messages listlengths 1 1 | ground_truth stringclasses 6
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-100, -41, 111, -91, 146, -129, -194],\n [-30, -120, -92, -288, -58, 43, 244],\n [99, -20, 139, 49, 246, -53, -159],\n [106, 78, -155, 111, -103, 119, 159],\n [149, 29, -90, 189, 100, -9, -32],\n [202, 70, 107, 128, 267, 64, -158],\n [-78, -52, -125, -4... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-42, -60, -54, 36, -54, 6, 66],\n [49, 70, 63, -42, 63, -7, -77],\n [63, 90, 81, -54, 81, -9, -99],\n [-70, -100, -90, 60, -90, 10, 110],\n [-56, -80, -72, 48, -72, 8, 88],\n [-7, -10, -9, 6, -9, 1, 11],\n [-7, -10, -9, 6, -9, 1, 11]]\n\nPresent the answ... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[40, 91, -114, -92, -5, -170, 97],\n [67, -109, -34, -119, -202, -84, -29],\n [-46, -74, 24, -4, -127, 118, -153],\n [-12, 31, -164, -82, -166, -36, -20],\n [-48, 86, 21, 60, 144, 26, 52],\n [-157, -48, -24, -253, -335, -2, -148],\n [264, -210, 3, 169,... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[102, 21, -71, 92, 54, 186, 82],\n [-48, -3, -3, 24, -75, -80, -47],\n [-114, 274, 136, -116, -197, 34, -87],\n [13, 143, -58, -1, -109, 83, 72],\n [-166, -99, 160, -54, -41, -274, -224],\n [-162, 69, 10, 102, -107, -22, -74],\n [-194, 42, 133, 10, -130, -150, -20... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-77, 77, 14, -14, 0, -63, 77],\n [8, -38, -11, 32, -12, 18, -74],\n [43, -53, -11, 18, -4, 39, -65],\n [64, 26, 17, -80, 36, 18, 134],\n [18, -58, -16, 44, -16, 30, -106],\n [-157, 127, 19, 2, -12, -117, 91],\n [-47, 17, -1, 22, -12, -27, -19]]\n\nPre... | 2 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-30, 93, 132, -27, -24, 108, -66],\n [24, 31, 99, 34, 44, 19, 59],\n [18, 36, 99, 27, 36, 27, 45],\n [38, -26, 11, 45, 52, -45, 89],\n [-34, -17, -88, -45, -56, 0, -82],\n [48, -6, 66, 60, 72, -30, 114],\n [-20, 62, 88, -18, -16, 72, -44]]\n\nPresent th... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[3, -104, -138, -1, -117, 68, 47],\n [-11, 24, 42, 9, 29, -36, -7],\n [-46, -125, -117, 41, -131, -16, 75],\n [85, 113, 63, -74, 110, 100, -84],\n [6, -7, -15, -5, -9, 16, 1],\n [78, 43, -21, -67, 33, 128, -49],\n [-78, -43, 21, 67, -33, -128, 49]]?\n\nPresent the... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-99, 99, -54, -99, -63, -63, 99],\n [110, -110, 60, 110, 70, 70, -110],\n [-77, 77, -42, -77, -49, -49, 77],\n [-11, 11, -6, -11, -7, -7, 11],\n [22, -22, 12, 22, 14, 14, -22],\n [66, -66, 36, 66, 42, 42, -66],\n [99, -99, 54, 99, 63, 63, -99]]?\n\nPresent the an... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[166, 106, -42, 45, -27, -21, -35],\n [230, 17, -111, -51, 87, -69, 23],\n [154, 29, -13, -32, 133, -161, 35],\n [-84, 43, 67, 60, -68, 26, -32],\n [-30, 148, 136, 123, -53, -79, -53],\n [-46, -139, -9, -114, 153, -81, 83],\n [40, 126, 82, 86, -16, -88... | 3 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[108, 86, 78, 37, -60, 35, -105],\n [-100, -48, -46, 19, -20, -33, 89],\n [2, 143, 113, -118, 62, -15, -131],\n [36, 170, 82, -174, 68, -67, -208],\n [-74, -181, -113, 108, -14, 31, 209],\n [26, 27, 77, 4, 38, 67, -5],\n [110, 107, 139, -18, 34, 82, -113... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[130, -82, 44, -2, 114, 80, 112],\n [-60, 17, -21, 116, -12, 68, -46],\n [-146, 100, -48, -50, -159, -145, -139],\n [140, -104, 48, 76, 138, 150, 114],\n [-140, 87, -51, 36, -72, -32, -86],\n [-97, 73, -32, -67, -114, -125, -91],\n [-95, 86, -39, -85, -30, -87, -1... | 3 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-132, 88, 99, 22, -99, -77, 88],\n [-21, 4, 19, -2, 2, -16, 14],\n [156, 16, -156, 40, -96, 136, -104],\n [-189, 36, 171, -18, 18, -144, 126],\n [198, -72, -168, 0, 42, 138, -132],\n [84, -56, -63, -14, 63, 49, -56],\n [-252, 48, 228, -24, 24, -192, 168... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[80, 0, -10, 0, -60, -10, 40],\n [56, 0, -7, 0, -42, -7, 28],\n [-172, 72, -121, 72, 198, 35, 100],\n [-65, 42, -75, 42, 89, 16, 76],\n [35, -30, 55, -30, -55, -10, -60],\n [48, -48, 89, -48, -82, -15, -100],\n [1, -42, 83, -42, -41, -8, -108]]\n\nPresent... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-17, 56, 75, -158, 252, 41, 44],\n [-11, -61, 14, 43, -28, 85, 104],\n [-41, 148, 21, -131, 176, -135, -69],\n [30, -176, -30, 104, -232, 102, 128],\n [32, -26, -48, 121, -140, -4, -89],\n [-39, -26, 17, -51, 0, -5, 137],\n [-6, -19, -61, 36, -188, -1... | 4 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-26, -40, 28, -5, -14, -21, -5],\n [39, 64, -76, -70, 90, -86, 47],\n [-49, -50, 42, -40, 104, -119, 108],\n [56, 52, -120, -115, -34, -89, -99],\n [7, -12, 16, 60, -134, 122, -113],\n [-21, -36, 4, -45, 0, -71, -8],\n [-17, -14, 30, 20, 28, 3, 42]]\n\n... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, 53, 27, -102, -12, 56, -88],\n [-165, 6, 126, 121, 198, -56, 30],\n [-4, 48, -64, 48, -108, 120, -40],\n [148, -6, -152, -37, -195, 62, 22],\n [70, 72, -55, -105, -8, 30, 47],\n [-78, 6, 55, 14, -65, 92, -173],\n [101, 93, -178, -7, -207, 176, 11]]?\n\nPresen... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-177, 29, -3, -26, 61, 19, -69],\n [62, 143, -64, 130, 68, -61, 60],\n [-210, 32, 23, -22, 72, 49, -116],\n [140, 22, 83, 98, -18, 69, -66],\n [-236, 35, -32, -50, 78, -3, -54],\n [206, -85, 97, 20, -98, 68, -26],\n [44, 68, 50, 100, 32, 50, -72]]?\n\nPresent the... | 3 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-69, -76, -26, -150, -99, 74, 135],\n [-212, -46, -24, -10, -139, 180, 64],\n [-325, -3, -14, 42, -87, 140, -8],\n [183, -73, 16, -68, -35, 32, 16],\n [21, -64, 70, 298, 124, -22, -167],\n [-9, 98, -7, 42, -77, 112, -101],\n [155, -63, -8, -36, 29, -68,... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[50, 13, -158, -77, -100, 18, 89],\n [-46, 112, 170, -91, -66, -56, 220],\n [71, -40, -221, -61, -66, 57, 32],\n [-24, -29, 104, -134, 100, 152, 181],\n [-127, 195, 177, 17, -9, -4, -54],\n [-150, 421, 122, 4, -266, -172, 1],\n [91, -176, -177, 76, 54,... | 4 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-18, 30, 2, 48, -178, 62, -26],\n [-14, -18, 5, -97, 175, -93, -34],\n [-7, 33, -1, 88, -231, 97, -3],\n [-56, 36, 11, -37, -119, -3, -100],\n [22, -6, -5, 41, -15, 29, 42],\n [-35, 33, 6, 11, -154, 34, -59],\n [32, -24, -6, 10, 94, -10, 56]]\n\nPresent... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[60, 24, -24, 0, 60, -54, -54],\n [134, 8, 76, -84, -10, 45, -75],\n [-76, -76, 160, -84, -220, 234, 114],\n [-66, 4, -60, 56, 30, -51, 29],\n [88, 39, -46, 7, 100, -93, -83],\n [-104, -72, 128, -56, -200, 204, 124],\n [28, 15, -22, 7, 40, -39, -29]]\n\nP... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[49, 70, -49, 56, -49, 28, -42],\n [14, 20, -14, 16, -14, 8, -12],\n [77, 110, -77, 88, -77, 44, -66],\n [77, 110, -77, 88, -77, 44, -66],\n [84, 120, -84, 96, -84, 48, -72],\n [14, 20, -14, 16, -14, 8, -12],\n [56, 80, -56, 64, -56, 32, -48]]?\n\nPresent the answ... | 1 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[108, 23, 39, 193, -95, -76, -74],\n [54, 11, -31, 4, 4, 4, 19],\n [42, 75, -3, 70, 14, 28, -7],\n [24, 92, 12, 86, 18, 36, -18],\n [99, -83, -16, 38, -85, -93, -13],\n [99, -21, -2, 90, -69, -65, -27],\n [-69, 7, -90, -233, 138, 117, 120]]\n\nPresent th... | 3 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[60, -30, -48, -18, -66, -54, 54],\n [60, -30, -48, -18, -66, -54, 54],\n [80, -40, -64, -24, -88, -72, 72],\n [-20, 10, 16, 6, 22, 18, -18],\n [-70, 35, 56, 21, 77, 63, -63],\n [-50, 25, 40, 15, 55, 45, -45],\n [-120, 60, 96, 36, 132, 108, -108]]\n\nPre... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[132, -132, -84, 108, 12, -96, 132],\n [-121, 121, 77, -99, -11, 88, -121],\n [22, -22, -14, 18, 2, -16, 22],\n [77, -77, -49, 63, 7, -56, 77],\n [-33, 33, 21, -27, -3, 24, -33],\n [88, -88, -56, 72, 8, -64, 88],\n [121, -121, -77, 99, 11, -88, 121]]\n\nP... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-22, -110, 110, 11, 77, -66, -44],\n [2, 10, -10, -1, -7, 6, 4],\n [0, 0, 0, 0, 0, 0, 0],\n [-22, -110, 110, 11, 77, -66, -44],\n [20, 100, -100, -10, -70, 60, 40],\n [-8, -40, 40, 4, 28, -24, -16],\n [-20, -100, 100, 10, 70, -60, -40]]\n\nPresent the... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[17, -5, -8, 77, 41, 30, 8],\n [0, -69, 18, -83, 17, 36, -53],\n [6, 94, 78, 6, 226, 10, -127],\n [14, -22, -2, 42, 38, 34, -7],\n [-2, 41, -34, 71, -69, -36, 77],\n [-7, -74, -74, 2, -214, -18, 125],\n [-6, 175, 54, 57, 157, -56, -55]]?\n\nPresent the answer in L... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-158, -2, 107, 240, -117, 192, 226],\n [41, 70, 6, 126, 31, 244, -48],\n [146, 147, -182, -42, 162, 113, -223],\n [278, -2, 91, -190, 50, -34, -99],\n [-104, -61, -61, -62, 27, -157, -67],\n [-185, -122, 144, 114, -130, -15, 165],\n [91, 13, -178, -17... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-118, -50, 56, 41, 25, -83, -48],\n [-94, -99, 79, -51, 81, 28, 116],\n [78, 176, -78, -51, -165, 87, -202],\n [-38, 13, -141, 65, -23, -76, -100],\n [-2, 0, 85, -32, 0, 31, 19],\n [68, -3, -51, -98, 18, 135, 128],\n [24, 90, -16, -47, -88, 63, -105]]\n\nPresent the... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-12, -48, -48, 98, 124, -76, -76],\n [-52, 54, 54, -12, -74, -111, -111],\n [-44, 72, 72, -54, -124, -72, -72],\n [76, -72, -72, 6, 92, 168, 168],\n [52, -54, -54, 12, 74, 111, 111],\n [-32, -18, -18, 78, 74, -111, -111],\n [52, -42, -42, -8, 46, 121, 121]]?\n\nP... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[10, 226, -24, 81, 183, 76, -9],\n [142, -25, 157, -3, 11, -29, -101],\n [140, -15, -4, -261, -105, 148, 138],\n [-192, 64, -132, 156, 76, -44, 8],\n [136, -83, 154, -33, -41, -42, -88],\n [-4, 152, 21, 135, 159, -1, -72],\n [168, 16, 61, -183, -43, 111, 58]]\n\nPres... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[210, -3, 238, 137, 156, 26, 50],\n [120, -14, -3, -19, -128, 159, 56],\n [-221, 70, -157, -65, 16, -74, -13],\n [148, -99, 184, 111, 90, -82, -86],\n [-58, 61, -1, 36, 97, -27, 15],\n [-150, 206, -45, -29, 167, 15, 181],\n [53, 121, 21, -34, 19, 152, 200]]\n\nPresen... | 4 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[32, -223, 91, 145, -188, -170, -7],\n [-189, -22, 41, -35, -5, -105, 123],\n [83, -35, -7, 34, -35, 26, -85],\n [90, -137, 66, 136, -107, -119, 60],\n [-24, 156, -65, -112, 112, 125, -31],\n [106, 62, 5, 47, 57, -3, 149],\n [-19, -37, 44, 37, -46, -87, ... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[4, 0, 24, 152, -80, 120, 24],\n [-5, 0, 50, 170, 110, -90, -120],\n [-14, 8, 84, 268, 87, -58, -143],\n [-43, 34, 74, 47, -8, -38, -79],\n [-50, 42, 72, 5, -77, 18, -36],\n [-76, 58, 92, -103, 37, -158, -130],\n [-27, 18, 58, 63, 86, -114, -117]]\n\nP... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-26, 185, -155, -73, 24, -81, -89],\n [102, 16, -65, 81, 67, 15, 255],\n [99, 46, -38, -54, 115, 10, 39],\n [-211, 55, -125, 132, -226, -31, -29],\n [-65, 73, -80, -30, -36, -10, -115],\n [38, -4, 48, -155, 91, 44, -223],\n [-28, 49, -113, 45, -28, 33, 31]]\n\nPrese... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-38, 32, -44, -3, 19, -21, 50],\n [-60, 90, -100, 110, 120, -90, 80],\n [24, -56, 56, -89, -89, 63, -36],\n [62, -58, 72, -117, -81, 57, -54],\n [-82, -77, 42, 160, -85, 84, -52],\n [-10, -50, 40, -13, -73, 57, -30],\n [124, 29, 26, 43, 118, -75, -66]... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-88, -48, -32, -32, 8, -24, 24],\n [-33, -18, -12, -12, 3, -9, 9],\n [-33, -18, -12, -12, 3, -9, 9],\n [-11, -6, -4, -4, 1, -3, 3],\n [22, 12, 8, 8, -2, 6, -6],\n [-66, -36, -24, -24, 6, -18, 18],\n [22, 12, 8, 8, -2, 6, -6]]\n\nPresent the answer in LaT... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-121, -99, 110, -77, 99, -99, 55],\n [-55, -45, 50, -35, 45, -45, 25],\n [132, 108, -120, 84, -108, 108, -60],\n [-121, -99, 110, -77, 99, -99, 55],\n [121, 99, -110, 77, -99, 99, -55],\n [-77, -63, 70, -49, 63, -63, 35],\n [99, 81, -90, 63, -81, 81, -45... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[88, 20, -96, -58, -82, 8, -46],\n [0, -100, -40, -10, -10, 120, -110],\n [-66, 40, 94, 49, 67, -72, 95],\n [22, -10, -30, -16, -22, 20, -28],\n [-88, -150, 44, 45, 69, 148, -97],\n [-99, -25, 107, 65, 92, -6, 49],\n [-99, -95, 79, 58, 85, 78, -28]]\n\... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[108, -12, -84, 72, -108, -132, -24],\n [90, -10, -70, 60, -90, -110, -20],\n [-81, 9, 63, -54, 81, 99, 18],\n [-99, 11, 77, -66, 99, 121, 22],\n [-18, 2, 14, -12, 18, 22, 4],\n [72, -8, -56, 48, -72, -88, -16],\n [72, -8, -56, 48, -72, -88, -16]]\n\nPres... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[5, -76, 49, -12, -32, -8, 33],\n [-129, -43, -33, 104, -44, 79, 3],\n [-188, -121, -272, 42, 130, -121, 35],\n [62, 55, -60, 16, 16, 23, 40],\n [-211, 61, -96, 202, -50, 176, -50],\n [-58, -176, 8, -72, 32, -134, 22],\n [-91, -70, 42, 110, -102, 121, ... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-168, 76, -37, -1, 87, 87, -78],\n [-77, 104, -23, 19, 216, 35, 100],\n [-3, 48, 211, -223, -33, 105, -72],\n [-98, 1, -162, 245, 106, 55, -76],\n [12, -83, -9, -14, -20, -192, -106],\n [95, -128, -165, 153, -30, -253, 0],\n [202, -184, -67, 69, -290, -138, -48]]... | 6 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[135, 100, 164, -167, -95, -25, 109],\n [7, 67, 60, -114, -33, 54, -32],\n [-68, 209, 87, -119, -348, 23, 215],\n [22, 7, 32, -45, 4, 33, 4],\n [-155, -151, -192, 238, 57, 62, 17],\n [73, -21, -4, 104, -31, -180, 115],\n [19, 50, 29, 13, -125, -73, 137]]... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[27, 33, -6, -33, 0, 9, -12],\n [9, 11, -2, -11, 0, 3, -4],\n [-72, -88, 16, 88, 0, -24, 32],\n [90, 110, -20, -110, 0, 30, -40],\n [54, 66, -12, -66, 0, 18, -24],\n [-81, -99, 18, 99, 0, -27, 36],\n [99, 121, -22, -121, 0, 33, -44]]\n\nPresent the answer in LaTex fo... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[15, 21, 30, -33, -15, -9, -9],\n [-30, -42, -60, 66, 30, 18, 18],\n [15, 21, 30, -33, -15, -9, -9],\n [0, 0, 0, 0, 0, 0, 0],\n [-40, -56, -80, 88, 40, 24, 24],\n [10, 14, 20, -22, -10, -6, -6],\n [-30, -42, -60, 66, 30, 18, 18]]\n\nPresent the answer in ... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[42, -16, 52, 38, 14, -60, -18],\n [-87, 37, -46, -71, -29, 51, -36],\n [-18, 9, 12, -12, -6, -15, -33],\n [-57, 23, -50, -49, -19, 57, 0],\n [-33, 16, 14, -23, -11, -18, -51],\n [15, -6, 14, 13, 5, -16, -1],\n [57, -25, 18, 45, 19, -19, 38]]\n\nPresen... | 2 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[13, 251, -268, 21, 116, 179, -142],\n [-66, 102, 64, 2, 26, 20, -89],\n [25, 71, 25, -56, -73, -53, -78],\n [-13, -86, 234, 50, 21, 132, 2],\n [-7, 199, -163, 148, 59, 161, -84],\n [83, 2, -114, 14, 99, 232, -11],\n [28, -30, -30, -40, -50, -85, 26]]\n\... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-219, 24, 138, -40, -224, -272, 48],\n [212, 78, 18, 58, 36, -3, 70],\n [174, 176, 182, -75, -15, -34, -131],\n [75, 43, 119, -208, 28, 63, -298],\n [172, -125, -143, 48, 80, 37, 126],\n [17, -18, 64, -80, -150, -209, 28],\n [-59, -110, 24, -163, -54, -63, -125]]... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0, 0, 0, 0],\n [66, -55, 11, -77, 132, -66, 11],\n [0, 0, 0, 0, 0, 0, 0],\n [48, -40, 8, -56, 96, -48, 8],\n [48, -40, 8, -56, 96, -48, 8],\n [-48, 40, -8, 56, -96, 48, -8],\n [-66, 55, -11, 77, -132, 66, -11]]\n\nPresent the answer in LaTex for... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[96, -41, 96, 37, 13, 8, 19],\n [15, -102, 84, 87, -3, -39, -84],\n [-126, -21, -72, 15, -21, -42, -93],\n [142, -8, 104, 10, 22, 34, 76],\n [209, -38, 172, 37, 31, 39, 88],\n [12, -55, 48, 47, -1, -20, -43],\n [22, -123, 104, 105, -3, -46, -99]]\n\nPrese... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-8, 88, 8, -96, -32, -32, 56],\n [-5, 55, 5, -60, -20, -20, 35],\n [8, -88, -8, 96, 32, 32, -56],\n [-3, 33, 3, -36, -12, -12, 21],\n [4, -44, -4, 48, 16, 16, -28],\n [-9, 99, 9, -108, -36, -36, 63],\n [10, -110, -10, 120, 40, 40, -70]]\n\nPresent the answer in LaTe... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-35, -20, 50, 30, 50, -20, -50],\n [-7, 10, -18, -26, -6, 6, 16],\n [7, -17, 32, 42, 14, -11, -29],\n [105, 18, -66, 6, -102, 30, 72],\n [-56, -11, 38, 0, 56, -17, -41],\n [70, 54, -128, -92, -116, 50, 126],\n [49, 63, -140, -122, -110, 53, 135]]?\n\nPresent the ... | 2 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[17, -9, 63, 58, -296, 176, 178],\n [124, 137, 118, -105, 67, -155, -32],\n [-133, -206, -108, 49, -76, 36, 122],\n [-27, -89, 21, 229, -163, 34, 266],\n [-55, -202, 3, -65, -276, -42, 332],\n [30, 94, -95, 98, 170, 22, -94],\n [-18, 5, -8, 208, -4, 3, 1... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-125, 237, -52, -201, 151, 180, 65],\n [51, 0, 47, 112, -40, -35, -6],\n [110, -86, 163, -148, -163, -122, 236],\n [-81, -19, 16, 255, -17, 88, -271],\n [138, -255, 197, 92, -265, -187, 52],\n [-4, -131, -66, 105, -8, -43, -139],\n [101, -256, 142, 162, -223, -155, ... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[3, -10, 2, 0, -2, 1, -6],\n [-9, 30, -6, 0, 6, -3, 18],\n [21, -70, 14, 0, -14, 7, -42],\n [-9, 30, -6, 0, 6, -3, 18],\n [6, -20, 4, 0, -4, 2, -12],\n [-15, 50, -10, 0, 10, -5, 30],\n [-6, 20, -4, 0, 4, -2, 12]]?\n\nPresent the answer in LaTex format: \\boxed{You... | 1 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-14, 16, -18, 127, 2, -13, 22],\n [70, -147, -61, -54, 40, 6, -46],\n [-20, -162, 12, -220, -112, 98, -178],\n [80, 4, -9, -106, 76, -25, 23],\n [106, 40, -46, 131, 122, -41, 62],\n [-6, -52, -18, 3, 18, -17, 30],\n [-65, 210, 14, 81, 87, -178, 271]]\n\... | 5 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[12, 42, 42, -12, 60, -54, -72],\n [-22, -77, -77, 22, -110, 99, 132],\n [-12, -42, -42, 12, -60, 54, 72],\n [6, 21, 21, -6, 30, -27, -36],\n [-12, -42, -42, 12, -60, 54, 72],\n [4, 14, 14, -4, 20, -18, -24],\n [20, 70, 70, -20, 100, -90, -120]]\n\nPrese... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[47, -133, 17, 64, 324, 68, 96],\n [-106, 5, 3, 38, -186, 64, -56],\n [-104, 84, -166, 140, 133, 100, 132],\n [62, -29, 107, -146, -209, -130, -96],\n [137, -227, 145, 5, 238, 34, -50],\n [90, 123, 17, -157, -199, -183, -72],\n [-27, -50, -18, 62, 130,... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[30, 178, 66, 28, -82, -162, 164],\n [59, -9, -190, 147, 20, 31, -92],\n [312, -26, 102, 251, -17, 58, -22],\n [178, 51, 91, -33, -101, 24, 41],\n [-60, -166, -138, -177, 138, 31, -47],\n [-104, 154, -148, -63, 5, -230, 148],\n [19, 332, -91, -1, -231,... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, 96, 66, 36, -45, 78, -60],\n [-111, 144, 60, 36, -19, 139, -131],\n [44, 22, -34, -54, 39, -2, -178],\n [56, 118, 104, 54, -84, 82, -52],\n [11, -161, -130, -81, 96, -134, 47],\n [49, -209, -146, -89, 98, -180, 101],\n [73, 116, 124, 72, -107, 79, -3]]?\n\nPr... | 3 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-35, 56, -21, 14, -77, 42, -7],\n [55, -88, 33, -22, 121, -66, 11],\n [-15, 24, -9, 6, -33, 18, -3],\n [40, -64, 24, -16, 88, -48, 8],\n [-50, 80, -30, 20, -110, 60, -10],\n [45, -72, 27, -18, 99, -54, 9],\n [60, -96, 36, -24, 132, -72, 12]]\n\nPresent ... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[46, 27, 18, 49, 13, -34, 39],\n [-39, -189, 17, -41, -49, 137, -23],\n [46, 149, 26, 55, 75, -130, 17],\n [-68, -219, 52, -63, -13, 144, -67],\n [31, 49, -147, 2, -149, 37, 95],\n [-23, -137, 169, 7, 131, 17, -83],\n [70, 176, -44, 65, 2, -116, 72]]\n... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-23, -8, 67, -49, 18, 58, 74],\n [-206, 211, -222, 166, -107, 86, 195],\n [17, -59, 131, 94, 124, -46, -37],\n [74, -146, 239, -258, 98, -76, -160],\n [100, -43, 194, -45, 42, 252, 109],\n [-35, -73, 52, 6, 92, -197, -75],\n [267, -171, -4, -135, -61, 19, -25]]?\... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[77, -12, 121, 45, 53, 95, -52],\n [-77, -30, -65, -59, 10, -32, 17],\n [-110, -102, -14, -104, 103, 43, -25],\n [-22, -36, 18, -26, 44, 32, -18],\n [11, -42, 71, -7, 68, 74, -41],\n [99, -12, 151, 59, 63, 117, -64],\n [-55, 6, -83, -33, -34, -64, 35]]\n\nPresent the... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-55, -15, -28, 37, 72, -44, 74],\n [-146, 151, 340, 36, -197, -53, -109],\n [132, -40, 242, 60, -50, -74, -40],\n [-114, 97, -218, -286, 68, 253, -55],\n [39, -52, -81, 39, 59, -28, 55],\n [-47, 49, -229, -217, 76, 201, -28],\n [73, 55, 86, 118, -122, -6... | 5 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-45, -36, 90, 18, -36, 45, -99],\n [50, 40, -100, -20, 40, -50, 110],\n [-40, -32, 80, 16, -32, 40, -88],\n [40, 32, -80, -16, 32, -40, 88],\n [20, 16, -40, -8, 16, -20, 44],\n [25, 20, -50, -10, 20, -25, 55],\n [-40, -32, 80, 16, -32, 40, -88]]\n\nPres... | 1 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[54, 210, 49, -26, 98, 160, -14],\n [-13, 84, 70, -147, 186, -42, 68],\n [3, 93, 56, -38, 53, 37, 31],\n [6, -57, -32, 83, -112, 60, -11],\n [48, -72, 25, 132, -19, -37, 76],\n [-6, -141, -17, 46, -31, -76, 53],\n [53, -57, -65, 133, -77, 48, -47]]\n\nPr... | 5 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[17, -8, 73, -16, 181, -62, -61],\n [81, 174, 9, 151, -72, -21, 132],\n [326, 276, 182, 52, -294, -128, 164],\n [-49, -122, 19, 157, 106, -29, 92],\n [90, -78, 124, 53, 7, -161, 42],\n [2, 157, -87, -34, -117, 57, -14],\n [54, -167, 101, 57, -50, -114, 7... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[60, 12, 24, 132, 132, -132, 132],\n [35, 7, 14, 77, 77, -77, 77],\n [30, 6, 12, 66, 66, -66, 66],\n [-40, -8, -16, -88, -88, 88, -88],\n [35, 7, 14, 77, 77, -77, 77],\n [-55, -11, -22, -121, -121, 121, -121],\n [60, 12, 24, 132, 132, -132, 132]]?\n\nPresent the a... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[16, -130, -97, -40, 185, -21, 108],\n [-6, 103, -239, 9, 100, 170, -21],\n [-45, 76, -201, 4, 118, 126, -8],\n [-17, 20, 150, -26, -121, -43, 89],\n [-113, -63, -115, -27, 217, -11, 74],\n [-103, -98, 2, -36, 151, -79, 101],\n [-148, 15, 35, -7, 50, -44, 24]]\n\nPre... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-45, 57, 7, 80, 25, -256, -140],\n [-314, 164, 41, 159, 122, -70, -122],\n [-103, 66, 3, -28, -14, 56, 47],\n [-4, 225, -122, 189, -127, 158, 16],\n [98, -60, -82, -64, 66, -56, 128],\n [8, -123, 43, -78, 36, 136, 51],\n [25, -244, 69, -15, 196, 150, 10]]?\n\nPre... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-140, 36, 130, 59, 4, 86, 0],\n [-22, 24, -12, 14, -28, 33, 4],\n [124, -66, -36, -47, 61, -93, 14],\n [-4, 20, -44, -4, -38, 8, -12],\n [-8, 30, -28, 21, -35, 49, 22],\n [6, 36, -44, 28, -42, 65, 40],\n [-94, 32, -44, -46, -80, -55, -132]]\n\nPresent th... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[36, 95, -38, -87, 103, -76, 83],\n [189, 120, -123, -177, 16, -134, 166],\n [150, -16, -123, 45, 41, -37, -3],\n [-60, 20, 85, 122, -73, 113, -114],\n [-91, -40, -18, 77, 158, 50, 16],\n [33, -151, -102, 169, 53, 90, -24],\n [76, 57, -78, -9, 48, -91, -103]]\n\nPres... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[83, 71, 134, -8, 96, -83, 85],\n [-20, -22, -74, -56, -80, 53, 19],\n [-94, -16, -205, -71, -198, 88, -20],\n [78, -42, 126, 2, 116, -4, 40],\n [-35, 35, -2, 74, 20, -48, -66],\n [-128, -188, -161, 83, -66, 149, -205],\n [-111, -183, -168, 34, -92, 163, -157]]\n\nPr... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[41, 83, -73, -4, 70, -19, 60],\n [-24, -51, 10, -52, 1, -49, -98],\n [-122, 37, -104, 52, 35, 7, 18],\n [-81, -84, 95, 82, -121, 94, 8],\n [3, 11, -67, -85, 79, -98, -89],\n [-165, -102, -29, -43, -8, -67, -185],\n [-130, -47, -4, 57, -48, 38, -25]]\n... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[20, 209, -125, -24, 25, -96, -70],\n [97, -75, 98, -49, -155, -33, -86],\n [-65, -129, 99, 149, -70, 77, -122],\n [19, -99, 88, -85, -13, 23, 80],\n [-190, 31, 68, 131, -181, -125, -113],\n [23, -201, 132, 7, -4, 134, 49],\n [135, -16, -26, -85, 40, 44, 77]]\n\nPres... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-162, 221, -65, -163, 26, -255, 33],\n [60, 88, 138, -21, 161, 31, -75],\n [-113, -63, -155, -16, 55, 47, 202],\n [-68, -32, 125, -4, 142, 126, 77],\n [11, 147, 62, -92, -25, -47, -73],\n [101, 1, 68, 18, -81, 59, -100],\n [13, -64, 46, 21, -49, 120, 17]... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-18, 33, -30, 18, 21, -3, 18],\n [-28, 54, -84, -20, 38, -18, 108],\n [2, -5, 22, 22, -5, 7, -42],\n [-18, 32, -16, 36, 19, 2, -12],\n [-28, 49, -14, 70, 28, 7, -42],\n [-44, 76, -8, 128, 42, 16, -96],\n [-28, 50, -28, 52, 30, 2, -12]]\n\nPresent the answer in LaTex... | 2 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[14, 35, 29, -34, -3, 18, -4],\n [35, 40, 3, -97, -80, -33, 30],\n [-21, -5, 8, 45, 47, -21, -4],\n [-11, 58, 70, 16, 79, -3, -15],\n [-46, -172, -124, 152, 14, 66, -30],\n [8, -37, -58, -25, -74, -48, 31],\n [-40, -43, -13, 98, 73, -12, -14]]\n\nPresent... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-38, -1, 85, -34, 41, -41, 104],\n [36, -29, -88, -75, -137, -44, -70],\n [-48, 5, -7, -130, -139, -87, -46],\n [-99, 54, 11, -98, -117, -52, -115],\n [-33, 30, 18, 21, 21, 21, -33],\n [129, -62, -140, 37, -53, 33, -47],\n [137, -93, -56, 36, 36, 5, 1... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-232, -203, -299, -147, -204, 233, -158],\n [4, -77, -64, -136, -140, 269, 14],\n [-73, -41, 32, -184, -54, 29, -121],\n [-203, -39, -200, 24, 38, -149, -155],\n [174, -132, 195, 291, 96, -242, 131],\n [-31, 180, 169, -176, -22, -50, 9],\n [192, 61, 170, -8, -76,... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[64, -44, -154, 187, 80, -70, -95],\n [139, -204, 309, -126, -99, -52, 50],\n [45, -81, -123, 61, 74, 35, 14],\n [77, -77, 28, -54, 70, 7, 28],\n [6, 0, 153, -98, -90, 26, 41],\n [220, -106, -256, -22, -84, -158, 162],\n [139, -108, -144, -29, 34, -28, 100]]?\n\nP... | 6 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-51, 291, 139, 109, -66, 335, 198],\n [98, 71, -75, 203, 160, 18, -150],\n [119, -96, -98, 74, 46, -135, 20],\n [221, 12, 223, 18, -53, 224, 37],\n [-8, -137, 141, -97, -84, 90, 79],\n [-196, -78, -208, 17, 33, -162, 41],\n [81, -23, -119, 184, 191, -... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-24, -60, 108, -144, -132, 84, -108],\n [29, -130, 36, -141, -25, 38, 27],\n [-66, 60, 112, -46, -158, 76, -182],\n [30, 30, -98, 110, 124, -74, 112],\n [-40, 80, 32, 40, -56, 16, -88],\n [2, -40, 28, -58, -30, 24, -14],\n [-55, 20, 118, -85, -159, 84, -167]]\n\nPre... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-76, 134, 381, -212, 280, 367, -255],\n [73, -14, 133, 74, 36, -114, 58],\n [-24, 213, -161, -112, 155, 33, 171],\n [91, -119, 239, 64, -103, -114, -224],\n [43, 131, 41, 72, -17, -92, -66],\n [49, 17, 121, 20, -97, 54, 83],\n [-125, 10, 78, -133, 194, 233, -220]... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[6, 10, -18, -10, -18, -6, 14],\n [-36, -60, 108, 60, 108, 36, -84],\n [-15, -25, 45, 25, 45, 15, -35],\n [30, 50, -90, -50, -90, -30, 70],\n [-27, -45, 81, 45, 81, 27, -63],\n [27, 45, -81, -45, -81, -27, 63],\n [-9, -15, 27, 15, 27, 9, -21]]\n\nPresent ... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-30, 90, 84, 42, 27, 84, -36],\n [0, 10, 26, 18, 43, 36, 16],\n [38, -120, -122, -64, -60, -128, 36],\n [-36, 110, 106, 54, 41, 108, -40],\n [24, -100, -140, -84, -142, -168, -16],\n [6, 10, 56, 42, 115, 84, 52],\n [13, -40, -39, -20, -16, -40, 14]]\n\nPresent the a... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[32, 123, 44, 103, 114, -27, -26],\n [28, 17, -24, 37, 106, -133, 46],\n [-18, -71, -26, -59, -64, 13, 16],\n [8, 9, -4, 13, 30, -33, 10],\n [26, 51, 2, 55, 96, -81, 16],\n [-21, 38, 53, 2, -83, 161, -73],\n [-19, 4, 27, -16, -73, 109, -43]]\n\nPresent the answer in ... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[34, -74, -42, -10, 16, 28, -38],\n [13, 17, -51, -75, -12, -10, 45],\n [-42, -2, 54, 6, 88, 132, -122],\n [-29, -15, 48, 26, 66, 97, -102],\n [-207, 217, 261, 45, 172, 246, -191],\n [-87, 82, 81, -45, 112, 171, -116],\n [22, -34, -51, -57, 18, 35, -15]]\... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[1, -61, 29, 131, 117, -25, 63],\n [97, -12, 3, 17, 107, 90, -41],\n [-22, 25, 92, 87, -124, -194, 157],\n [-118, 11, 67, 50, -117, -202, 114],\n [100, -3, -12, -62, -70, 35, 99],\n [106, 108, 55, -162, -191, -37, 13],\n [-99, -28, -15, -24, 115, 29, -117]]?\n\nPr... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[65, -181, 98, -154, -113, 134, -124],\n [4, 32, 5, 40, -15, 86, -140],\n [-44, -116, -64, 16, -70, -32, 124],\n [-112, -100, -136, 138, -70, 26, 70],\n [-98, 28, -189, 209, -17, 13, 55],\n [-44, 124, -101, 158, 38, 10, -34],\n [55, -79, 169, -186, -69, -157, 105]... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-24, 30, -12, 37, -27, 22, -15],\n [89, 65, 224, -21, 184, -103, 225],\n [75, -64, -106, -62, -116, 21, -167],\n [43, -101, -80, -87, -40, -5, -93],\n [-190, 45, -102, 129, -72, 96, -40],\n [35, 50, 194, -8, 184, -87, 225],\n [-32, -17, -14, 0, 11, 4, 9]]\n\nPresent... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-84, -251, -63, -33, 258, -95, 303],\n [-93, 16, -217, 33, -4, -1, -40],\n [169, -95, 198, -62, -98, -165, -127],\n [-239, 169, -117, 40, 75, 263, 45],\n [-140, -54, -54, -77, 131, 52, -15],\n [-18, -121, -173, -84, 75, -38, -58],\n [-17, -14, -81, 25... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[20, 35, 116, -31, 118, -188, -35],\n [48, -136, -88, -180, 12, 116, 72],\n [33, -27, 68, -100, 112, -108, 0],\n [14, -9, -124, 31, -142, 92, 19],\n [15, -29, 2, -53, 29, -5, 12],\n [-10, -101, 58, -142, 151, 75, 43],\n [-34, -94, 78, -117, 165, 103, 40]]... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-42, 18, -30, 60, 0, 0, 18],\n [-77, 33, -55, 110, 0, 0, 33],\n [-7, 3, -5, 10, 0, 0, 3],\n [77, -33, 55, -110, 0, 0, -33],\n [28, -12, 20, -40, 0, 0, -12],\n [77, -33, 55, -110, 0, 0, -33],\n [-56, 24, -40, 80, 0, 0, 24]]\n\nPresent the answer in LaTex ... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[52, -33, 103, -115, 24, -58, -22],\n [-42, -52, -148, 30, 36, 38, -48],\n [-56, -15, -66, 50, 65, -12, 31],\n [26, 101, 209, 13, -32, -64, 122],\n [47, 6, -5, -26, -85, 53, -63],\n [-119, 83, -35, 194, 64, -21, 168],\n [91, -88, 17, -172, -25, 5, -143]]\n\nPresent t... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[54, -7, 26, -132, -48, 13, 76],\n [81, 90, -245, -32, -50, 60, -235],\n [45, 47, -109, -60, -57, 49, -95],\n [-122, -72, 230, 72, 27, -28, 188],\n [8, 72, -140, -24, -87, 88, -158],\n [3, 34, -103, 64, 16, 8, -125],\n [109, -39, 11, -84, 69, -85, 89]]?\n\nPresent... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-166, -79, 64, 83, 123, 109, 21],\n [-135, 67, 17, 155, 50, 64, 93],\n [109, 174, -116, 101, -106, 62, -25],\n [-6, 195, -68, 129, -45, 141, -24],\n [187, 217, -161, 61, -146, 144, -139],\n [-190, -80, 130, 0, 104, -116, 161],\n [32, 78, -33, 49, -53, -65, 70]]?\... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[167, 56, -111, 5, -71, 170, -48],\n [6, 16, -130, -184, 115, 112, 171],\n [-72, 99, 67, -32, 286, -76, -18],\n [-31, 11, -42, -169, 151, 20, 168],\n [128, 30, -34, -96, 4, 80, 84],\n [-42, 93, -33, -6, 204, 24, -54],\n [76, 97, -17, 64, 68, 59, -126]]\n\... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[0, 128, 142, 36, 66, 108, 70],\n [35, 1, -76, 67, -58, -79, -35],\n [-6, 62, 82, 6, 42, 66, 40],\n [66, 22, -121, 132, -99, -132, -55],\n [-54, -146, -43, -144, 15, 0, -25],\n [81, 123, -42, 189, -72, -81, -15],\n [-63, 11, 151, -117, 111, 153, 70]]?\n\nPresent t... | 2 | MATH |
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