messages listlengths 1 1 | ground_truth stringclasses 8 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the rank of the matrix:\n[[68, -22, 22, 100, 84, 150, -54, -20, -120],\n [-118, 53, -29, -86, -90, -129, 45, 34, 156],\n [72, -48, 8, -40, -4, -60, 24, -20, -40],\n [-256, 152, -40, 32, -56, 48, -24, 72, 208],\n [376, -239, 49, -140, 23, -210, 87, -105, -250],\n [-218, 157, -17, 190, 56, 285,... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-221, -416, -36, -176, -316, -632, 54, -245, -317],\n [325, 294, -104, 199, 425, 779, 100, 409, 184],\n [-271, -356, -412, 210, -238, 402, 26, -127, 3],\n [-66, 718, 388, -58, -16, 197, -398, 276, -25],\n [29, 44, -70, 214, 108, 305, 29, -85, 472],\n ... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[86, -45, -359, 306, 266, -139, -183, 350, -211],\n [458, -21, 145, -366, 32, -271, 351, -148, 65],\n [163, -257, -2, -158, -33, 6, 321, -485, 333],\n [-444, -336, -512, 624, 118, 196, -274, -50, 28],\n [-611, -28, -52, 336, -159, 341, -306, -34, 4],\n... | 4 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[154, 182, -306, -15, -272, -109, -293, -122, -185],\n [8, -227, 153, 33, 272, 46, 104, -58, 50],\n [-92, 52, 68, -14, -32, 30, 94, 108, 70],\n [-208, 71, 187, -25, -16, 78, 236, 234, 170],\n [-64, 388, -204, -60, -448, -56, -112, 152, -40],\n [-26, -125... | 2 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-17, -12, -25, 25, -8, 7, -31, 0, -20],\n [173, 93, 37, -37, -136, -376, 1, -66, -43],\n [229, 144, 205, -205, -24, -279, 227, -40, 120],\n [-168, -93, -56, 56, 112, 337, -30, 58, 19],\n [-28, -3, 84, -84, 112, 187, 130, 38, 109],\n [20, 15, 36, -36, 16... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[179, 102, -56, 320, -33, 544, -28, 148, -159],\n [683, 512, 231, -411, -219, -87, 76, 73, -632],\n [-332, 462, -376, -30, -267, -196, 73, -33, -736],\n [-346, 234, 177, 485, -114, 317, -58, -375, -179],\n [435, 212, -95, -338, -180, 383, 212, 644, 7],\n [-257, 93, -... | 7 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[162, -63, -144, -162, 126, -81, 90, -54, -63],\n [234, -91, -208, -234, 182, -117, 130, -78, -91],\n [144, -56, -128, -144, 112, -72, 80, -48, -56],\n [18, -7, -16, -18, 14, -9, 10, -6, -7],\n [90, -35, -80, -90, 70, -45, 50, -30, -35],\n [-126, 49, 112, 126, -98, 6... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-229, 243, -44, 295, 134, 388, -45, 253, -144],\n [77, -98, 252, -361, 165, -122, 135, -290, 30],\n [-156, 79, 159, -49, 288, 252, 104, 2, -95],\n [-357, -113, 100, -139, 354, 100, -87, -69, -222],\n [153, 139, 363, -282, 215, 110, 279, -234, 63],\n [... | 4 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[98, -70, -126, 0, 77, 126, -21, 14, 84],\n [140, -100, -180, 0, 110, 180, -30, 20, 120],\n [126, -90, -162, 0, 99, 162, -27, 18, 108],\n [28, -20, -36, 0, 22, 36, -6, 4, 24],\n [168, -120, -216, 0, 132, 216, -36, 24, 144],\n [84, -60, -108, 0, 66, 108, ... | 1 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-83, 288, 45, 83, 256, 45, -42, -466, 393],\n [47, -90, -201, 18, 238, -176, 17, -179, 394],\n [254, -234, -310, -369, -208, -280, 61, 103, -49],\n [-5, -26, -169, 30, 264, -187, 71, -143, 404],\n [-93, 392, 427, -44, -372, 416, -123, -59, -556],\n [186... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[160, -105, 255, 114, -504, -261, -19, -317, 651],\n [-116, 244, -114, -5, -30, -117, -101, -17, -108],\n [-32, 59, -42, -36, 447, 353, -31, -5, -282],\n [-701, 54, -529, -189, 616, 237, 116, -32, -448],\n [30, 196, 72, -476, 391, -504, -279, 7, -210],... | 7 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-240, -100, 87, -458, -37, -217, 251, 583, -138],\n [-483, -322, 141, 209, -97, 233, -108, 137, -108],\n [397, 461, 276, -28, -13, -109, -36, -123, 449],\n [-200, 262, -480, 230, -260, -200, -220, -34, 251],\n [885, -706, 509, -220, 165, -113, 596, 185,... