[User]
Calculate the rank of matrix A where A =
[[-60, -32, 14, -52, 24, 98, -12, 66, 40],
 [44, 26, -18, 24, -22, -66, 2, -52, -30],
 [-32, 45, -182, -374, -95, 196, -173, -53, 5],
 [194, 125, -111, 48, -115, -267, -19, -244, -135],
 [-220, -149, 148, -14, 143, 286, 41, 287, 155],
 [156, 68, 10, 220, -36, -290, 72, -150, -100],
 [-86, -113, 225, 300, 151, -15, 163, 190, 75],
 [-156, -144, 222, 204, 168, 114, 132, 258, 120],
 [12, -24, 90, 180, 48, -90, 84, 30, 0]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[-182, -61, -191, -8, 194, 139, -33, 179, 165],
 [-14, -40, -23, -38, 44, 46, -15, 47, 21],
 [-126, -156, -159, -126, 228, 210, -63, 231, 141],
 [-336, 77, -308, 186, 202, 67, 6, 152, 260],
 [-280, 118, -244, 212, 124, 2, 24, 76, 204],
 [-98, -93, -117, -68, 154, 135, -39, 153, 103],
 [378, -25, 361, -144, -278, -137, 15, -229, -307],
 [-98, -8, -97, 22, 84, 50, -9, 73, 83],
 [84, -83, 62, -114, 2, 47, -24, 22, -50]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[25, -15, 65, -75, -25, 50, 15, 20, 35],
 [-60, 36, -156, 180, 60, -120, -36, -48, -84],
 [5, -3, 13, -15, -5, 10, 3, 4, 7],
 [-30, 18, -78, 90, 30, -60, -18, -24, -42],
 [50, -30, 130, -150, -50, 100, 30, 40, 70],
 [-45, 27, -117, 135, 45, -90, -27, -36, -63],
 [-50, 30, -130, 150, 50, -100, -30, -40, -70],
 [-60, 36, -156, 180, 60, -120, -36, -48, -84],
 [70, -42, 182, -210, -70, 140, 42, 56, 98]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[70, 156, 213, -29, -168, 36, 134, 16, 135],
 [-105, -15, -185, 86, 106, -77, -73, 8, -112],
 [-5, -301, -23, -84, 10, 95, -275, -170, -144],
 [-355, 33, -26, 211, -326, -53, -507, -368, -391],
 [35, -233, -38, -83, 70, 69, -141, -72, -65],
 [185, -193, 339, -220, -210, 217, -83, -156, 94],
 [-120, 348, 105, 153, -228, -90, 78, -6, 15],
 [-275, -18, -104, 165, -158, -59, -386, -249, -316],
 [185, -113, 237, -178, -90, 149, 49, -32, 140]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[166, 129, 252, -193, 614, 44, 941, -403, 552],
 [-211, -117, -198, 146, -45, 301, 193, -116, -192],
 [396, 193, 214, -234, -64, -186, -43, 441, 184],
 [-61, -528, 31, 243, -304, 64, -221, -257, -116],
 [116, -209, 180, 377, -202, -21, 130, 346, -352],
 [48, -301, -330, -114, -270, 344, -138, -58, -237],
 [417, -284, -369, -72, 2, 281, -99, -483, -25],
 [-946, 39, -102, -154, 75, -61, -171, -167, -125],
 [-552, 433, -155, -98, -35, -78, -190, 591, -425]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[151, 138, 186, -98, -164, -178, -34, 13, -182],
 [-17, -206, 113, -43, 238, 243, -27, 178, -95],
 [-23, -64, 7, 15, 92, 91, 7, 30, -13],
 [-121, -178, -71, 133, 314, 303, 69, 2, 17],
 [13, 94, -142, -226, -452, -378, -162, 91, 322],
 [-142, -438, -3, -103, 356, 409, -95, 353, 113],
 [-170, 214, -418, 338, -66, -96, 186, -448, 282],
 [140, 188, 19, -341, -602, -531, -213, 141, 187],
 [-100, -320, 110, 174, 620, 578, 110, 86, -226]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[174, -16, -222, -180, -182, -64, 156, 24, -92],
 [-215, -16, -33, 154, 67, -48, -166, -20, -2],
 [-388, -47, 320, 453, 221, -255, -400, -58, 100],
 [238, 31, -38, -219, -79, 137, 214, 28, -12],
 [209, -40, -37, -96, -173, -230, 116, 14, -54],
 [-221, -70, 203, 329, 67, -375, -279, -41, 36],
