messages listlengths 1 1 | ground_truth stringclasses 6 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the rank of the matrix:\n[[-25, -8, 28, -25, 105, -140, 182],\n [-3, -93, -9, -25, 134, -227, 153],\n [-143, -177, 178, -89, -261, 33, -98],\n [-96, 4, 45, -134, -162, 124, -65],\n [-107, -240, 71, 3, -208, 24, -197],\n [2, -123, 12, 7, -38, -31, -84],\n [110, -32, 177, -245, -74, -267, 104]]... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[20, 80, 110, 120, 0, -40, 20],\n [24, 96, 132, 144, 0, -48, 24],\n [-10, -40, -55, -60, 0, 20, -10],\n [16, 64, 88, 96, 0, -32, 16],\n [6, 24, 33, 36, 0, -12, 6],\n [0, 0, 0, 0, 0, 0, 0],\n [10, 40, 55, 60, 0, -20, 10]]\n\nPresent the answer in LaTex for... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[72, 48, 60, 12, 132, 144, -36],\n [-84, -96, -114, -90, 30, 0, -66],\n [-26, -4, -7, 21, -109, -108, 49],\n [126, 124, 149, 97, 47, 84, 45],\n [-16, 6, 5, 29, -106, -102, 53],\n [-16, -4, -6, 10, -60, -60, 26],\n [-10, -20, -23, -27, 43, 36, -31]]\n\n... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-80, -100, -110, 100, 70, -120, 0],\n [-126, -148, -64, 110, -37, -18, -76],\n [98, 118, 83, -100, -16, 66, 36],\n [68, 78, 13, -50, 49, -24, 56],\n [76, 96, 116, -100, -82, 132, -8],\n [84, 104, 104, -100, -58, 108, 8],\n [-18, -22, -19, 20, 8, -18, -4]]\n\nPresent... | 2 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-119, 147, 25, -54, -81, -27, 227],\n [8, 104, -16, -79, 4, -16, 115],\n [-213, 263, -51, -81, 361, -99, 382],\n [-76, 84, 87, -185, -69, -111, 64],\n [-108, 324, -150, -90, 516, -90, 408],\n [167, -106, -124, 190, 44, 186, -76],\n [29, -100, -208, -54,... | 6 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[44, 77, -33, 110, -77, 99, -66],\n [28, 49, -21, 70, -49, 63, -42],\n [-36, -63, 27, -90, 63, -81, 54],\n [8, 14, -6, 20, -14, 18, -12],\n [-12, -21, 9, -30, 21, -27, 18],\n [-12, -21, 9, -30, 21, -27, 18],\n [48, 84, -36, 120, -84, 108, -72]]\n\nPresen... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[177, 56, 205, -153, 128, 116, 47],\n [-118, 111, -175, -9, 18, -135, -106],\n [89, 207, 68, -229, 189, 23, -14],\n [161, -127, 159, -21, 18, 203, 128],\n [-84, 73, -169, 18, 19, -131, -149],\n [84, -208, 82, 133, -85, 90, 21],\n [-229, 58, -212, 87, -99, -176, -43]]... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[100, -30, 40, 90, 120, 90, 120],\n [-120, 36, -48, -108, -144, -108, -144],\n [-50, 15, -20, -45, -60, -45, -60],\n [-10, 3, -4, -9, -12, -9, -12],\n [-50, 15, -20, -45, -60, -45, -60],\n [110, -33, 44, 99, 132, 99, 132],\n [-90, 27, -36, -81, -108, -81, -108]]\n\nP... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[82, -31, -87, 57, -103, 16, -90],\n [93, -8, -74, 35, -105, 14, -66],\n [65, 124, 66, -117, -17, -10, 126],\n [-150, -4, 104, -38, 162, -20, 84],\n [-68, 96, 136, -124, 116, -24, 168],\n [21, 32, 14, -29, -9, -2, 30],\n [141, 9, -93, 30, -150, 18, -72... | 2 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-186, -81, 122, 0, 171, -25, 96],\n [14, 33, -65, 67, 25, 3, -113],\n [-46, 93, 66, -107, 209, 94, -40],\n [-52, 34, 6, -49, 47, 36, 51],\n [-107, 36, -33, 27, 101, 20, -21],\n [-51, -59, -84, 60, -260, -117, 76],\n [119, -207, 106, 203, 139, -47, -61]]... | 5 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-44, -77, 33, 77, -22, -99, 22],\n [40, 70, -30, -70, 20, 90, -20],\n [36, 63, -27, -63, 18, 81, -18],\n [24, 42, -18, -42, 12, 54, -12],\n [48, 84, -36, -84, 24, 108, -24],\n [36, 63, -27, -63, 18, 81, -18],\n [36, 63, -27, -63, 18, 81, -18]]\n\nPresen... | 1 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-152, -8, -188, -96, -120, 56, -72],\n [-2, 57, 53, 33, 80, -89, 79],\n [-16, 1, -18, -9, -10, 3, -5],\n [-116, 16, -122, -60, -60, 8, -24],\n [-132, 17, -140, -69, -70, 11, -29],\n [42, 28, 77, 42, 70, -56, 56],\n [-40, -50, -96, -54, -100, 90, -86]]\n... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-126, 59, -97, 130, 51, -21, -57],\n [113, -132, 6, -77, 94, 218, 221],\n [72, -39, 228, -160, -32, -240, 96],\n [-105, 78, -80, 81, 12, 36, -175],\n [84, -3, -127, 80, -131, 45, 43],\n [89, 4, -93, 38, -136, 59, -15],\n [208, -19, 136, -147, -253, -1... | 4 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-193, 45, -121, -103, 59, -3, 122],\n [-209, -78, 83, -241, 125, 33, 181],\n [47, 81, -24, 98, -301, 85, -140],\n [-66, 4, 138, -106, -214, 172, 10],\n [212, -5, 14, 206, -190, -51, -239],\n [12, -36, 48, -10, -28, -5, -28],\n [110, 25, 103, 41, -100, 1... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-186, -90, -30, -144, 14, 183, 40],\n [8, 57, -22, -34, 44, 19, 29],\n [44, 143, -34, -38, 48, -9, 67],\n [32, 35, 26, 58, -108, -87, 19],\n [32, 84, 26, 56, -156, -110, 58],\n [-80, -106, 16, -12, -48, 46, -22],\n [38, 84, 2, 20, -50, -59, 42]]\n\nPresent the answe... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-103, -148, 99, -31, 4, 11, -18],\n [-55, -44, 107, -7, -52, 103, 70],\n [-74, -120, 50, -26, 24, -30, -44],\n [-36, -78, -6, -18, 42, -69, -66],\n [48, 60, -60, 12, 12, -30, -12],\n [-61, -68, 89, -13, -28, 61, 34],\n [47, 56, -63, 11, 16, -37, -18]]?\n\nPresent... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-44, 16, 13, 36, 59, 59, -6],\n [74, -22, 25, -8, -57, -77, -2],\n [67, 91, 157, 62, 107, -19, 26],\n [10, 124, 33, -72, 67, -13, 72],\n [-111, 33, 27, 90, 141, 147, -18],\n [-74, -59, -121, -40, -57, 41, -19],\n [18, 126, -30, -156, 6, -54, 96]]\n\nPres... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[136, 144, -4, -88, -124, -104, 76],\n [185, 228, 31, -74, -152, -76, 83],\n [-157, -180, -11, 82, 136, 92, -79],\n [23, -20, -51, -78, -44, -108, 41],\n [-9, -8, 2, 8, 9, 10, -6],\n [14, 24, 10, 4, -8, 8, 2],\n [93, 100, -1, -58, -84, -68, 51]]\n\nPre... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[74, -168, -52, 30, -82, 24, 76],\n [37, 70, -23, -141, 188, 16, -147],\n [-225, -28, 118, 45, -39, 36, 142],\n [32, 29, -14, 0, 3, -14, -29],\n [145, -15, -82, -69, 68, -2, -101],\n [-217, 40, 121, 57, -40, 12, 111],\n [133, 3, -68, 15, -32, -30, -49]]\n\nPresent th... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-121, 132, -99, 132, -55, -22, -44],\n [-33, 36, -27, 36, -15, -6, -12],\n [121, -132, 99, -132, 55, 22, 44],\n [55, -60, 45, -60, 25, 10, 20],\n [0, 0, 0, 0, 0, 0, 0],\n [-88, 96, -72, 96, -40, -16, -32],\n [110, -120, 90, -120, 50, 20, 40]]?\n\nPresent the answ... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[22, 8, 20, 24, -16, -6, -20],\n [-88, -32, -80, -96, 64, 24, 80],\n [-132, -48, -120, -144, 96, 36, 120],\n [-99, -36, -90, -108, 72, 27, 90],\n [-44, -16, -40, -48, 32, 12, 40],\n [0, 0, 0, 0, 0, 0, 0],\n [132, 48, 120, 144, -96, -36, -120]]\n\nPresent ... | 1 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-12, 72, -53, 128, 72, -101, 65],\n [45, 162, 59, 43, -15, -10, 13],\n [-42, 36, -254, 2, 186, -236, -70],\n [43, 84, -11, -165, -16, 4, -140],\n [-34, -84, -3, 86, 10, 3, 79],\n [-1, 42, -119, -83, 73, -98, -99],\n [54, 0, 177, -126, -152, 187, -47]]\n... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[18, 27, 18, 125, -80, -58, -71],\n [-48, -14, 96, 182, -36, -156, -94],\n [-48, -59, 62, 88, 51, -89, -33],\n [57, -94, -73, 43, 86, 71, 7],\n [-189, 69, 223, -3, -41, -242, -30],\n [-108, 105, 106, -144, -53, -77, 39],\n [-15, -58, 65, 242, -11, -138, -111]]\n\nPre... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-151, -36, 73, -15, 192, 154, 85],\n [176, 176, -40, 106, -256, -68, 66],\n [-20, -116, 126, 54, 92, 190, 41],\n [-133, -32, 62, 158, -39, 184, 76],\n [0, -50, 176, 239, -121, -91, 64],\n [8, -244, 112, 49, 8, -87, -46],\n [24, -76, -79, -166, 85, 17, 5]]?\n\nPre... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-183, 171, 13, -85, 156, 297, 68],\n [47, 103, -213, 153, 46, 107, 70],\n [-39, 142, -216, 120, 75, 77, -23],\n [-7, -294, 327, -265, 115, 11, 31],\n [4, -24, 14, -18, 82, 116, 70],\n [-33, -190, 306, -270, 31, 19, 69],\n [-98, 18, 132, -152, 46, 118, 58]]\n\nPresen... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-99, -29, 206, -91, -124, 210, 130],\n [90, -44, 85, -34, -144, 192, -199],\n [-45, 17, -16, 7, 55, -63, 108],\n [71, 111, -39, 71, 110, -80, 22],\n [-71, -157, -152, -31, -26, -124, -76],\n [51, 19, 181, -37, -74, 216, 64],\n [123, -47, -178, 59, 95, -147, -77]]\n\... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[43, -129, 51, 220, -179, -11, -8],\n [-158, 61, -38, 20, -33, 33, -49],\n [215, -30, -84, 149, -16, -151, 17],\n [79, 208, -149, 160, 91, -267, -183],\n [169, -12, -66, 128, -27, -141, -18],\n [156, 82, -241, 57, 13, -192, -2],\n [-186, -45, 123, 24, 6, ... | 5 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[168, 119, 236, -189, 108, -95, 265],\n [-83, 222, 147, -230, 186, -137, -66],\n [150, 102, 126, -120, 99, -114, 143],\n [69, 98, 221, -186, 116, -115, 83],\n [-63, 20, -82, -180, -58, 172, 191],\n [71, 110, 266, -94, 150, -118, 27],\n [28, 107, 189, 45,... | 6 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[44, 214, -78, 79, -61, 7, 12],\n [-172, -206, 240, -128, 2, -134, -84],\n [26, 25, 112, 4, -115, 9, 102],\n [148, 39, -100, 62, -23, 131, 136],\n [48, 154, -40, 60, -66, 18, 40],\n [102, 89, -102, 63, -18, 82, 74],\n [-124, -52, 200, -68, -64, -116, -44... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-84, 104, -24, 88, 144, 12, -140],\n [36, 109, 46, 48, 24, 27, -65],\n [93, 63, 68, 2, -60, 24, 10],\n [0, -86, -20, -48, -48, -18, 70],\n [78, 57, 58, 4, -48, 21, 5],\n [-12, 64, 8, 40, 48, 12, -60],\n [117, 64, 82, -6, -84, 27, 25]]\n\nPresent the answer in LaTex ... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-66, 54, 24, 30, -42, 36, -54],\n [-55, 45, 20, 25, -35, 30, -45],\n [132, -108, -48, -60, 84, -72, 108],\n [-11, 9, 4, 5, -7, 6, -9],\n [-66, 54, 24, 30, -42, 36, -54],\n [-22, 18, 8, 10, -14, 12, -18],\n [-55, 45, 20, 25, -35, 30, -45]]\n\nPresent t... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-140, 230, -108, -139, 61, 56, 135],\n [-123, 117, -77, -16, 89, 175, -71],\n [7, -46, -14, -68, -69, -45, 103],\n [-172, 309, -113, -92, 140, 118, 48],\n [124, -176, 94, 107, -53, -76, -87],\n [-110, 301, -57, -24, 158, 52, 2],\n [51, 191, 81, 148, 163, -79, -133]]... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-96, 15, 54, -67, -11, 6, 74],\n [16, 55, -74, 37, -99, -106, 26],\n [6, 81, -96, 41, -143, -150, 50],\n [63, -12, -33, 43, 11, 0, -50],\n [39, -60, 39, 3, 99, 96, -66],\n [-116, -2, 88, -90, 22, 44, 76],\n [-24, 90, -84, 22, -154, -156, 76]]\n\nPresent the answer i... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[38, 132, 60, -146, 73, 78, -147],\n [142, -97, 104, -11, -29, 11, -52],\n [-8, 83, -184, 93, 103, 113, 126],\n [-122, 188, 2, -10, -56, 41, -53],\n [-106, -90, -54, 8, 4, -129, 77],\n [-81, 49, -8, -41, 4, -32, -20],\n [152, -21, 42, -77, 91, 72, -69]]\n... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-219, 172, -226, -23, -63, -20, -141],\n [27, -79, -96, 35, -159, -136, -92],\n [-171, 190, -151, -80, 30, 73, -6],\n [-37, 73, 16, -14, 3, -5, -11],\n [-33, -85, 52, 169, -59, -126, -236],\n [-226, 258, -190, -54, -108, -72, -140],\n [55, 26, 49, -104, ... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[117, 161, -9, -34, 92, 15, -68],\n [-52, -36, 44, -88, 24, -4, 32],\n [75, 95, -15, 2, 44, 9, -44],\n [44, 92, 32, -104, 92, 8, -24],\n [-106, -98, 62, -108, 4, -10, 64],\n [71, 83, -22, 22, 29, 8, -42],\n [-78, -54, 66, -132, 36, -6, 48]]\n\nPresent the... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[51, 38, 92, -118, -72, 53, 42],\n [134, -30, 52, -12, 24, 68, -48],\n [8, 5, 98, -32, -20, 91, 18],\n [65, 40, 56, -122, -72, 15, 36],\n [70, -80, -16, 132, 112, 50, -96],\n [110, -41, -26, 36, 52, 3, -66],\n [-19, -57, 78, 110, 76, 128, -42]]\n\nPres... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[354, -78, -89, 203, -142, 302, -13],\n [72, 14, 51, 2, -22, 174, 103],\n [-143, -94, 47, -167, 196, -394, -163],\n [223, -127, -229, 12, -199, 114, 108],\n [10, -62, 72, 137, -69, 126, -11],\n [-128, 226, 127, 27, 141, -24, -105],\n [-93, -180, -59, -156... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[60, 125, 75, -111, -234, 238, 212],\n [-141, -230, 83, 137, 43, -154, 68],\n [-16, -202, 109, 86, -37, -61, 148],\n [-70, -90, -5, -42, 124, -273, -3],\n [27, -30, -119, 213, 0, 15, -172],\n [155, -125, 214, -108, -72, 41, 222],\n [88, 31, 12, -244, -21, -148, 225]]... | 6 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[112, 280, -47, -23, 112, 14, 47],\n [19, -111, 95, 70, -72, 6, -20],\n [-61, -31, -195, -9, 99, -54, 54],\n [3, -129, -28, 65, -104, 8, -49],\n [-198, -294, 9, 124, 13, -2, -87],\n [5, -106, -7, 132, 31, -20, 12],\n [-136, -232, 68, 18, -26, -20, -24]... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-44, -22, -7, 155, 0, 33, -71],\n [103, 99, 1, 173, -66, -12, 2],\n [-71, -119, -27, -127, 18, 64, -10],\n [-65, 9, 22, -73, 75, -46, 9],\n [-50, 16, 81, -151, 62, -145, 9],\n [-17, -153, 67, -13, 128, -75, -69],\n [-80, -90, -23, 224, -85, 92, -141]]... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[28, 20, -68, -28, 88, 96, 176],\n [70, -54, 38, -70, -204, 32, 40],\n [-3, -17, 37, 3, -70, -40, -76],\n [61, -53, 45, -61, -202, 16, 12],\n [-64, 36, -8, 64, 132, -56, -88],\n [-6, 31, -56, 6, 125, 50, 98],\n [-15, 19, -23, 15, 74, 8, 20]]?\n\nPresent the answer... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-153, 81, 137, -10, -191, -80, -114],\n [103, 86, 83, 81, 100, 126, 28],\n [-13, 43, -45, 118, 18, 33, 12],\n [-93, 13, -111, 78, 23, -29, -49],\n [51, 114, 231, -3, -36, 75, -27],\n [98, -24, 92, -144, 95, 39, -8],\n [77, -36, -41, 11, 45, 34, 73]]\n\nP... | 4 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-25, -183, -49, -193, 38, 238, -142],\n [100, -88, -116, -36, 24, 108, -300],\n [-284, -344, 23, 70, -164, 160, -19],\n [-88, -52, -119, 220, -50, -6, -89],\n [-163, -247, -20, -48, -81, 177, -52],\n [60, -59, -73, 94, -38, 1, -218],\n [159, 110, 44, -3... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-38, 176, 120, 134, 16, 86, 36],\n [79, 77, 27, 14, 58, -58, -99],\n [-132, -66, -6, 18, -84, 114, 162],\n [25, -55, -41, -48, 2, -40, -27],\n [144, -33, -59, -89, 70, -153, -171],\n [-15, 165, 107, 116, 26, 60, 9],\n [-71, -88, -36, -25, -56, 47, 90]]\n... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[70, 0, -35, 35, -56, -14, 84],\n [60, 0, -30, 30, -48, -12, 72],\n [30, 0, -15, 15, -24, -6, 36],\n [-60, 0, 30, -30, 48, 12, -72],\n [-60, 0, 30, -30, 48, 12, -72],\n [-90, 0, 45, -45, 72, 18, -108],\n [10, 0, -5, 5, -8, -2, 12]]\n\nPresent the answe... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-10, -10, 110, -100, 80, 80, 70],\n [-5, -5, 55, -50, 40, 40, 35],\n [-9, -9, 99, -90, 72, 72, 63],\n [3, 3, -33, 30, -24, -24, -21],\n [10, 10, -110, 100, -80, -80, -70],\n [-3, -3, 33, -30, 24, 24, 21],\n [-1, -1, 11, -10, 8, 8, 7]]\n\nPresent the answ... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-21, -88, 140, 111, 19, 136, -2],\n [-104, 42, -291, -153, -58, -82, 35],\n [52, 32, 179, 48, -42, -66, -15],\n [52, -254, 124, 27, 268, 28, -104],\n [142, 204, 6, -6, -46, -74, 14],\n [77, -96, 171, 111, 127, 116, -41],\n [4, -68, -80, -60, 100, -34, -3... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[77, 55, 11, -121, -44, -88, 77],\n [-7, -5, -1, 11, 4, 8, -7],\n [77, 55, 11, -121, -44, -88, 77],\n [14, 10, 2, -22, -8, -16, 14],\n [14, 10, 2, -22, -8, -16, 14],\n [-49, -35, -7, 77, 28, 56, -49],\n [-7, -5, -1, 11, 4, 8, -7]]\n\nPresent the answer... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[155, -18, -263, -62, 111, 92, 73],\n [82, 248, 2, -142, -44, -28, -140],\n [23, 162, -40, -85, -122, -60, 12],\n [42, 54, 20, -263, -38, -43, 35],\n [256, 65, -147, -177, -18, 186, -65],\n [-40, -227, 43, 131, 69, 79, 43],\n [155, -7, -32, -128, -16, 138... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-11, -19, 25, -9, -19, 0, -34],\n [-33, -53, 67, -27, -53, 2, -93],\n [44, 60, -68, 36, 60, -8, 100],\n [-55, 9, -83, -45, 9, 52, 64],\n [44, 56, -60, 36, 56, -10, 91],\n [44, 76, -100, 36, 76, 0, 136],\n [-33, -69, 99, -27, -69, -6, -129]]?\n\nPresent the answer... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[59, 82, 9, 65, -44, 56, 54],\n [2, -128, -108, 76, -24, -8, -182],\n [20, 136, 64, 121, -151, -18, 20],\n [66, -160, -104, 182, -68, -10, -250],\n [-82, 66, 81, -123, 29, -53, 107],\n [52, -196, -298, 78, 50, 142, -222],\n [45, -22, 75, -12, 48, -17, 42]]?\n\nPre... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-36, 120, -153, -62, 137, 13, -27],\n [42, 12, 36, 28, -49, 7, -54],\n [-18, -12, -9, -10, 16, -4, 27],\n [64, 0, 72, 48, -88, 8, -72],\n [4, 120, -108, -32, 82, 18, -72],\n [44, 120, -63, -2, 27, 23, -117],\n [68, 24, 54, 44, -76, 12, -90]]\n\nPresent t... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-27, -12, 82, 14, -27, -33, 70],\n [-63, 78, -3, -38, -10, -24, -31],\n [-18, 84, -114, -52, 28, 24, -122],\n [45, -78, 43, 42, -4, 6, 63],\n [27, 18, -93, -18, 30, 36, -81],\n [-45, 126, -131, -74, 28, 18, -151],\n [-36, 48, -8, -24, -4, -12, -24]]\n... | 2 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[38, -98, -195, 346, 317, -134, 180],\n [188, -213, -45, -6, -67, -99, 108],\n [-103, -73, -80, -16, 209, 4, -21],\n [-44, 121, 63, -246, 11, 108, 34],\n [70, -60, 103, -92, -176, -59, -150],\n [190, -323, -116, 210, -11, -191, 60],\n [81, -280, -188, 27... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[128, -220, -64, 104, -54, -56, 168],\n [92, -244, 22, -54, -170, -146, 22],\n [241, -324, 36, 70, -87, -173, 125],\n [61, -200, -60, 34, -83, -69, 133],\n [89, -24, -180, -60, -211, 80, 132],\n [282, -140, 61, -5, -58, -113, 63],\n [135, 121, 61, -244, -... | 5 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-114, 25, 149, 6, 176, -14, -1],\n [-47, -90, -35, -221, 5, -71, -42],\n [111, -33, 37, 270, 123, 79, 121],\n [17, -214, 109, 174, 97, 129, -48],\n [-110, -98, 86, -166, 7, 30, -187],\n [-131, -207, 32, 74, -113, 241, -283],\n [-72, -158, 195, -54, 290,... | 6 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[42, 5, 86, -226, 92, -26, -138],\n [15, -120, -143, 195, -17, 126, -24],\n [93, 109, -1, -155, -59, -2, -66],\n [-178, -94, 96, 118, 109, 17, -4],\n [45, -32, 23, -113, 63, -27, -54],\n [-185, -163, 57, 171, 137, 102, -86],\n [2, -61, -50, 52, 16, 103, ... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[219, -63, 72, -6, -9, -168, -42],\n [24, -191, -25, 67, 70, -64, -80],\n [-217, -28, -34, 16, 60, 136, -27],\n [-148, -67, 121, -57, 99, 64, -135],\n [-10, -88, 249, 45, 161, -96, -149],\n [215, 27, -40, -46, -103, -104, 48],\n [48, 75, -290, -40, -184, ... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-62, -96, -48, -16, -56, 86, 0],\n [71, 132, 85, 3, 96, -66, -19],\n [-33, -36, -5, -19, -8, 68, -13],\n [5, 60, 75, -35, 80, 70, -45],\n [46, 48, 4, 28, 8, -98, 20],\n [7, 84, 105, -49, 112, 98, -63],\n [-23, -96, -100, 36, -108, -57, 52]]\n\nPresent... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[50, -107, 268, 166, -131, -41, 12],\n [-71, -16, 94, 100, -60, -122, -90],\n [131, -111, -23, -107, 0, -43, -52],\n [-148, 24, 214, 182, -124, -32, 26],\n [-245, 30, 64, -58, -122, -66, -10],\n [-228, 96, -101, -177, -27, 50, 78],\n [-8, 32, -115, 97, 101, -190, ... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-60, -132, 108, 0, 96, 36, -132],\n [-50, -110, 90, 0, 80, 30, -110],\n [-25, -55, 45, 0, 40, 15, -55],\n [15, 33, -27, 0, -24, -9, 33],\n [-40, -88, 72, 0, 64, 24, -88],\n [45, 99, -81, 0, -72, -27, 99],\n [5, 11, -9, 0, -8, -3, 11]]\n\nPresent the answer in LaTex ... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[8, -24, 10, -2, -24, -10, -18],\n [12, -36, 15, -3, -36, -15, -27],\n [-8, 24, -10, 2, 24, 10, 18],\n [-16, 48, -20, 4, 48, 20, 36],\n [20, -60, 25, -5, -60, -25, -45],\n [-20, 60, -25, 5, 60, 25, 45],\n [-40, 120, -50, 10, 120, 50, 90]]\n\nPresent th... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-82, 153, -28, -24, 52, 10, -35],\n [-202, 133, -4, 51, 154, 166, 100],\n [-7, 54, -108, -42, -137, -60, 46],\n [-46, 106, -101, 120, 74, 101, -102],\n [-293, 79, -163, 19, -178, 83, 150],\n [-185, 15, -71, 87, 138, 113, -56],\n [28, 137, -18, -85, -3... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[49, -196, 168, -132, -36, -64, -19],\n [-147, 188, 111, 213, -129, 181, 44],\n [128, -160, 55, 233, -225, 60, 239],\n [-61, 67, -150, 7, 252, 154, -34],\n [-54, 134, -92, 39, -40, -6, 97],\n [-178, 176, 105, -159, 81, 12, -139],\n [135, -91, 93, 42, -141, -77, 25... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-109, 153, 308, -37, 3, 48, 55],\n [135, 0, -312, -72, -170, -24, 74],\n [-31, 47, -15, -88, -149, -84, 79],\n [90, -40, -83, 36, -2, -35, 6],\n [-113, 84, -98, -197, -248, 23, 52],\n [138, 94, -16, -9, -72, 91, 56],\n [69, 165, 165, -21, -76, -42, 160]]\n\nPresent ... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[149, 17, 6, 6, 92, -65, 61],\n [22, -147, 137, -220, -330, 15, -200],\n [57, 112, 7, 44, 52, 42, -25],\n [-9, 144, 66, -66, -72, 114, -99],\n [3, -117, -3, -16, -48, -55, -1],\n [-95, -27, -25, -58, 42, -27, 121],\n [-3, 72, 91, -143, -129, 79, -91]]?\n\nPresent ... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[190, 66, -109, 261, -3, 132, -115],\n [-53, -45, -67, -155, -34, 6, -245],\n [91, -131, -7, 222, 45, 162, 128],\n [-129, 47, 193, -129, -138, -16, 43],\n [57, -59, -146, -22, -17, 192, -216],\n [-59, -179, -27, -92, -19, 115, -128],\n [-53, -127, 12, -86, -31, 17... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[116, -81, 166, 21, 160, -46, 40],\n [-53, -122, -36, -155, -111, 145, 18],\n [41, 138, -84, 123, -44, 38, -52],\n [-115, 116, -222, -43, -243, 89, -78],\n [175, -127, 113, -51, 59, 125, -17],\n [-49, -90, 96, -92, 37, -73, 77],\n [97, 15, 72, 199, 247, -... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[122, -20, -127, 51, -25, -51, 12],\n [164, 69, -181, 56, -107, -134, -127],\n [215, 57, -338, 244, -159, 60, -126],\n [-16, 111, 88, -137, -17, -34, -151],\n [-315, -76, 402, -196, 189, 89, 237],\n [-239, -137, 349, -250, 192, -113, 104],\n [-127, 19, 114, 13, 16, 2... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[286, 310, -279, 83, -38, -94, 16],\n [265, 223, -108, 44, -11, -41, -13],\n [-169, -198, 17, 89, -146, 41, 99],\n [287, 230, -44, 171, 87, -46, 45],\n [-21, 126, 226, -22, 430, -30, -143],\n [-202, -91, -69, -137, -46, -9, -57],\n [14, 97, -24, 170, 139, -50, 42]]\n... | 6 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-9, -296, 21, -22, 76, -246, -34],\n [-128, 78, -52, -145, 223, 73, 157],\n [11, 48, -43, 29, -101, -27, -116],\n [199, -98, -102, 325, -265, -120, -41],\n [-155, -8, 91, -232, 274, 46, 114],\n [-68, -106, -32, -31, 1, -156, -132],\n [-198, 28, 3, -240,... | 6 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[39, 37, -97, -1, 19, 204, 88],\n [44, 99, -143, -11, -11, 286, 121],\n [-34, 4, 60, -12, -36, -84, -42],\n [25, 9, -58, -7, 22, 195, 79],\n [30, -90, -9, 12, 83, 109, 47],\n [-11, -93, 68, -1, 44, -1, -7],\n [16, 92, -75, 6, -39, -15, 3]]\n\nPresent the ... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-14, 63, -28, -28, 77, -56, 28],\n [24, -108, 48, 48, -132, 96, -48],\n [12, -54, 24, 24, -66, 48, -24],\n [-16, 72, -32, -32, 88, -64, 32],\n [-16, 72, -32, -32, 88, -64, 32],\n [-8, 36, -16, -16, 44, -32, 16],\n [6, -27, 12, 12, -33, 24, -12]]\n\nPrese... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[79, 103, -73, -67, -40, -107, -17],\n [-50, 26, -166, -178, -202, -46, 62],\n [54, -4, 60, 61, 61, -50, -28],\n [-100, 6, -38, -73, -31, 72, -20],\n [-137, -31, 29, -70, 5, 17, -97],\n [-67, -55, 7, 12, -9, 95, 34],\n [-125, 13, -31, -70, -7, 117, -33... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-35, 71, 54, 80, -61, 34, 60],\n [120, -99, -41, -16, 122, -90, -56],\n [-41, 161, -66, 32, -23, 142, 28],\n [51, 123, -11, 14, -40, 138, 31],\n [159, -49, 222, 160, -61, -86, 98],\n [-134, 150, -189, -110, 3, 180, -47],\n [13, -34, -181, -120, 137, 4, -108]]\n\nPre... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[188, -38, 71, 179, 125, -350, -138],\n [61, 103, 66, -3, 51, 19, 33],\n [-207, 136, -32, 215, 12, 22, 266],\n [208, -129, -28, -152, 149, -122, -68],\n [66, -9, -150, 171, -136, 7, 312],\n [-61, -38, -10, 100, 23, -126, -57],\n [76, -1, -5, 55, 40, -52, ... | 6 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[53, 43, -32, -231, -63, 91, -13],\n [4, 120, -4, -36, -160, -12, 180],\n [16, 231, 131, 19, 44, -64, -31],\n [-119, -106, -175, -29, -64, -111, 47],\n [-9, -15, -17, -89, 101, -5, -158],\n [-49, -126, -144, -74, -40, 6, 0],\n [-204, 22, -255, -176, -3... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-44, 200, 4, -47, 39, 43, -4],\n [-14, 36, 37, 68, 126, 53, -20],\n [-69, 14, -53, -4, 7, 42, -67],\n [-6, -9, 90, 101, 103, -50, -94],\n [-107, 247, 14, -40, 86, 20, -66],\n [-87, 58, -113, -24, -52, 114, -124],\n [-28, 43, -71, -22, -46, 88, -48]]\n\nPresent the a... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-333, 254, 182, 222, -67, 218, -134],\n [-134, 3, -131, 25, -36, -161, 4],\n [41, -78, -15, -12, 268, -21, -142],\n [38, -112, -150, 88, 200, -106, -12],\n [135, -67, -84, -45, 225, -25, -72],\n [277, 124, -164, -28, 34, -49, -52],\n [141, -66, 74, -4, 1... | 6 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[48, 98, -227, -83, 227, 133, 122],\n [85, -65, 126, -116, -223, 38, 159],\n [18, 73, -33, -158, 103, 139, 162],\n [-48, 11, -138, -119, 148, 134, 109],\n [-13, 136, -201, 45, 57, -176, -189],\n [216, -132, -14, 135, -35, 41, 199],\n [-114, 18, 80, -74, ... | 6 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-96, 15, 12, 146, -60, -216, -33],\n [21, -168, -163, -21, -42, 67, -81],\n [-12, -109, 40, 82, 113, -18, -134],\n [-174, 6, 6, 90, -125, -150, 75],\n [-16, -44, -123, -93, -106, 84, 69],\n [7, -34, 14, -38, 192, -20, -165],\n [58, 48, 40, 76, 8, -71,... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-1, 3, -72, -55, 86, -96, 75],\n [-36, 15, -112, -58, 89, -139, 96],\n [69, -27, 168, 75, -114, 204, -135],\n [-73, 27, -136, -47, 70, -160, 99],\n [-28, 6, 64, 72, -114, 94, -84],\n [12, 0, -96, -84, 132, -132, 108],\n [45, -12, -40, -67, 107, -67, 69]]... | 2 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[-35, 30, -72, 17, -39, -53, -32],\n [-11, 6, -21, 8, -9, -20, -14],\n [56, -96, 138, 10, 108, 38, -4],\n [26, -116, 98, 60, 118, -52, -84],\n [26, -76, 79, 29, 80, -13, -38],\n [29, 6, 45, -38, 3, 74, 62],\n [19, 106, -19, -104, -95, 148, 158]]\n\nPrese... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[131, -53, -37, 56, 64, -179, -108],\n [-25, 111, 48, 74, 55, 165, 216],\n [-203, 15, -63, -21, -130, 64, 152],\n [-10, 25, -109, -79, -68, -25, 153],\n [34, -151, -23, -15, 42, 78, -147],\n [90, -103, 79, 61, 100, -22, -259],\n [-73, -5, -112, -190, -177, -114, 20]]... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[81, 16, 36, -2, 49, 19, -11],\n [-64, -261, -95, 15, 29, -164, -22],\n [-357, 22, 42, -8, -19, -15, -47],\n [-198, -141, -20, 19, 16, -135, -38],\n [52, 144, -15, -20, -91, 125, 50],\n [-117, 102, 159, 12, 124, -4, -74],\n [-175, -62, 12, -18, 122, -13, ... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[43, 9, 62, -194, -66, 131, -76],\n [-67, -135, 177, -73, 208, 5, 16],\n [-104, -140, -28, 44, 24, -141, 44],\n [73, 117, -64, 4, -120, 65, -34],\n [65, 76, -78, -66, -71, 39, -17],\n [-55, -112, 96, -56, 169, -32, 31],\n [22, 34, 112, 56, 196, 40, 32]]\n\nPresent th... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0, 0, 0, 0],\n [33, -18, 36, -36, 18, -12, 30],\n [99, -54, 108, -108, 54, -36, 90],\n [44, -24, 48, -48, 24, -16, 40],\n [-99, 54, -108, 108, -54, 36, -90],\n [-121, 66, -132, 132, -66, 44, -110],\n [-110, 60, -120, 120, -60, 40, -100]]\n\nPres... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-107, 34, 26, -3, 97, 36, -164],\n [14, -172, -68, 174, -46, 72, 80],\n [-90, -88, 19, 45, 59, 56, 4],\n [-28, -6, -29, 67, 22, 36, -110],\n [-92, 62, 41, -47, 90, 12, -138],\n [36, -178, -91, 205, -66, 76, 70],\n [-147, -176, 22, 101, 90, 104, 26]]\n... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[6, 5, 8, -8, -1, 9, -10],\n [-36, -30, -48, 48, 6, -54, 60],\n [-36, -30, -48, 48, 6, -54, 60],\n [0, 0, 0, 0, 0, 0, 0],\n [36, 30, 48, -48, -6, 54, -60],\n [-12, -10, -16, 16, 2, -18, 20],\n [-60, -50, -80, 80, 10, -90, 100]]\n\nPresent the answer in... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-66, 8, 110, 3, -164, -21, 109],\n [38, -76, 3, -39, -12, 5, -49],\n [107, -146, -24, -76, -70, 31, 72],\n [-42, 35, -75, 20, 224, -16, -182],\n [-125, -90, -175, -122, 26, 157, -34],\n [-189, 19, -56, -47, -55, 91, 52],\n [-52, -368, -218, -303, -123, 260, -56]]\n\... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[15, 10, 45, -45, -30, 15, 55],\n [-24, -16, -72, 72, 48, -24, -88],\n [36, 24, 108, -108, -72, 36, 132],\n [9, 6, 27, -27, -18, 9, 33],\n [18, 12, 54, -54, -36, 18, 66],\n [3, 2, 9, -9, -6, 3, 11],\n [36, 24, 108, -108, -72, 36, 132]]?\n\nPresent the answer in La... | 1 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[90, -27, -27, -99, -36, 36, -18],\n [80, -24, -24, -88, -32, 32, -16],\n [90, -27, -27, -99, -36, 36, -18],\n [80, -24, -24, -88, -32, 32, -16],\n [-50, 15, 15, 55, 20, -20, 10],\n [40, -12, -12, -44, -16, 16, -8],\n [30, -9, -9, -33, -12, 12, -6]]\n\nP... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-81, 0, -27, -75, -96, -15, 123],\n [124, 80, -132, 20, -96, 140, -92],\n [-123, -48, 63, -57, 0, -93, 129],\n [74, 46, -75, 14, -52, 81, -57],\n [104, 88, -156, -8, -144, 148, -52],\n [-61, -62, 114, 17, 116, -102, 18],\n [108, 0, 36, 100, 128, 20, -... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-53, 127, -198, 67, -197, -131, -146],\n [-45, -37, 87, 10, 153, 83, 173],\n [-103, 115, -75, 35, -68, 16, 142],\n [-328, 128, -10, 10, 82, -176, -250],\n [50, 14, 46, -20, -31, 51, 307],\n [-29, -9, 156, 96, 62, -151, -128],\n [-223, 77, -82, -204, 46, -43, 60]]... | 6 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-50, -13, 81, 96, -18, 143, 130],\n [30, 17, 104, -64, -44, 100, 24],\n [-165, -177, 1, 257, -4, 44, 91],\n [94, 71, -50, -129, 130, -170, 45],\n [-17, 82, -59, 201, -16, 118, -63],\n [-39, -208, 38, -193, 46, -233, 86],\n [60, -11, -59, -205, -32, -1... | 5 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[48, -173, -44, -7, -14, -80, -138],\n [135, 44, -85, 116, 15, 72, -24],\n [-90, -38, 55, -86, -18, -57, 6],\n [105, 66, -60, 122, 41, 89, 18],\n [96, 9, -63, 71, 2, 35, -36],\n [45, 24, -15, 120, 93, 80, 48],\n [-141, -78, 78, -182, -77, -127, -30]]\n\n... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[104, 52, -27, 111, 16, 186, 201],\n [-156, -114, 246, -101, 16, 50, -61],\n [-20, 100, -100, 68, -37, -97, -35],\n [-132, 123, 207, -9, -126, -30, 33],\n [-90, 58, 57, 18, -14, 80, 48],\n [2, -61, -91, -29, 63, -3, -62],\n [201, -16, 14, -73, -84, -157, 4]]?\n\nP... | 5 | MATH |
[
{
"content": "Compute the rank of the given 7x7 matrix:\n[[24, 17, 15, -8, -34, -23, 4],\n [3, -32, -69, 62, 43, -16, -31],\n [-48, -73, -111, 88, 122, 31, -44],\n [-57, -42, -39, 22, 83, 54, -11],\n [-72, -51, -45, 24, 102, 69, -12],\n [66, 11, -33, 44, -44, -77, -22],\n [-63, -17, 18, -30, 51, 71, 15]]\n\nPre... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-94, 34, -47, -102, -180, -199, -63],\n [-75, -199, -59, -134, 33, 247, 196],\n [123, 53, 183, 232, 70, 164, -159],\n [58, 203, 114, 96, 232, 13, 79],\n [-144, -71, -83, -230, -98, -228, 7],\n [-76, 64, 3, -48, -186, -200, -118],\n [-107, -23, 186, -5... | 6 | MATH |
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