\n [10, 5, 13, -4, -28, -7, 30, 9, 18, 28, -33, 23],\n [-8, 18, 21, 31, 31, -27, 23, -8, 9, -17, 28, -17],\n [-32, 13, -19, 13, 22, 1, -3, -21, 33, 31, 16,... | 56 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[8, 2, 21, -22, -22, -28, -4, 11, 3, 6, 19, 12],\n [14, 20, -21, 22, -8, 26, 21, 10, 6, 12, 34, 19],\n [-26, 16, -24, 7, -18, -13, 17, -24, 13, 24, 7, 35],\n [7, 5, 29, 21, 26, 26, 31, -18, 18, 20, 18, -4],\n [-10, -35, -18, -15, -8, -15, 18, 5, 18, 10, 30, -31],\n... | 216 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-16, 0, -19, -22, 4, -25, -18, -4, 8, 31, 8, -23],\n [0, 1, -22, 25, 35, 20, 28, 26, 23, -4, 32, -5],\n [0, 0, -30, -9, 10, -20, -14, -31, 8, 9, -7, 7],\n [0, 0, 0, -19, -33, 25, 12, -18, 30... | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-7, 26, -12, -19, 0, 2, 23, -13, 2, 2, 12, -20],\n [26, -20, -6, -10, 24, -2, -8, 2, -14, -11, -2, -22],\n [-12, -6, 30, 28, 0, -2, 4, -12, -12, 9, -12, 8],\n [-19, -10, 28, -15, -9, 6, -12, 29, -12, 0, -1, 12],\n [0, 24, 0, -9, -2, -12, 19, -30, -10, -25, -15, -1... | 336 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[18, -18, 31, 28, 16, -15, 16, 12, -15, -2, -18, -34],\n [0, -12, -21, -26, -12, -21, -10, 34, -33, 28, 26, 31],\n [0, 0, -22, -17, -14, -3, -29, -35, 3, 1, 14, 4],\n [0, 0, 0, -33, -25, 30, 4, -25, 29, -23, 34, -35],\n [0, 0, 0, 0, 18, 0, 8, -22, 20, 20, -24, -29]... | 996 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-19, -6, 4, -9, -5, 35, 20, -6, -18, -7, -14, -4],\n [0, -14, 18, 23, 9, 17, 10, -11, 7, -10, 30, -12],\n [0, 0, 27, 23, -24, 14, -6, 15, -3, 20, -9, 11],\n [0, 0, 0, 31, 35, -26, 13, -17, 10, 13, -24, 7],\n [0, 0, 0, 0, -26, -30, -17, 12, 14, 30, 24, 23],... | 269 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[30, 20, -5, 5, -26, 13, 32, -18, 14, 1, -18, 12],\n [0, -26, 5, 2, -9, -32, 4, 12, -16, 34, 5, 20],\n [0, 0, 21, -8, -15, 24, 24, 6, -20, 22, 20, 0],\n [0, 0, 0, -18, 23, 18, -14, -25, 8, -27, -10, 0],\n [0, 0, 0, 0, 21, -6, 3, 17, 13, -2, -35, -14],\n [0, 0, 0, 0... | 987 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-5, 2, 16, -12, -20, 9, -22, -11, -21, 20, 34, -22],\n [22, 10, 26, 25, -11, -20, -26, -1, -13, -18, -17, -28],\n [-11, -26, -18, -6, 27, 20, -16, 24, -19, 4, -28, 28],\n [-14, 1, -26,... | 376 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[26, 6, -14, 0, -6, 14, -6, -16, -18, 2, 10, -33],\n [6, 30, -11, -10, 23, -2, 0, 22, -18, -12, -30, -8],\n [-14, -11, 28, -14, 16, -10, 6, -12, -10, 12, -8, 10],\n [0, -10, -14, -32, 18, -12... | 632 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[33, 5, -25, 8, -4, 27, -7, 1, 12, 25, -28, 23],\n [0, -24, 30, -4, -13, -17, -9, -13, 