 [87, 42, 49, -100, 39, 198, 98, 12, 34],
 [-307, -40, -233, 172, 7, -122, -216, -22, -70],
 [-250, 2, 362, 306, 244, -26, -256, -40, 132]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-156, -117, -65, -221, -65, -182, -143, -234, 78],
 [-12, -9, -5, -17, -5, -14, -11, -18, 6],
 [36, 27, 15, 51, 15, 42, 33, 54, -18],
 [24, 18, 10, 34, 10, 28, 22, 36, -12],
 [60, 45, 25, 85, 25, 70, 55, 90, -30],
 [-24, -18, -10, -34, -10, -28, -22, -36, 12],
 [-96, -72, -40, -136, -40, -112, -88, -144, 48],
 [-12, -9, -5, -17, -5, -14, -11, -18, 6],
 [192, 144, 80, 272, 80, 224, 176, 288, -96]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-359, -23, -252, -49, -52, 573, -241, -15, -242],
 [420, 222, 108, 179, 176, 167, 575, -534, 307],
 [98, 195, 481, -224, 28, 106, 147, 36, -197],
 [-173, -203, 83, -99, -20, 344, 21, -71, -95],
 [-283, 160, 303, -166, -658, 255, 170, 70, 85],
 [91, 444, 123, -26, -180, 507, 170, -106, -175],
 [421, 392, -448, 325, 708, 197, 165, -554, 85],
 [-421, 78, -174, -164, -34, -217, -561, 411, -231],
 [-352, -241, 257, -223, -592, -323, -222, 518, -28]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[-556, 224, -164, 32, -435, -239, 192, 661, 185],
 [329, 34, -442, -96, 205, -235, 58, -638, -508],
 [374, -594, 324, -228, 603, -84, -169, -456, -338],
 [-130, 106, 41, -205, 181, 83, 520, 79, 58],
 [67, -296, 341, -104, 346, 62, -69, -139, -183],
 [-696, -22, -250, -7, -280, -389, -317, 282, 442],
 [233, -248, -32, -121, 102, -145, 199, -467, -556],
 [46, -27, -44, 5, -255, -250, 172, 332, -215],
 [-906, -461, 340, -219, -366, -481, 2, 403, 506]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-230, -118, 272, -130, -338, -40, -66, 269, -398],
 [-150, 420, 182, -84, 70, 8, 254, 274, 408],
 [543, -290, -481, 390, 53, 76, 3, -360, 24],
 [172, 20, 66, 15, 150, 386, -174, 166, -14],
 [21, 252, 129, -76, 283, 300, -33, 174, 274],
 [-46, -223, 76, -80, -130, 46, -283, 30, -437],
 [315, 629, -113, 1, 269, 249, -332, 321, 229],
 [497, 351, -201, 84, 453, 505, -446, 129, 177],
 [-214, 413, 260, -159, -180, -74, 41, 455, 33]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[-148, -29, -50, -16, -19, 36, 86, 55, -45],
 [44, -119, 85, -200, 241, 701, -4, -121, 291],
 [-383, -69, -335, 134, -44, 16, -104, -105, -130],
 [-99, 280, -184, -58, -461, -301, -60, -174, -127],
 [167, -224, -23, 390, 390, -224, -304, 6, -39],
 [390, 25, 263, -112, 134, 181, -50, -47, 217],
 [-270, 42, -141, 48, -195, -273, 132, 114, -210],
 [-8, 83, -100, 0, -117, -22, -122, -153, 3],
 [106, 93, 79, -296, -54, 513, -2, -203, 257]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[64, 304, 107, 141, -193, -106, 236, -120, 55],
 [-165, -118, -1, 103, 43, -227, 271, -42, 32],
 [-141, -174, 80, -14, 88, -111, 4, -43, 69],
 [76, 390, 295, 97, -228, -116, 108, -180, 116],
 [169, 62, 149, -147, -79, 351, -451, -166, 216],
 [-126, -56, -272, 164, 74, -298, 494, 216, -272],
 [-57, 44, 137, -35, 40, -149, -29, 78, -91],
 [94, 12, 130, -170, 18, 208, -411, -3, 44],
 [216, 404, 183, -15, -207, 122, -144, -68, 25]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[374, 314, 649, 424, -157, 341, 325, 454, -48],
 [-232, -121, 72, -339, 74, 351, 193, 192, -224],