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[95, -191, -156, 106, -43, 72, 361, -12, -49],\n [-44, -18, -332, -32, 232, -38, 464, 140, 120],\n [385, -427, 419, -340, -330, -485, -340, -294, 558],\n [12, 121, 340, 190, -172, -34, -139, -450, 16],\n [-113, -57, -516, 85, 150, 131, 308, 441, -279],\n [-138, -20, ... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-92, 66, 30, 14, 176, 64, 156, -22, -18],\n [-60, 153, -79, -53, -136, -182, -308, 93, 167],\n [187, -249, 34, 33, -110, 91, 91, -69, -151],\n [-369, 234, -171, -64, 208, -185, -55, -182, -158],\n [267, -81, 90, 16, -271, 26, -176, 227, 263],\n [45, -99, -38, -5,... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-172, 1, -91, -10, -46, -19, 487, 247, -708],\n [-65, -27, 393, 408, 82, 362, 423, -39, -448],\n [91, -566, -195, -193, 541, -180, 31, -192, 467],\n [-44, 299, 440, 296, -62, 249, -424, 277, 134],\n [137, -512, 400, 488, 162, 509, 744, -666, 174],\n [62,... | 6 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-80, 96, 103, 60, -45, 246, -76, -64, -98],\n [-11, 179, -6, 115, 120, -240, 140, 28, -117],\n [-447, 591, 402, 435, -160, 408, 212, -156, -413],\n [94, -110, -118, -70, 54, -276, 80, 72, 110],\n [-440, 394, 347, 335, -279, 336, 290, -114, -217],\n [4... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[519, 265, -196, 271, -5, -277, -52, 721, 214],\n [-159, 232, 214, -324, -346, -162, 19, 262, -26],\n [-48, 59, 48, 143, -122, -530, -325, 184, -115],\n [442, -63, -340, 444, 267, -49, 34, 207, 156],\n [-524, 49, 322, -469, -274, -42, 71, -117, -317],\n [293, 296, -2... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[150, 146, -168, -241, 101, 236, -123, -174, -57],\n [138, 174, -152, -271, 91, 244, -101, -146, -71],\n [12, -90, -20, 107, 13, -50, -41, -50, 43],\n [-66, -342, 56, 451, -31, -292, -31, -22, 155],\n [108, 244, -112, -346, 66, 264, -46, -76, -106],\n [-6, 200, 20... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-153, -61, 103, -163, -149, -173, 5, -209, 235],\n [-126, 138, 306, -186, 42, 234, 150, -318, -150],\n [-195, 25, 252, -236, -100, -15, 86, -346, 112],\n [-6, -62, -66, 10, -58, -126, -46, 38, 118],\n [81, 157, 92, 52, 188, 341, 94, 14, -352],\n [228, -8... | 2 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-214, -211, 121, -319, 16, 246, 298, -256, 96],\n [480, 52, -9, -138, -353, -186, -387, -40, -17],\n [-98, 73, -311, 293, 238, -209, -73, 37, 450],\n [45, -54, 600, -74, 30, 570, -537, -267, 195],\n [185, 193, 202, 142, 61, 72, -612, -237, 250],\n [-24,... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[161, -40, 117, -193, 182, 267, 195, 260, 333],\n [26, -28, 17, -23, 312, 354, -117, 147, 269],\n [-53, 182, 333, 2, 420, 284, -34, 494, 315],\n [487, -273, -117, -26, 112, 100, 36, 29, -34],\n [-215, 140, 94, -41, -162, -152, 165, 51, 96],\n [-169, 223, 327, -494, 3... | 5 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[238, 330, -265, 383, 87, -64, -471, -124, 73],\n [-598, -352, -120, -463, -77, 22, -441, -10, -502],\n [-445, 19, 330, -258, 142, 130, 45, 109, -557],\n [34, 501, 190, -87, 102, 33, 11, -97, -586],\n [-573, -517, 391, -271, 189, 195, 484, 422, -144],\n ... | 8 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-264, 176, 225, -337, -27, 70, 27, -141, 43],\n [-216, 144, 270, -270, 270, 0, 234, -270, 18],\n [162, -108, -180, 204, -126, -15, -120, 162, -18],\n [24, -16, 75, 37, 327, -70, 233, -159, -23],\n [30, -20, -105, 33, -267, 45, -199, 159, 11],\n [-126, 84, 255, -1... | 2 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-112, -86, -44, 118, 224, -226, -256, 124, -342],\n [-1, -14, 40, 70, 119, -103, -97, 139, -267],\n [88, 54, 76, -22, -56, 74, 104, 44, -2],\n [100, 70, 60, -70, -140, 150, 180, -40, 170],\n [38, 38, -12, -86, -154, 144, 150, -134, 292],\n [-61, -18, -1... | 2 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[305, -65, 44, -205, 107, -46, 53, -36, -143],\n [-317, 354, -395, 340, 268, 155, 94, -15, 191],\n [210, 73, 45, 122, -231, -24, -103, -163, -244],\n [294, -402, 413, -418, -201, -181, 16, 78, 60],\n [-411, -203, 181, -10, -198, -34, -51, 191, 331],\n [-... | 5 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-368, -340, -580, -187, 592, -15, -8, -450, 465],\n [141, -242, -189, 172, -52, -319, 170, -51, -87],\n [-414, 261, 72, 196, 20, -29, -60, 219, 435],\n [-333, -460, -585, 61, 111, -258, -164, -647, 52],\n [165, -324, -292, 526, 81, -126, 408, 274, 117],... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-249, 688, -149, -101, -141, 182, -191, 13, 355],\n [-224, 282, -39, -78, -20, 227, -139, 42, -50],\n [68, -55, 284, -238, 278, 4, -20, 162, 0],\n [17, -33, -252, 121, 147, -317, -230, 565, -251],\n [-65, 89, 155, -143, 45, 178, 9, -93, 47],\n [3, -148, -382, 289, -... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-240, -32, 288, 160, 272, 288, 256, -192, 128],\n [-30, -4, 36, 20, 34, 36, 32, -24, 16],\n [150, 20, -180, -100, -170, -180, -160, 120, -80],\n [-135, -18, 162, 90, 153, 162, 144, -108, 72],\n [180, 24, -216, -120, -204, -216, -192, 144, -96],\n [45,... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-125, -38, 213, -187, -221, 122, 334, -125, 397],\n [132, 26, 709, -386, -61, -148, -308, 454, -9],\n [277, -110, -40, 147, -82, -175, -104, 176, -261],\n [-228, 258, -77, 52, 40, 210, -106, 133, -108],\n [0, 242, -238, 196, -169, 122, 80, -221, -361],\n [306, -201,... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-297, -382, -280, -127, -118, 301, -122, -330, -96],\n [-153, 141, 358, -278, -344, -43, 81, -292, -350],\n [-64, -133, -250, 21, 42, 128, -61, 26, 130],\n [95, -21, 504, 77, 3, -97, -9, -277, -414],\n [-40, -83, -120, -110, 76, -248, 156, -3, 24],\n [176, -78, 234,... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[319, -510, -4, -455, -49, 122, -492, 404, -119],\n [82, 347, -501, 178, 25, 17, 343, -544, 300],\n [661, -284, -581, -147, 183, 199, -144, -1, 140],\n [-509, 406, 403, 195, 77, 148, -2, 574, -133],\n [-352, 237, 517, -17, 21, -173, -148, 113, -238],\n [-... | 7 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[45, -371, -65, -244, -337, -72, -67, 342, 169],\n [-183, -340, -45, -408, 131, 555, 32, -83, 342],\n [-7, 287, 186, -17, -189, -23, -118, 193, -582],\n [-252, -246, 14, -175, 376, 477, 139, -207, 394],\n [-552, -565, 77, -160, 169, 205, 177, -169, 196],\... | 8 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-258, -23, -42, -299, -324, -144, -22, -46, 139],\n [-181, 116, -267, -233, 121, 203, -94, -121, -105],\n [-71, -214, -173, -7, 93, 105, 2, 91, 119],\n [-69, 63, 249, -120, -429, -327, 36, -33, 102],\n [-292, -312, -280, -234, -102, 48, -16, 90, 264],\n ... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-244, 700, -7, 313, -527, -419, 171, -339, 1],\n [275, -99, -44, 470, -449, 283, -67, 142, -448],\n [357, -425, -540, -18, 27, 606, -252, 336, -64],\n [190, -216, -199, -17, -49, 503, -407, 107, 229],\n [-109, -90, -326, -138, 35, -171, -73, -211, -40... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[84, 127, 153, 33, -153, -236, -86, 137, 180],\n [-433, 96, -189, 109, -215, 129, 120, -8, -145],\n [10, -173, -390, -147, 144, 89, -251, -119, -143],\n [293, -265, 292, -256, 26, 149, -68, -251, 5],\n [100, -109, -243, 45, 501, 24, -142, 261, 214],\n [-161, -9, -213... | 5 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-100, 90, -232, -109, -71, -81, -358, -329, 26],\n [-418, -186, -76, -268, -290, -273, -55, 4, -109],\n [-243, -102, -50, -122, -128, -124, -6, 47, -45],\n [37, 60, -82, -169, -177, -157, -314, -404, -53],\n [-235, -174, 78, -33, -55, -52, 257, 330, -46... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[27, 450, 462, 99, -357, 138, -408, 318, 189],\n [-213, -284, -538, -111, 517, 524, -304, 280, -465],\n [69, 275, 104, 142, -62, 109, -246, 115, -38],\n [384, 224, 244, 92, -236, -512, 280, -432, 236],\n [-15, -233, -642, 24, 584, 289, -98, -33, -516],... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[188, -189, -222, 108, -359, 372, 89, -328, -391],\n [562, 147, 31, 530, -133, 42, 129, -246, -156],\n [-129, 244, 198, -146, 32, -27, -419, 113, 522],\n [27, -13, -445, 75, 169, 280, 171, -242, -35],\n [-343, -502, -264, -52, 545, -132, 111, 42, -248],\n [138, -1... | 8 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[59, 138, 301, 218, 126, 16, 515, -231, 11],\n [37, -29, 105, 240, 219, 82, 127, -64, -219],\n [-101, -39, -219, -470, -345, -95, -361, 174, 366],\n [-7, 194, 65, 380, 56, -71, 115, -99, -406],\n [-65, -122, 188, -68, 101, 100, 103, -15, 60],\n [-218, 48... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-294, -315, 325, 330, 257, 505, -160, -539, -125],\n [-67, 284, -233, -123, -201, -561, 160, 403, -233],\n [31, -151, 156, -41, 65, 174, -351, 31, 164],\n [-32, 98, -174, 334, -226, -105, 585, 325, 32],\n [-392, -76, 180, 88, 95, -90, -333, -71, -358],\n... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-42, -12, -18, 33, -9, 45, 48, -30, -30],\n [238, 68, 102, -187, 51, -255, -272, 170, 170],\n [-84, -24, -36, 66, -18, 90, 96, -60, -60],\n [-168, -48, -72, 132, -36, 180, 192, -120, -120],\n [238, 68, 102, -187, 51, -255, -272, 170, 170],\n [-140, -4... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-150, -210, 195, 15, -120, -60, 195, 135, 45],\n [-150, -210, 195, 15, -120, -60, 195, 135, 45],\n [-90, -126, 117, 9, -72, -36, 117, 81, 27],\n [60, 84, -78, -6, 48, 24, -78, -54, -18],\n [40, 56, -52, -4, 32, 16, -52, -36, -12],\n [-40, -56, 52, 4, -32... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-77, -199, -66, 178, 36, 3, -188, -70, -257],\n [127, -488, -344, 103, 1, 120, -315, -115, -337],\n [59, 175, -96, 36, 10, 313, -246, 338, 501],\n [-357, 62, 183, -45, 577, -663, 403, 255, -255],\n [138, 87, -106, 265, 28, 208, -191, -151, 206],\n [108, ... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-32, 59, 232, -67, -15, 72, -138, 158, 14],\n [-72, -198, 396, -198, -18, 288, 36, 72, 252],\n [16, 107, -64, 53, 1, -88, -74, 38, -98],\n [-10, 109, 107, -8, -9, -12, -138, 127, -56],\n [-44, -58, 266, -112, -14, 152, -44, 98, 112],\n [-40, -278, 156... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[561, 232, 647, 31, -336, 108, -113, 198, 461],\n [-279, 564, 8, -140, -183, -5, 476, -125, -128],\n [474, -622, 437, -418, 515, 491, -255, -201, 205],\n [394, -151, -71, -403, -5, -151, -12, -542, 643],\n [-131, -34, -360, -382, 275, 6, 317, -329, -71... | 6 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-132, -781, -425, 96, -237, 498, 102, 70, -651],\n [315, 265, 84, -376, 173, -241, -276, -24, 155],\n [-61, -94, 93, -253, -98, 108, -467, 639, -288],\n [22, 12, -81, -213, 0, 244, -69, 392, 392],\n [-293, -162, -288, 87, -177, 361, 329, 333, 370],\n [-106, -469,... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-212, 139, 195, -465, 790, -137, 130, 80, 304],\n [24, 438, 312, -439, 92, -158, -35, 242, -264],\n [-322, -347, -56, -361, 252, 686, 238, -510, 98],\n [258, -88, -65, 84, -45, -35, -59, -236, -208],\n [168, -3, 113, 643, -325, 208, -137, -307, 345],\... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-394, -584, -155, 21, 474, -254, -317, -412, -398],\n [-43, 182, 110, -346, 390, -208, -767, -123, -592],\n [-96, -210, 155, 276, -145, -179, 210, -25, 283],\n [-30, -380, -496, 365, 217, -117, -51, 71, -189],\n [-40, -366, -626, 157, 175, 233, 235, -... | 5 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[74, 116, -336, 256, -116, -202, 32, -350, 534],\n [-116, 1, -346, 177, -45, -197, 30, -222, 520],\n [60, 6, 87, 139, -232, -227, 191, -177, 22],\n [-125, -153, 24, 341, -389, -616, 460, -241, 221],\n [334, 267, -124, 89, -39, 121, -140, -270, 170],\n [-... | 4 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[145, -477, -194, 157, -186, -172, 287, 212, 317],\n [207, -192, -70, 209, -184, -192, 295, 50, 106],\n [61, 273, 198, -148, 55, 99, -365, -44, -426],\n [-312, 165, 72, -169, 169, 145, -218, -162, -46],\n [-318, 291, 228, -310, 224, 274, -512, -150, -279... | 5 