28, -5, 32, 12],\n [0, 0, 11, 23, -15, 8, -4, -31, -17, 25, 1, -6],\n [0, 0, 0, -15, -7, -24, 5, -13, 20, -20, 0, 5],\n [0, 0, 0, 0, 14, 23, -8, 9, 12, -1, 7, -9],\n [0,... | 9 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[6, -12, 5, -9, 22, -7, -22, 3, 21, -2, -6, 12],\n [-12, -22, -6, 14, 2, -31, -5, 8, 12, 25, -18, 15],\n [5, -6, -12, 6, -10, 24, -18, -18, -6, -1, 8, -10],\n [-9, 14, 6, 33, 30, 10, 1, 10, -18, 20, -10, -2],\n [22, 2, -10, 30, -5, -5, 10, -8, 1, 14, 2, 10... | 32 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[8, 10, 17, -20, 23, -8, -23, -9, -33, 0, -25, -21],\n [27, 29, -7, -17, 30, 6, 11, 22, 19, 26, 32, -6],\n [11, -20, 33, 34, 23, -6, -27, -6, 12, 34, -31, 8],\n [7, -20, -20, 32, -13, 29, 2, ... | 880 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-24, -5, -19, 1, -26, -26, 9, -5, -32, 3, 3, -12],\n [0, 11, -11, -29, 26, -24, -5, -22, 12, -10, 1, -11],\n [0, 0, -2, 28, -31, -30, 29, -29, -2, -25, -5, -14],\n [0, 0, 0, -18, -16, 27, -28, -24, 6, -7, 32, -19],\n [0, 0, 0, 0, 16, -20, -11, 32, -28, 3, ... | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-32, -13, 28, 32, -17, -4, -21, -10, -16, -30, -30, 30],\n [0, -26, -4, 12, -21, -28, 4, -10, -14, 26, -29, -27],\n [0, 0, 34, 24, 12, -25, -12, -20, -35, 23, 8, -10],\n [0, 0, 0, -13, -27, -6, 2, -21, 18, -12, -22, 14],\n [0, 0, 0, 0, 25, 23, 19, -17, -7, 3, 22, ... | 795 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-17, 1, -21, 7, 30, 5, 25, 27, 6, 0, -21, 24],\n [0, -29, 31, -7, 30, -3, 33, -25, 35, 8, -18, 6],\n [0, 0, 14, -18, -13, 20, -1, 21, -10, 18, -30, 9],\n [0, 0, 0, 23, 15, -18, -29, 13, 13, -15, -15, 10],\n [0, 0, 0, 0, -18, -9, 8, -14, -1, 11, -30, 9],\n ... | 244 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-24, -14, 29, -30, 23, 16, 22, 19, 3, -29, -19, 6],\n [-8, -34, -19, 19, 34, 6, -13, 9, 2, -25, 30, 0],\n [-25, 5, 6, -22, 10, 21, 6, -27, -10, 4, -5, 33],\n [8, 3, -22, -2, -16, 16, 1... | 368 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-17, -10, 20, -19, 31, 32, -11, 4, 4, 4, 16, 30],\n [-23, -10, 19, -18, 2, -17, 13, -15, -20, 16, -19, 6],\n [-27, -30, 27, -35, 4, 23, 5, 20, 5, -28, -19, 8],\n [-10, 9, -8, -4, 6, 11, 21, ... | 640 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[5, -12, -32, -23, 10, -16, 18, 1, 4, 6, 0, 8],\n [-12, 13, -5, 2, 8, 0, -8, -2, -9, 32, 17, -16],\n [-32, -5, -9, 15, 4, -8, -1, 14, 8, 11, 8, -15],\n [-23, 2, 15, -10, 16, 9, 10, 12, -6, -25, 6, -16],\n [10, 8, 4, 16, 8, 0, -6, -19, 8, -15, -1, 0],\n [-16... | 323 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[34, -13, -32, 24, -34, -32, -21, -33, -32, -13, -31, -21],\n [23, -34, 0, -5, -25, -4, 30, 