 [235, -50, -331, 109, 433, 345, 638, 384, 77],
 [-166, -37, -126, 209, 108, -91, -281, -344, -310],
 [-2, -79, -214, 73, -57, 420, 40, 198, -245],
 [134, -420, 414, -52, -388, -394, -222, -188, 296],
 [-315, -439, -245, -304, -219, -347, -288, -386, 161],
 [-100, -195, 432, 220, -265, -336, -271, -435, -50],
 [436, 150, 95, 204, -191, -113, 7, -126, 282]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[1019, -195, -438, -724, -288, 570, 192, 402, -321],
 [-198, 319, 132, -123, 174, 157, -272, 141, -474],
 [-393, 113, 183, 42, 254, 168, -160, 155, -141],
 [68, -35, 236, 152, 110, -108, -427, -203, -282],
 [-159, 158, 63, 248, -64, -391, 72, -407, 277],
 [7, 132, -218, 242, -292, -512, 155, 23, 133],
 [61, -601, -198, -120, -78, 268, 400, 282, 381],
 [-346, 15, 130, 610, 8, -559, -116, -144, 306],
 [221, 317, -437, -657, -163, 507, 460, 566, -173]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[134, 112, 68, -101, -181, -680, 408, -107, -180],
 [-407, -127, 283, 198, 238, -194, 339, 182, 254],
 [-70, 868, -159, -361, -565, -119, -412, -407, 188],
 [104, -343, 101, 39, -559, 174, 127, 581, 455],
 [-62, 44, 276, 229, -71, 501, -520, 77, 147],
 [14, 412, 128, -236, -256, -62, 56, -442, 564],
 [110, -322, -107, 110, -41, 462, -320, 354, -154],
 [-106, 533, -359, -146, -24, -90, -115, -298, -16],
 [529, -388, -44, -34, -57, -420, 696, -302, 165]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[245, -19, -245, -166, 68, -134, 173, -60, 506],
 [518, -34, -93, -97, 413, 308, -63, 38, -150],
 [-168, 63, 138, 145, -78, -12, 96, -368, -98],
 [309, 44, 155, -181, 170, 536, -405, -48, -106],
 [343, 95, -62, -109, 187, 128, -34, -246, 274],
 [-225, -68, 280, 188, -17, 268, -78, -74, -694],
 [-262, 57, 183, 409, 20, -119, 333, -530, -495],
 [74, 520, 183, 476, 284, -267, -129, -334, -253],
 [-183, 264, 59, 289, -32, -380, 47, -140, 8]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-158, 334, -129, -781, -6, -80, 38, -257, -63],
 [-330, 257, 18, -299, -83, -334, 250, -28, -10],
 [131, -853, -115, -47, 188, 225, -112, 77, 797],
 [398, -394, -155, 375, 116, 236, 376, 280, -113],
 [-29, -122, -795, 364, 51, -391, 354, -325, -206],
 [261, 22, -441, 306, 55, -201, -340, -208, 148],
 [-22, -44, -320, 189, 14, -125, -558, -376, 463],
 [313, 114, -385, 457, 27, -190, -208, -101, -22],
 [417, 23, -308, 685, 28, 100, -324, -80, 94]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[26, -433, -95, 23, -165, -247, 138, -66, 64],
 [-120, 5, 9, -106, 147, -175, 99, 24, -7],
 [666, -70, 216, 527, 30, 146, -561, -174, 131],
 [-277, 159, -91, -208, -188, 281, 127, 106, -89],
 [573, 52, 106, 468, -37, 188, -402, -142, 76],
 [-25, -84, -62, -30, 341, -620, 292, -46, 22],
 [403, 130, 106, 317, 293, -190, -193, -112, 57],
 [-241, -140, -38, -206, 133, -324, 236, 34, -2],
 [-71, 87, -83, -38, -246, 297, 25, 42, -51]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[58, 16, -288, -64, 122, -110, -458, 174, 84],
 [407, 121, 64, -267, 52, -389, 43, 265, 338],
 [262, 86, 261, -131, -1, -266, 378, 96, 186],
 [-139, -45, 124, 91, -104, 193, 209, -173, -130],
 [-56, -5, 274, 93, -43, 24, 446, -128, -88],
 [-426, -114, -209, 307, 93, 278, -254, -164, -346],
 [119, 30, 143, -85, -74, -45, 201, -1, 88],