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[124, -237, -85, -443, 260, 331, -354, 128, -176],\n [123, 365, -17, 125, -269, 205, -118, 210, -64],\n [198, -649, 523, -123, -282, 380, -396, 159, 256],\n [216, 549, -42, 356, -74, -174, -150, 47, -22],\n [456, 240, 10, -312, 156, 244, -102, -61, -25],... | 7 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-197, -353, 362, 35, -472, -212, 365, -402, 196],\n [183, 10, 401, 222, 302, -186, 38, -239, -189],\n [-280, -518, 149, 95, -187, 114, 154, -724, 377],\n [-440, -363, 75, -44, 41, 243, -67, -538, 478],\n [-310, -76, 255, -208, -174, -98, 144, -174, 101],... | 7 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[172, 202, -107, 223, 287, -158, 290, -251, 105],\n [-248, 89, 14, -3, -132, 342, 1, 211, -186],\n [-260, 334, -66, 291, -162, 533, -144, 411, -188],\n [217, 168, -83, 243, 282, -185, 443, -409, 164],\n [138, 377, -184, 325, 408, -102, 315, -173, 42],\... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-217, -223, 238, 331, 415, -143, -347, -135, 395],\n [145, 172, 77, -176, 72, 117, -266, -345, -464],\n [-97, 155, 209, -76, 187, 37, -448, -254, 326],\n [463, 222, 493, -90, 133, 934, 217, 323, -298],\n [519, 262, 221, -459, -301, 545, 337, 160, -272],\n [-198, 260... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[195, -15, -60, 195, -150, 270, -135, 15, -195],\n [52, -4, -16, 52, -40, 72, -36, 4, -52],\n [-182, 14, 56, -182, 140, -252, 126, -14, 182],\n [143, -11, -44, 143, -110, 198, -99, 11, -143],\n [-169, 13, 52, -169, 130, -234, 117, -13, 169],\n [-195, 15, 60, -195, 15... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-144, 232, 56, 132, -116, -142, -200, -260, -134],\n [-278, 138, 195, -377, -68, 173, 18, -78, 585],\n [-232, 130, 112, 0, -36, -64, 156, 10, 208],\n [-138, -40, 89, -175, 44, 89, 282, 188, 389],\n [-206, -27, 129, -227, 46, 107, 360, 225, 519],\n [-1... | 3 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-127, 41, -12, -168, 209, 30, -295, -453, 216],\n [-198, -248, 55, -224, 214, -145, 703, 96, 196],\n [66, -239, 87, -40, 36, 264, -22, 200, -318],\n [-212, -156, -223, 136, 154, -278, 755, 498, -70],\n [-376, 25, -366, -175, 294, 276, -105, 114, -142],\... | 7 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[197, -41, 99, -66, 223, -387, -52, -204, 126],\n [135, -27, 69, -42, 153, -261, -30, -138, 90],\n [-202, -2, -148, -62, -236, 228, -173, 137, -276],\n [-165, -15, -135, -90, -195, 135, -210, 90, -270],\n [101, -17, 55, -22, 115, -183, -6, -98, 78],\n [-40, -56, -... | 2 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-214, 23, 432, -212, 281, -174, 183, 29, 152],\n [203, -441, -729, 577, -94, 254, -486, 234, 433],\n [177, 127, -536, -137, -175, -444, -280, -141, 87],\n [240, 195, -96, -49, 507, -4, -83, 322, -141],\n [404, 54, -366, -227, -33, 250, -278, 226, -38],\... | 7 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[211, 218, 49, -325, -82, -225, -7, 281, -338],\n [-129, -247, -407, -4, 403, 120, -229, -164, 104],\n [83, -22, 243, -318, -313, -377, 226, -104, 142],\n [173, 28, -225, 636, 284, 494, -476, -241, -291],\n [-665, 91, -223, -6, 824, 122, -560, -82, -198]... | 8 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[351, -220, -368, -8, 125, -31, -239, -165, -11],\n [217, -103, -314, 98, -97, 26, -49, 34, 152],\n [-313, 580, 281, 410, 37, 152, 83, 33, 163],\n [42, -348, -108, -436, 66, -127, -103, -304, -342],\n [59, 163, -353, 276, -15, -45, 81, 56, 366],\n [249, ... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-35, 63, -7, 63, 56, 91, -70, 91, 7],\n [25, -45, 5, -45, -40, -65, 50, -65, -5],\n [-85, 153, -17, 153, 136, 221, -170, 221, 17],\n [-20, 36, -4, 36, 32, 52, -40, 52, 4],\n [65, -117, 13, -117, -104, -169, 130, -169, -13],\n [70, -126, 14, -126, -112, -182, 140, -1... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[117, 42, -388, 63, -493, -97, -95, 116, 534],\n [104, -26, 142, 239, 15, -126, -55, -224, -150],\n [153, -67, 29, 282, -104, -116, -109, -87, 20],\n [2, 158, -84, -7, -267, -162, 29, -322, 100],\n [89, -300, 206, 185, -210, 225, -224, 139, -217],\n [141,... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[129, 166, 216, 90, -122, -195, 63, 13, -159],\n [-81, 82, 258, -120, -262, -195, 7, 13, -243],\n [-105, 2, 114, -120, -150, -75, -17, 5, -123],\n [-207, 58, 339, -255, -394, -240, -20, 16, -342],\n [198, -44, -300, 240, 356, 210, 22, -14, 306],\n [75, 30... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[279, 32, 115, -445, 327, 425, 215, -570, -55],\n [150, 113, -6, -522, 443, -23, -117, -227, 197],\n [12, -311, 259, 112, -90, 203, 255, -149, 90],\n [-8, -74, -512, -173, 190, 160, -414, -1, -131],\n [218, 105, -373, -206, 142, -59, -297, -81, 410],\n... | 7 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[69, -261, -93, -407, 544, 299, 501, 248, 134],\n [-114, 262, -537, -678, 506, 122, 2, 165, -63],\n [863, 374, -580, -838, -434, -239, -231, 146, 331],\n [-37, -450, -72, 87, 118, -48, 293, -67, 382],\n [480, 290, 237, -241, -245, 227, 215, 54, -331],\n [-355, -285, ... | 8 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-428, 287, 23, 112, 222, 119, 84, 184, 89],\n [-258, 458, 5, 310, -157, 139, -85, 53, 332],\n [2, -328, 183, -293, -15, -119, 406, 69, -584],\n [-126, 181, -120, -324, -159, 118, -7, 67, -3],\n [368, -359, 93, -165, -142, -75, -107, -199, -135],\n [315,... | 5 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[142, -143, -61, -261, -189, 83, -15, -518, 415],\n [33, 67, 41, 26, 24, -34, -37, 37, -47],\n [-361, -47, 177, 178, 290, 131, 78, 245, -99],\n [112, -4, -284, 44, -180, -140, 68, 272, -268],\n [-393, -59, 289, 134, 346, 197, 48, 81, 53],\n [228, 160, -3... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-24, -3, -150, -75, 141, 90, -81, -15, -156],\n [31, -28, 130, 65, -112, 24, -93, 13, 329],\n [30, -10, 160, 80, -146, -52, 16, 16, 250],\n [-8, -41, -130, -65, 135, 206, -275, -13, 108],\n [-47, -9, -300, -150, 283, 190, -178, -30, -293],\n [20, 15, 150... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[72, 0, -70, 128, 278, -82, 48, 132, 24],\n [-303, 233, -121, -387, -146, 336, -67, 147, 156],\n [-188, -21, 106, 31, -156, 157, 77, 147, -231],\n [-129, -86, 206, 230, -103, 120, 194, 202, -463],\n [-77, 155, -391, -297, 342, -36, -233, 129, 660],\n [... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[64, 58, 196, -12, 220, 112, -86, 204, -90],\n [-13, 318, 43, -134, 595, 360, 72, 248, -313],\n [-81, -296, 197, 404, -171, 38, 170, -204, 233],\n [-196, 30, -318, -222, 231, -48, -121, -133, -105],\n [19, 105, 76, 5, 343, 69, -300, 173, -157],\n [206,... | 6 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-45, -126, 9, -81, -117, 63, -72, 81, -117],\n [-65, -182, 13, -117, -169, 91, -104, 117, -169],\n [-10, -28, 2, -18, -26, 14, -16, 18, -26],\n [25, 70, -5, 45, 65, -35, 40, -45, 65],\n [-45, -126, 9, -81, -117, 63, -72, 81, -117],\n [-55, -154, 11, -99... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-372, -192, 162, 357, 132, 414, 137, 63, -281],\n [-376, -15, -33, 661, 171, 246, 32, 3, -625],\n [372, -153, 791, 9, -280, 197, -79, -344, -359],\n [-17, 151, -48, 56, 93, 180, 109, -150, -105],\n [-517, 299, 188, 461, -129, 276, -10, -121, -154],\n [-586, -54, ... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[270, 270, -108, -90, -144, -270, 252, -216, -198],\n [210, 210, -84, -70, -112, -210, 196, -168, -154],\n [135, 135, -54, -45, -72, -135, 126, -108, -99],\n [-150, -150, 60, 50, 80, 150, -140, 120, 110],\n [-105, -105, 42, 35, 56, 105, -98, 84, 77],\n [-210, -210, 8... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-149, -109, -126, -17, 5, -3, -14, 115, -40],\n [68, -133, -119, -44, -226, 7, -188, -73, -467],\n [304, 187, -395, -30, 57, -30, 206, -225, 44],\n [322, 284, -759, -56, -207, -131, -112, -721, -78],\n [-151, -118, 74, -138, -156, 142, -114, -333, 119],\... | 6 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[94, -360, -88, -104, 98, 109, -135, 194, -19],\n [36, 144, 110, 252, 24, -186, 276, 54, 226],\n [140, -616, -189, -314, 130, 182, -427, 385, -16],\n [-114, -220, 165, -242, -164, 428, -414, 377, -230],\n [246, -304, -130, 124, 238, -307, 111, 296, 437],\n [-280, 152... | 4 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-113, 103, 25, -71, 9, 277, -151, 1, 304],\n [-125, 115, 45, -110, -35, 300, -210, -5, 335],\n [-40, 70, 73, -182, -191, 108, -287, -42, 160],\n [147, 152, -13, -108, -167, -124, -58, 48, 91],\n [-326, -189, 445, -125, -417, 61, 60, 277, -149],\n [-91, ... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-207, 252, 255, -58, -30, 131, 235, 92, -132],\n [113, -128, -140, 67, -45, -29, -60, 17, -22],\n [-306, 360, 378, -132, 36, 138, 258, 48, -72],\n [300, -336, -372, 192, -144, -60, -132, 72, -96],\n [-98, 140, 119, 49, -147, 154, 259, 189, -266],\n [71, -68, -89, 88... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[406, -396, 198, 243, 82, -56, -643, -513, -369],\n [219, -706, -42, 31, 571, 78, -309, -76, 118],\n [91, 27, 69, -406, -618, -39, 71, 598, -359],\n [-184, 285, -181, 46, 98, -406, 234, -59, 38],\n [-642, -131, -166, 259, 61, -204, 323, 645, -187],\n [232, -96, 113, ... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-102, 136, -116, 255, 34, -128, -228, -72, 83],\n [92, -62, 348, -510, -110, -74, 428, -88, -186],\n [-474, -69, 78, 84, 390, 12, -447, 186, -225],\n [-230, -73, -66, 154, 230, 104, -311, 170, -67],\n [184, -179, -106, -31, -32, 292, 115, 174, 50],\n ... | 3 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[265, 253, -2, -224, 173, -319, -492, -90, 74],\n [170, -147, 53, 504, 374, 359, -48, -495, -140],\n [15, 208, 395, 122, -439, 361, 232, -75, -163],\n [-151, -56, 394, 515, -300, 367, 328, -12, -73],\n [-235, -271, 257, 383, -463, 440, 616, 222, -83],\n ... | 8 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-324, -140, 106, 92, 256, -40, -42, -50, -90],\n [314, 63, -32, 112, -174, 83, -118, 187, 56],\n [26, -86, -508, 39, -125, 241, -256, -304, -97],\n [-116, 58, 235, -153, 85, -171, 245, 27, 46],\n [-234, -161, 313, 299, 307, -46, -147, 226, -72],\n [88, 1... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[478, 694, 471, 220, -9, 204, 275, -94, 103],\n [-348, 2, -786, -134, -534, -159, 68, -249, -225],\n [-210, -83, -716, -23, -308, -246, 20, -251, -184],\n [290, -249, 17, 148, 386, 16, 182, -216, -124],\n [-33, 65, -99, 618, 187, 65, 219, 15, 482],\n [... | 7 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-198, -375, 340, -127, 141, 261, -104, 383, -175],\n [76, 416, -314, 46, -130, -146, 36, -338, 250],\n [210, -58, -153, 49, -123, -24, 169, -41, -42],\n [-276, -348, 297, -135, 258, -60, -405, 324, -228],\n [-308, -307, 196, -331, -2, 608, -95, 466, 26],... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-181, -200, -130, 17, -123, 53, -132, 47, -366],\n [-468, -356, 329, 78, -172, 116, 219, 28, -312],\n [-313, -380, 148, 165, -152, 202, 248, -510, 293],\n [273, 234, -210, 283, -115, 101, -302, 48, -76],\n [397, -59, -285, -242, 198, -263, -517, 33, -2],... | 7 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[360, -345, 240, 382, -194, -164, 4, 397, -197],\n [-226, 257, -88, -204, 453, 275, -421, -227, 156],\n [-729, -79, 201, -533, -704, -563, 614, -145, 382],\n [-95, -669, 474, 132, 189, -140, 10, 232, 227],\n [-456, 378, 22, -464, -1175, -605, 497, 10, 53... | 8 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-259, 163, -84, -359, 157, 159, -453, -199, 443],\n [365, 162, -87, 79, 19, 687, 9, 440, 354],\n [-33, -275, 566, -221, -353, 136, 304, 176, -419],\n [-63, -492, 323, 150, -335, 86, -179, 132, -108],\n [-116, 303, -159, -75, -272, 45, 154, 199, 23],\n [57, 150, -466... | 8 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-202, 274, 28, 83, -41, -238, 211, -4, -132],\n [42, 182, -118, 291, 153, -282, 293, -320, 170],\n [-140, 94, 70, -84, -82, -50, -4, 134, -158],\n [-96, -395, 57, 455, 51, 144, -415, -143, -169],\n [92, -369, -21, 319, 118, 137, -311, -195, 37],\n [-1... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[19, 251, 35, -127, -180, -17, 77, -231, 251],\n [17, 135, 18, -64, -86, -14, 35, -128, 135],\n [-6, -126, -18, 66, 96, 6, -42, 114, -126],\n [54, 98, 8, -20, 4, -40, -14, -116, 98],\n [-2, -338, -50, 186, 280, 6, -126, 298, -338],\n [18, 156, 21, -75, -1... | 2 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[102, -17, -68, 221, -221, 272, 255, -238, -17],\n [42, -7, -28, 91, -91, 112, 105, -98, -7],\n [72, -12, -48, 156, -156, 192, 180, -168, -12],\n [-42, 7, 28, -91, 91, -112, -105, 98, 7],\n [-12, 2, 8, -26, 26, -32, -30, 28, 2],\n [-24, 4, 16, -52, 52, -... | 1 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-137, -145, 53, -236, -6, -30, 137, -259, -53],\n [-171, 223, -101, -130, -88, -64, -59, 121, -153],\n [187, -234, 145, 331, 163, 11, -72, 6, 178],\n [134, -446, 216, 232, 170, -86, -14, -224, 196],\n [167, -94, 59, 199, 81, 69, -16, 32, 124],\n [-243, ... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-92, 41, 288, -37, -149, -153, -486, -116, -171],\n [146, 63, -396, 349, 145, -99, 102, -46, 183],\n [-11, 127, -16, 13, -248, -175, -396, 65, -122],\n [-95, -20, 210, -108, 44, 30, 0, -55, -24],\n [-134, -58, 480, -218, -172, -33, -429, -105, -249],\n [251, -57, -3... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-240, -346, -84, -214, -462, 328, -488, 64, -120],\n [288, 210, 108, 102, 342, -192, 384, -48, 72],\n [-318, -125, -123, -32, -267, 107, -319, 38, -42],\n [-114, 266, -55, 223, 226, -267, 191, -30, 94],\n [186, 157, 69, 82, 243, -145, 269, -34, 54],\n [12, -148, 10,... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-99, -63, -230, -9, 238, 214, 62, -73, -14],\n [73, -13, 74, 215, -220, -86, -194, 171, -148],\n [86, 169, 140, 152, -525, -58, -388, 370, -123],\n [52, 0, 105, -40, 82, -143, 89, -152, 110],\n [-53, -100, 87, -273, 145, -71, 379, -131, 55],\n [-26, 70, -114, -59, 2... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-80, -40, -20, 45, -45, -60, -20, -5, -5],\n [160, 80, 40, -90, 90, 120, 40, 10, 10],\n [-192, -96, -48, 108, -108, -144, -48, -12, -12],\n [144, 72, 36, -81, 81, 108, 36, 9, 9],\n [272, 136, 68, -153, 153, 204, 68, 17, 17],\n [64, 32, 16, -36, 36, 48, 1... | 1 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-60, 10, -324, 253, 141, -90, -294, 157, 121],\n [80, -90, 248, -207, -119, 74, 162, -79, -31],\n [-25, -45, -253, 189, 103, -67, -270, 149, 134],\n [-15, -95, -315, 229, 123, -81, -366, 205, 196],\n [-130, 210, -250, 228, 136, -82, -72, 20, -58],\n [-1... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[227, -147, 105, -2, -24, -46, -87, -185, 2],\n [-419, 330, 266, -174, 425, -181, 200, 193, 128],\n [268, -186, -534, 300, -490, 254, -130, -44, -192],\n [-124, -78, -216, -92, 137, -113, -52, 88, 79],\n [141, -66, 261, -35, -134, 108, -17, -85, -20],\n [... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[34, 16, -3, -905, -498, -326, 425, -402, 207],\n [264, 334, 167, 169, -82, 300, -146, 335, 367],\n [114, -303, 156, 157, 418, -92, 321, -389, -532],\n [-258, -220, -460, 425, -404, 475, 54, 267, -619],\n [-97, -167, -176, 9, -291, -340, 425, 37, -316]... | 8 | MATH |
[
{
"content": "Compute the rank of the given 9x9 matrix:\n[[-162, 23, -100, -98, -106, 111, 275, -148, -70],\n [84, 302, -51, 19, -155, 285, -36, 317, 45],\n [-87, -99, 9, -15, 42, -72, 69, -147, 0],\n [-467, -90, 104, 76, 117, 18, 208, -316, 323],\n [-86, 40, 76, 84, 54, 36, -60, 36, 178],\n [388, 395, -133, -3... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[382, -129, -196, -282, 229, 125, -50, 490, -101],\n [-45, 236, -160, 345, -148, 145, 6, -135, -345],\n [288, -121, -440, -403, 250, 194, -211, 806, 66],\n [357, -265, -467, -114, 237, 137, -399, 209, -125],\n [-233, -89, 266, 343, 60, -127, 154, -131,... | 8 | MATH |
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