14, 33, -35, -24, -18],\n [11, 13, -17, 4, 16, 11, 35, 33, 30, -30, -33, 1],\n [-22, -31, 0, -10, 2... | 192 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[23, 25, -28, -33, -11, -29, -29, 19, 29, -15, 33, 5],\n [6, -16, 0, 11, 1, -23, 14, -21, -19, -3, 21, -2],\n [17, 1, -11, -3, -27, -14, 35, 18, -21, 33, 10, -6],\n [-6, 14, -8, 32, 33, -5, 5, 4, 11, 13, 13, 35],\n [34, -26, 17, -12, -11, -20, -27, 11, 27,... | 816 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, -18, -24, -28, 17, 0, 7, -23, -27, -17, 33, 11],\n [4, 33, -17, 12, 26, -13, 5, 10, -26, 26, -35, 11],\n [-3, 20, 25, -33, 10, -7, -21, -27, 20, -24, 20, -28],\n [-1, -34, -25, -23, -4, -2, -1, -26, 12, 17, 31, -17],\n [2, -13, 16, 2, -20, 31, 20, 27, -... | 384 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[26, 34, 2, -25, 12, -22, 21, 4, 12, -13, 0, 21],\n [34, 13, 4, 1, 10, 4, 7, -8, -23, 12, -10, -24],\n [2, 4, -6, 26, 18, -17, 10, 0, 0, -22, -6, -10],\n [-25, 1, 26, -21, -17, 16, -27, 11, -20, -26, -14, 8],\n [12, 10, 18, -17, 25, -2, -12, -22, 4, -16, 6, 0],\n [... | 16 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-26, -8, 30, 23, -35, -22, -32, 19, -30, 9, -4, -15],\n [0, 3, 8, 27, 11, 22, 16, 30, 33, -9, -30, 15],\n [0, 0, -30, -8, 24, -28, 14, 24, -34, -22, 20, -25],\n [0, 0, 0, -25, -23, -27, 31, -25, 6, -8, 6, 32],\n [0, 0, 0, 0, -25, 23, -19, 6, -10, -18, 30,... | 997 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[5, 12, -5, 8, 10, 3, -10, 8, -3, 26, 2, 12],\n [12, 20, 24, 21, 3, 12, -20, -23, -19, 3, -18, 34],\n [-5, 24, 21, -2, -4, 16, -20, -22, 28, -12, -8, -8],\n [8, 21, -2, 19, -14, -16, -11, -19, -1, -32, 2, -6],\n [10, 3, -4, -14, 12, -2, -6, 8, -6, 10, 4, 1... | 256 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[34, -21, 25, -30, 29, 11, -21, -1, -20, 9, -18, 32],\n [0, 13, 0, -15, 30, 5, -20, 35, 20, -21, 28, -7],\n [0, 0, 15, -20, -25, 1, -29, -35, 5, -29, 28, 14],\n [0, 0, 0, 30, 16, 7, 1, ... | 990 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-24, -4, 16, 16, 17, -4, 12, -12, -2, 23, 6, 7],\n [-4, -10, 20, 0, -16, -6, -21, -20, 10, 10, -10, -2],\n [16, 20, 0, -2, -9, 17, 27, -1, 6, -3, 23, -8],\n [16, 0, -2, 13, -2, 8, -6, -1, 29... | 968 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-12, -2, -19, 11, 0, -26, -7, 8, 16, 2, -1, 0],\n [-2, -8, -1, 16, 24, -13, 22, -4, 1, -5, -14, -8],\n [-19, -1, 12, 14, -23, 26, 4, 0, 9, 3, 7, 6],\n [11, 16, 14, 31, 18, -2, 27, -4, -24, -19, 22, -25],\n [0, 24, -23, 18, 3, -4, 4, 34, 8, 17, -15, 0],\n ... | 888 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, 2, -12, -32, -30, 4, 18, 28, -10, -4, -4, -18],\n [2, 32, 8, 0, -3, 18, 14, 19, 2, -23, 10, 