 [-202, -62, 254, 148, -158, 270, 422, -274, -200],
 [-75, -5, -271, 82, 219, -119, -395, 137, -44]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[140, 14, -28, 70, 182, 224, 14, -252, -14],
 [-180, -18, 36, -90, -234, -288, -18, 324, 18],
 [30, 3, -6, 15, 39, 48, 3, -54, -3],
 [100, 10, -20, 50, 130, 160, 10, -180, -10],
 [-140, -14, 28, -70, -182, -224, -14, 252, 14],
 [-180, -18, 36, -90, -234, -288, -18, 324, 18],
 [-140, -14, 28, -70, -182, -224, -14, 252, 14],
 [180, 18, -36, 90, 234, 288, 18, -324, -18],
 [-180, -18, 36, -90, -234, -288, -18, 324, 18]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[439, 80, 250, -122, -465, -76, 336, -1, 65],
 [595, 145, 199, 119, -866, 95, 544, 186, -222],
 [42, 192, 27, -509, -554, 387, -171, 206, -28],
 [-53, -163, 290, -256, -131, -313, 132, 498, 288],
 [42, -217, 412, -213, -51, -465, 181, 144, 441],
 [156, 227, -119, 190, 35, 299, 17, -257, -81],
 [-211, -99, -10, 77, 31, 60, -208, -325, 40],
 [221, 107, -102, 97, -155, 122, 88, -205, -234],
 [148, 350, -160, -251, -374, 565, -134, 37, -192]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[164, 6, -110, 53, -171, 79, 51, 36, -122],
 [178, -36, -170, 14, -385, 107, 109, 116, -264],
 [-174, -54, 60, -105, -42, -60, 6, 48, -18],
 [172, -6, -130, 43, -237, 89, 69, 60, -166],
 [-138, -108, -30, -150, -339, -15, 87, 156, -216],
 [-398, -96, 170, -212, 33, -151, -21, 60, 44],
 [250, 108, -50, 182, 203, 71, -47, -124, 120],
 [-20, 30, 50, 25, 165, -25, -45, -60, 110],
 [14, 0, -10, 4, -17, 7, 5, 4, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-126, -362, 146, -244, -450, 28, -84, 86, -12],
 [236, 30, -193, -4, 60, -22, 203, 226, -108],
 [-131, 73, 96, 66, 75, 8, -119, -179, 78],
 [96, -8, -76, -16, 0, -8, 84, 104, -48],
 [-213, 55, 164, 62, 45, 16, -189, -253, 114],
 [-119, -77, 105, -42, -105, 14, -98, -77, 42],
 [347, -91, -267, -102, -75, -26, 308, 413, -186],
 [5, -137, 13, -98, -165, 6, 14, 87, -30],
 [106, 314, -124, 212, 390, -24, 70, -78, 12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-52, -50, -73, -78, -118, 6, 10, -95, -27],
 [-264, -294, 167, -106, 30, -206, -34, -431, -59],
 [-258, -282, 92, -142, -54, -170, -22, -428, -68],
 [-42, -30, -198, -138, -258, 66, 30, -90, -42],
 [109, 137, -278, -69, -257, 177, 47, 158, -6],
 [-3, -33, 399, 213, 465, -177, -63, 33, 57],
 [211, 233, -107, 99, 7, 153, 23, 347, 51],
 [-263, -283, 34, -177, -125, -147, -13, -442, -78],
 [10, 38, -366, -190, -422, 166, 58, -18, -50]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[52, 103, 69, -28, -77, -44, -138, 59, 129],
 [-395, 144, 81, -13, 118, 98, 498, 245, 77],
 [-289, -117, -164, -65, 198, 183, 530, -5, -351],
 [-3, -88, -111, 35, 114, 80, 138, -57, -159],
 [-397, 93, -38, 91, 177, 371, 646, -7, -350],
 [188, -248, -424, -77, 229, 238, 151, -251, -630],
 [-267, 83, 410, 92, -406, -72, -167, -177, 118],
 [313, -99, -268, 61, 138, 185, -94, -215, -357],
 [-561, 12, 275, -65, -169, -58, 348, 61, 64]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[69, 83, 15, 14, 16, 22, -22, 86, 42],
 [183, -177, 84, 225, 234, 30, -243, 81, -63],
 [-438, -482, -51, -165, -76, 80, 73, -661, -245],
 [280, 139, 94, 138, 171, 124, -201, 246, 84],
 [70, 118, -26, 40, -36, -140, 60, 200, 56],
 [-115, -288, 62, -31, 113, 262, -158, -387, -133],
 [-202, -201, -61, -47, -79, -116, 106, -203, -105],
 [-146, -207, -89, 53, -77, -316, 140, -31, -105],
 [183, 44, 84, 93, 151, 154, -184, 97, 35]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-6, 327, -471, -351, 414, 54, 132, -390, -354],
 [-8, 306, -443, -331, 390, 52, 126, -367, -334],
 [-8, 176, -258, -194, 228, 32, 76, -214, -196],
 [106, 203, -189, -101, 138, -34, -32, -148, -94],
 [272, 126, 77, 157, -138, -148, -234, 85, 178],
 [-68, -194, 212, 132, -168, 12, -4, 170, 128],
 [138, -111, 288, 264, -288, -102, -186, 249, 276],
 [90, -95, 220, 196, -216, -70, -130, 189, 204],
 [-42, 209, -337, -265, 306, 58, 124, -282, -270]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[83, 60, -29, 583, -155, -194, -303, 829, -120],
 [449, 108, -170, 31, 193, 69, -287, 249, -704],
 [171, 54, -102, 62, -236, -75, 542, 92, 222],
 [651, 447, -52, -14, 57, -17, 296, -67, -278],
 [552, -134, 22, -141, 474, -42, 102, -500, -352],
 [-42, -109, -14, -164, 319, -76, -157, -34, -2],
 [199, 511, -392, 514, 155, -109, 7, 420, -296],
 [219, 248, -390, -85, 411, 49, 172, -110, -438],
 [294, -226, -119, -108, 651, 121, -237, -408, -824]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[11, -6, 1, 4, -1, 3, 12, -10, -12],
 [55, -30, 5, 20, -5, 15, 60, -50, -60],
 [-66, 36, -6, -24, 6, -18, -72, 60, 72],
 [-77, 42, -7, -28, 7, -21, -84, 70, 84],
 [143, -78, 13, 52, -13, 39, 156, -130, -156],
 [-77, 42, -7, -28, 7, -21, -84, 70, 84],
 [198, -108, 18, 72, -18, 54, 216, -180, -216],
 [-22, 12, -2, -8, 2, -6, -24, 20, 24],
 [55, -30, 5, 20, -5, 15, 60, -50, -60]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[70, -140, -30, -110, -60, 130, 80, 70, -100],
 [-14, 28, 6, 22, 12, -26, -16, -14, 20],
 [-98, 196, 42, 154, 84, -182, -112, -98, 140],
 [-7, 14, 3, 11, 6, -13, -8, -7, 10],
 [-35, 70, 15, 55, 30, -65, -40, -35, 50],
 [84, -168, -36, -132, -72, 156, 96, 84, -120],
 [-7, 14, 3, 11, 6, -13, -8, -7, 10],
 [42, -84, -18, -66, -36, 78, 48, 42, -60],
 [-56, 112, 24, 88, 48, -104, -64, -56, 80]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[422, 305, -114, -96, 266, -366, -302, 29, 13],
 [-26, -161, -363, -73, -340, -83, 431, -54, -27],
 [186, -319, 712, -102, -335, 389, 29, 106, -267],
 [-71, -262, 525, 201, -258, 491, -157, 405, -279],
 [40, -425, 33, 385, -364, 23, 64, -280, 435],
 [126, -87, -70, -240, -118, 82, 420, -211, 333],
 [-410, -22, 107, 128, 60, 61, -130, 13, -308],
 [-247, 399, -799, 203, 431, -318, -121, 61, 336],
 [191, -216, 188, 173, -345, 205, -81, 377, -199]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[5, 186, -242, -160, 265, -414, 164, -82, 53],
 [-129, -405, 24, -189, -303, 455, 463, 350, -226],
 [-155, 536, -241, 47, 182, -308, 90, -233, 375],
 [51, 36, -228, -42, 151, -104, -150, 238, -1],
 [9, -332, -233, -423, -676, 102, 555, -125, -430],
 [285, -478, -477, -224, -511, -301, 79, -115, -139],
 [-149, -70, -116, -116, -275, 67, 306, -170, -164],
 [44, -454, 68, 166, -384, 471, -95, 317, 87],
 [69, -57, 19, 394, 186, 3, -596, 91, 247]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-3, 173, -284, 145, 244, -23, 269, -172, -59],
 [167, 532, 220, -252, -87, 233, 204, 384, -389],