18],\n [-12, 8, -27, -9, -22, 16, 14, 9, -10, -24, 6, 2],\n [-32, 0, -9, 34, 20, 12, -10, -8, -9, 26, -1, -20],\n [-30, -3, -22, 20, 34, 19, 14, 0, -24, 28, 14, -6],\n ... | 728 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[11, -1, 35, -12, -9, -19, -10, -2, 16, 12, -18, -16],\n [-10, -11, 13, 32, 8, 20, 21, -17, 8, 16, 0, 12],\n [-34, -1, -12, 34, 18, -1, -7, -14, -11, 11, 9, -4],\n [10, 3, -31, 32, 5, -29, 7, -6, 18, 1, -16, 23],\n [0, -34, -24, -29, 20, -2, 16, 10, -3, -32, -24, 2... | 84 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[35, 27, 17, -18, 8, 21, 32, 12, 28, -13, 34, 12],\n [-25, 17, 10, -13, 15, -34, -21, -6, 35, 29, -19, -18],\n [-16, -28, 12, -5, -30, -1, -25, -11, -9, -14, 19, 18],\n [-7, 29, -21, -15, 9, -11, -28, 4, 27, 33, 13, 0],\n [2, 29, 5, -35, 25, -18, -1, -1, 23... | 192 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-11, -2, 2, 16, -12, 4, 0, -10, 15, 7, -4, -8],\n [-2, 30, -4, 13, 10, -4, 24, 22, 17, 1, 14, -20],\n [2, -4, 10, -4, -27, -8, -2, -33, -15, -12, 9, -22],\n [16, 13, -4, -22, -2, 20, 3... | 216 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[35, -15, 32, 23, 10, 11, 18, 24, -2, 6, -1, -2],\n [-15, 32, -22, 28, 1, -3, 0, -4, 32, -20, 10, 16],\n [32, -22, 17, 9, 8, 22, 18, 0, -25, -25, 16, 20],\n [23, 28, 9, 24, -2, 11, 26, -20, -... | 456 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-2, -35, 25, 4, 25, -21, -23, -1, 8, 21, -4, 34],\n [0, -24, 5, 17, 27, -18, -14, -35, -34, 33, -31, 4],\n [0, 0, -26, 35, -28, -12, 31, 13, 23, -23, -9, -6],\n [0, 0, 0, -8, -21, 25, -21, 30, -10, -32, 20, 26],\n [0, 0, 0, 0, 2, -20, 2, 16, -17, -25, 19, 6],\n [0... | 600 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-31, 32, -27, -24, -35, -29, -24, -3, 31, -18, 31, -31],\n [0, -1, 20, 10, 5, 7, 24, 23, -9, -20, 12, 0],\n [0, 0, 10, 6, 13, -23, -13, 33, -7, 17, -5, 16],\n [0, 0, 0, -8, -30, 29, 12, 35, 5, -13, 23, -34],\n [0, 0, 0, 0, -29, -29, 14, 26, 15, -30, 29, 17],\n [0,... | 0 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[-5, -26, 20, -10, -9, 18, 17, 28, 19, 15, -18, -21],\n [32, 31, -15, 33, -27, 24, -22, 32, -26, -33, 17, -13],\n [-21, 16, -27, -28, -15, 21, 23, -26, -27, -30, -29, 29],\n [-21, -24, -7, -17, -16, -5, 14, -15, 23, 21, -16, 19],\n [-2, -20, 34, 18, -28, -3... | 136 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[9, -16, 12, -2, 19, -5, -23, 2, -3, 10, -15, -14],\n [-16, 1, 5, 22, -4, 2, 22, 0, -18, 13, -20, -17],\n [12, 5, -8, 11, -14, -7, 2, 10, 6, -7, -8, 2],\n [-2, 22, 11, 31, 10, -21, 12, ... | 56 | MATH |
[
{