 [-131, 9, 368, -427, 250, -453, -645, -160, 83],
 [-87, 156, 150, -370, -2, -223, -247, -142, 267],
 [2, 126, -351, 210, 338, 146, 276, -134, -275],
 [67, -244, 2, 96, -108, 204, -79, -98, 86],
 [125, 341, 111, -99, 176, 195, 84, 216, -503],
 [-40, -165, -37, 151, -270, -401, 108, -160, 628],
 [238, 359, -191, 363, 256, -99, 540, -132, -140]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[5, -65, -20, 65, -50, 65, -70, -65, 10],
 [3, -39, -12, 39, -30, 39, -42, -39, 6],
 [-17, 221, 68, -221, 170, -221, 238, 221, -34],
 [-12, 156, 48, -156, 120, -156, 168, 156, -24],
 [-16, 208, 64, -208, 160, -208, 224, 208, -32],
 [-3, 39, 12, -39, 30, -39, 42, 39, -6],
 [-2, 26, 8, -26, 20, -26, 28, 26, -4],
 [-9, 117, 36, -117, 90, -117, 126, 117, -18],
 [2, -26, -8, 26, -20, 26, -28, -26, 4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[111, 84, 309, 39, 60, 381, 45, -57, 462],
 [113, 4, 11, 13, 92, 59, -165, -51, 74],
 [19, -6, -23, 0, 18, -17, -45, -8, -20],
 [97, -52, -197, -7, 100, -173, -285, -39, -206],
 [-178, -14, -46, -23, -142, -124, 240, 81, -154],
 [-165, -12, -39, -21, -132, -111, 225, 75, -138],
 [-223, -12, -37, -27, -180, -133, 315, 101, -166],
 [263, -22, -91, 20, 226, 11, -465, -116, 20],
 [-165, -70, -255, -40, -110, -345, 75, 80, -420]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-224, 117, -283, 200, -199, -16, 76, -209, -210],
 [409, -467, 359, -107, -145, 270, -77, -88, 197],
 [146, 39, 219, -50, 159, 56, 38, 103, 132],
 [-238, -35, -335, 30, -179, -136, -82, -87, -184],
 [309, -105, 369, -33, 81, 204, 57, 18, 195],
 [-215, 318, -180, 176, 24, -59, 136, -61, -138],
 [175, -160, 174, -63, -6, 96, -29, 7, 103],
 [-51, -116, -94, -124, -10, -115, -132, 81, -10],
 [-144, 411, -109, 510, -193, 238, 390, -415, -216]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-6, -51, -51, 15, 24, -45, 51, 3, -21],
 [-26, -221, -221, 65, 104, -195, 221, 13, -91],
 [-16, -136, -136, 40, 64, -120, 136, 8, -56],
 [6, 51, 51, -15, -24, 45, -51, -3, 21],
 [-14, -119, -119, 35, 56, -105, 119, 7, -49],
 [30, 255, 255, -75, -120, 225, -255, -15, 105],
 [6, 51, 51, -15, -24, 45, -51, -3, 21],
 [0, 0, 0, 0, 0, 0, 0, 0, 0],
 [-18, -153, -153, 45, 72, -135, 153, 9, -63]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-71, -244, 603, -69, -433, 68, 139, 216, 316],
 [-186, -474, -140, 275, 217, 159, 386, -6, -105],
 [-21, 18, 228, -352, 255, 75, 84, 27, -161],
 [656, 106, 603, -180, -410, -63, -146, -420, 25],
 [-225, 242, -170, -71, 417, 220, 149, 360, -166],
 [-570, -339, 501, -39, -15, 184, -53, -326, -189],
 [794, -73, 17, -423, -757, -652, -257, -581, 261],
 [185, 380, 741, -145, -288, 222, -236, -268, -126],
 [592, 316, -407, -392, 321, -442, -464, 25, -56]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[267, 2, 341, -110, -92, -424, -190, -341, -284],
 [48, 187, -352, -103, 252, -420, 350, -353, 408],
 [-216, 269, -317, 69, -272, -54, 415, 37, 1],
 [115, 413, -279, -477, 66, -186, 70, -182, 38],
 [239, -8, 478, -187, -227, 221, 62, 275, -338],
 [84, -235, 16, 48, 127, 302, -83, -73, 62],
 [25, -350, 162, 331, -108, -667, 252, 14, -210],
 [-161, 546, -454, -420, -122, 299, 158, 239, -8],
 [22, -150, 327, -37, -324, 352, 179, 733, -501]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-88, 88, -8, -48, 136, 0, -48, 56, -80],
 [66, -66, 6, 36, -102, 0, 36, -42, 60],
 [55, -55, 5, 30, -85, 0, 30, -35, 50],
 [-77, 77, -7, -42, 119, 0, -42, 49, -70],
 [88, -88, 8, 48, -136, 0, 48, -56, 80],
 [198, -198, 18, 108, -306, 0, 108, -126, 180],
 [-55, 55, -5, -30, 85, 0, -30, 35, -50],
 [-11, 11, -1, -6, 17, 0, -6, 7, -10],
 [121, -121, 11, 66, -187, 0, 66, -77, 110]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-225, 225, -195, 210, -210, 0, -15, -240, 225],
 [-180, 180, -156, 168, -168, 0, -12, -192, 180],
 [180, -180, 156, -168, 168, 0, 12, 192, -180],
 [150, -150, 130, -140, 140, 0, 10, 160, -150],
 [-105, 105, -91, 98, -98, 0, -7, -112, 105],
 [-210, 210, -182, 196, -196, 0, -14, -224, 210],
 [-210, 210, -182, 196, -196, 0, -14, -224, 210],
 [225, -225, 195, -210, 210, 0, 15, 240, -225],
 [-135, 135, -117, 126, -126, 0, -9, -144, 135]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[286, 279, -421, 219, -404, 193, -200, 270, 4],
 [-194, 147, 347, 156, 539, 304, -279, 6, 263],
 [54, -164, -84, -133, -189, -253, 231, -88, -143],
 [215, 195, 151, 345, 405, -44, -22, -100, 296],
 [111, 298, -141, -148, -256, 137, 43, -43, -111],
 [5, 36, 85, -510, -182, -259, 495, -411, -287],
 [20, -202, -455, -287, -760, -107, 118, 173, -388],
 [113, 141, -176, 339, -26, 230, -327, 285, 163],
 [218, -62, -122, 83, -107, -269, 189, -64, -13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[2, 94, -255, 56, -85, -241, 47, -120, -168],
 [-239, 355, 247, -550, -393, 178, 123, 238, 30],
 [44, 310, 384, -322, -428, 416, 144, 2, -178],
 [412, -194, 176, -318, -338, 319, -361, -92, -113],
 [23, -17, -68, 176, -346, 48, -197, 268, -217],
 [-194, -103, 133, -324, 404, 132, -323, 358, 227],
 [108, -76, 138, 172, -492, 72, 100, -98, 38],
 [-130, -255, -86, -190, 495, -25, -548, 370, 147],
 [295, -348, 76, -191, -246, 82, -268, -89, 187]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-24, 118, -93, 615, 43, 34, 472, -66, 96],
 [-51, -497, 0, -213, 297, 11, -10, -118, 377],
 [-536, -287, 362, 162, 79, -356, -297, -182, 8],
 [115, -79, -26, -314, -138, 58, -315, 194, -132],
 [-144, -265, 49, 269, 66, 16, 163, 10, 166],
 [-127, 34, 101, 177, -44, -7, 128, 3, -17],
 [-105, 238, 45, 410, -205, -91, 3, 72, -251],
 [-151, -514, -25, 290, -51, -149, -415, 168, -13],
 [-247, -339, 260, -417, 113, -106, -286, -79, 114]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[459, -171, -17, 266, -331, -11, 13, 523, 53],
 [-82, 123, -260, 189, 369, 411, 82, -174, -164],
 [73, 395, -198, 130, 310, -280, -457, -165, 150],
 [-80, -303, 178, 228, -177, 405, 376, -514, -282],
 [135, -160, 200, 254, 275, 103, 205, 547, 84],
 [-477, 86, 75, -50, 714, 309, 230, -260, -92],
 [-161, -50, -5, -374, 22, 8, 137, 417, 49],
 [-206, 273, -38, -467, 133, -454, -311, 131, 231],
 [8, -223, -98, -81, -345, 342, 285, 11, -207]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[34, -28, 8, 4, -32, -24, -22, 6, 4],
 [170, -140, 40, 20, -160, -120, -110, 30, 20],
 [102, -84, 24, 12, -96, -72, -66, 18, 12],
 [51, -42, 12, 6, -48, -36, -33, 9, 6],
 [-306, 252, -72, -36, 288, 216, 198, -54, -36],
 [-187, 154, -44, -22, 176, 132, 121, -33, -22],