"content": "What is the determinant of the matrix:\n[[3, 6, 17, 24, 2, -24, -24, 22, -26, 20, 0, -33],\n [11, 4, -15, 20, 15, -15, -13, 32, -28, 25, -2, -1],\n [-22, -11, -4, 4, -14, -22, 3, -11, -35, -7, -10, 2],\n [20, -11, -14, 34, 32, 21, 29, 6, 11, 34, -14, 6],\n [20, -16, 31, -19, -8, 34, 15, -2, 17, -1... | 432 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-18, -20, 28, -29, 26, -10, -29, -15, -19, 9, 23, 9],\n [-35, -17, 11, -27, 2, -6, -21, 4, -5, -19, 16, 10],\n [11, -15, -14, 10, -3, -14, 2, 17, 33, -21, -27, -5],\n [2, -24, 29, 8, -... | 824 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[-33, 28, -25, -26, -24, 6, -1, -29, 6, 28, 32, -1],\n [0, -13, -20, -8, 6, 9, -4, -19, -26, -4, -27, -4],\n [0, 0, -16, -21, -11, 16, 31, 11, 30, 22, 25, 3],\n [0, 0, 0, 21, -20, -16, 19, -7, 26, -4, -24, -14],\n [0, 0, 0, 0, 34, 28, -17, 16, -21, 27, 30,... | 214 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-27, -22, 22, 16, -30, 3, -14, 4, -28, 1, -9, -14],\n [-29, -17, -29, -25, -6, -26, 20, -17, 0, -15, 11, 0],\n [-17, 3, -11, -2, -32, -30, 24, -26, -25, -16, -19, 34],\n [-10, 19, -34, 28, 5... | 360 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-1, -13, 26, 12, -18, -28, -4, -32, 7, -17, 24, 1],\n [-13, 25, 1, -5, -9, 18, 3, 14, 0, -6, -4, 4],\n [26, 1, 33, 8, -18, 4, 23, 6, -8, 0, -7, 28],\n [12, -5, 8, 28, -9, -21, -8, 2, -... | 832 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[17, -3, -34, -3, -34, -15, 16, -13, -17, -19, 11, 7],\n [30, 9, -19, 33, -4, 16, -23, 27, -19, -8, 15, 22],\n [-13, 3, 4, 33, 29, -18, -5, 28, -8, -27, -29, -28],\n [-7, 25, 22, -10, 24, -19, -30, 7, 24, -31, -6, 26],\n [25, 10, -1, 33, -12, 6, -33, -18, ... | 64 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-33, -1, 4, 10, -32, 15, 21, 21, -10, -27, 23, -24],\n [-33, -20, 34, -10, 12, 27, 2, -31, 32, -20, -23, -32],\n [14, -35, 10, 35, 2, 23, 1, 0, 0, -16, 8, -17],\n [-6, -35, 4, -2, -12, 19, 1... | 496 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[5, 1, 13, -17, -33, 35, -10, 0, -8, -30, -10, -29],\n [0, -18, -29, -9, -19, -31, -1, -25, -3, 11, -28, 6],\n [0, 0, -23, -15, -25, 35, -13, -13, -15, -8, 24, -23],\n [0, 0, 0, -23, 35... | 9 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[35, 0, -7, 12, 9, 2, -25, 22, -5, 3, -7, -9],\n [0, 26, -26, 6, 21, 4, 26, -2, 18, 6, 17, -30],\n [0, 0, -9, -34, -15, 20, -22, -26, 5, -30, -17, 15],\n [0, 0, 0, -21, 15, 3, 10, -12, ... | 200 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[15, -6, -5, 19, 12, -5, -17, -10, -32, 10, -21, 18],\n [-5, -3, 35, 29, -9, 4, 6, 13, 35, -3, 8, -7],\n [-33, 29, 16, 3, 12, 18, 0, 6, 21, -22, -28, -21],\n [-7, -7, -29, -23, -16, -35, -25, -22, 21, 10, 33, -29],\n [-14, -35, 12, 12, -19, -5, -20, 2, -29, -19, 12... | 952 | MATH |
[
{
"content": "Determine the value of det(A) where A =\n[[20, -35, 35, 15, 3, 14, 34, 18, 20, -4, -9, 11],\n [14, 12, 35, -30, -5, 9, -34, 32, 3, 31, 19, 28],\n [13, 31, 30, 24, 0, 11, -26, -19, 25, -6, -23, 33],\n [-17, 19, -29, -14, 11, -13, 4, -28, -4, -21, 26, -22],\n [34, -4, 0, -22, 9, -1, -33, -24, -6, 29... | 856 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-4, 8, 31, -22, 24, -32, 28, -18, -17, 27, 26, -31],\n [24, -28, 3, 2, 29, -6, -28, -35, 3, 30, 3, -6],\n [20, 4, -19, -6, 25, 13, 32, -35, 29, -4, 25, 9],\n [-18, 21, -5, -31, 30, 10, 25, 23, -10, 30, -5, -22],\n [1, -4, -11, 26, -15, 7, -8, -14, -7, 14, 0, -23],... | 208 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[-14, -23, -14, -28, -15, -23, 8, 35, 8, 17, 7, 31],\n [0, 17, 6, -25, -10, -11, -32, -7, -27, 18, -16, -26],\n [6, -22, 25, -27, -17, 30, 20, 4, 27, 32, 23, 34],\n [-23, -8, 18, -30, -... | 32 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-33, 1, -24, 32, 3, -6, -13, -22, 24, 32, 29, 8],\n [0, 21, -31, 1, 2, -25, 23, 35, 10, 30, -2, -18],\n [0, 0, 18, -7, 19, 28, -12, -10, 5, -7, -28, -8],\n [0, 0, 0, -23, -9, -16, 13, 4, 19, -12, 19, 24],\n [0, 0, 0, 0, -21, 21, 33, 12, -18, -25, 16, -27],\n [0, 0... | 128 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[17, 11, -11, 29, 18, 5, -11, -27, 30, 20, -4, -32],\n [-3, -9, -5, -5, -26, -32, 1, 20, -21, -23, 28, -7],\n [-20, -17, 21, 35, 24, 17, 22, 27, -17, 3, -33, 0],\n [-24, -34, 29, 0, 0, 13, 3,... | 200 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-20, 32, 1, -21, 4, -3, -15, 3, -16, 18, 33, -5],\n [0, -16, 26, -35, 33, 12, -26, -5, 24, -31, 34, 22],\n [0, 0, -13, -18, -3, 4, 32, 20, -23, 25, -12, -22],\n [0, 0, 0, -35, -33, -10, 23, ... | 924 | MATH |
[
{
"content": "Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:\n[[-3, 21, 12, 21, -25, 35, -25, 9, -3, 9, -1, -12],\n [-21, -22, -17, -11, -23, 29, -14, -11, 1, -3, -15, 33],\n [-33, 26, -3, 1, 20, -25, -17, -14, -17, 2, -33, -4],\n [-12, -25, 13, 4, 8, 28... | 944 | MATH |
[
{
"content": "Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:\n[[14, -23, -12, -7, -12, -33, -14, 3, -2, -12, 8, 7],\n [-23, -13, -8, -28, 12, 0, -8, 14, -2, -4, 3, -5],\n [-12, -8, -30, 28, 8, -14, 16, 2, -12, 10, 8, 1],\n [-7, -28, 28, -23, -18, -... | 304 | MATH |
[
{
"content": "Compute |A| for the matrix A =\n[[-31, 3, -20, -14, -34, -8, 4, -10, -18, 6, 2, -15],\n [0, 21, 3, 8, -33, 22, 1, 5, -14, -16, -16, 19],\n [0, 0, -35, -28, 29, 5, 17, 29, 13, 28, 24, -32],\n [0, 0, 0, 16, 20, -12, -22, -30, 7, -28, 28, 16],\n [0, 0, 0, 0, 16, 5, 31, 27, -11, -4, -8, 26],\n [0, 0, ... | 998 | MATH |
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