 [-238, 196, -56, -28, 224, 168, 154, -42, -28],
 [221, -182, 52, 26, -208, -156, -143, 39, 26],
 [119, -98, 28, 14, -112, -84, -77, 21, 14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[101, 934, 381, -178, -637, -13, 156, 547, -507],
 [126, 182, 137, -477, -437, -324, -279, 265, 673],
 [-165, -345, 94, 681, 263, -73, 204, -253, -296],
 [-62, -120, 105, -447, -353, -477, -310, 438, 487],
 [-453, -763, -26, 129, 148, -371, -392, -802, 537],
 [-53, 372, 314, 13, 26, 182, -268, -249, 302],
 [65, 52, -207, -565, 125, 253, -334, 44, 369],
 [183, -226, -368, 274, 538, 439, 333, -155, -335],
 [-84, 42, -211, -22, 337, 451, 64, -141, -508]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-186, -75, 8, 41, -68, 51, -188, 26, 335],
 [-394, -317, -203, 389, -186, 112, 158, -61, -157],
 [-109, -120, -361, 105, 286, -375, -275, 21, -200],
 [-146, -502, -807, -15, -179, -339, 191, -73, -708],
 [173, -141, -466, -87, -244, -50, 653, -131, -776],
 [110, 158, 130, 114, 419, -193, 415, -36, -132],
 [503, 525, 598, -425, 287, -281, 58, -82, 313],
 [-45, -107, 555, 213, 459, 156, 172, 163, -3],
 [112, -288, 202, -222, -458, -400, 594, -138, -262]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-130, -120, 190, -180, -30, 80, 200, 120, 130],
 [208, 192, -274, 204, 66, -110, -266, -204, -136],
 [-208, -192, 159, 118, -135, 41, 59, 250, -140],
 [130, 120, -195, 194, 27, -83, -209, -118, -142],
 [-104, -96, 187, -242, -3, 85, 223, 82, 188],
 [-65, -60, 0, 176, -72, -17, -71, 98, -163],
 [117, 108, -121, 22, 57, -42, -90, -128, 3],
 [-39, -36, 7, 86, -39, -6, -30, 56, -81],
 [-130, -120, 200, -208, -24, 86, 218, 116, 154]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[-36, 96, 96, 168, 84, -72, 72, -84, 96],
 [-6, 16, 16, 28, 14, -12, 12, -14, 16],
 [-21, 56, 56, 98, 49, -42, 42, -49, 56],
 [-36, 96, 96, 168, 84, -72, 72, -84, 96],
 [30, -80, -80, -140, -70, 60, -60, 70, -80],
 [-33, 88, 88, 154, 77, -66, 66, -77, 88],
 [-45, 120, 120, 210, 105, -90, 90, -105, 120],
 [-9, 24, 24, 42, 21, -18, 18, -21, 24],
 [-9, 24, 24, 42, 21, -18, 18, -21, 24]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[117, -123, 137, 409, 172, -35, 368, 276, -117],
 [36, 378, 33, 57, -267, -195, -255, 279, 333],
 [-314, -1, -201, -148, -411, 245, -217, -53, 75],
 [-190, -254, -63, 165, -113, 237, 207, 45, -181],
 [286, -34, 98, -75, 484, -132, 112, -156, -67],
 [399, 276, 330, 366, 231, -498, 153, 393, 123],
 [89, 346, -3, -333, -80, -231, -414, -124, 262],
 [357, 81, 202, 257, 413, -244, 229, 207, 33],
 [-100, -17, -275, -332, 61, 343, -213, -245, 145]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-336, -63, -154, -123, -384, 297, -66, -309, -165],
 [-48, -177, -1, 124, -217, 154, -449, -428, 119],
 [246, -367, 277, -556, 902, -99, 68, 318, 788],
 [-144, 24, -44, -344, 204, 68, 336, 188, 56],
 [-182, 243, 74, 417, -633, 172, -65, -131, -532],
 [-312, 314, 293, 134, -59, 371, 78, -85, -4],
 [28, 184, 140, 459, -166, 60, -302, -249, -17],
 [-108, 470, 276, 135, 274, 94, 366, 271, 19],
 [102, -169, 74, -298, 599, -24, -46, 9, 596]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[0, 39, -12, 36, 30, 51, 24, 48, -33],
 [0, 91, -28, 84, 70, 119, 56, 112, -77],
 [0, 26, -8, 24, 20, 34, 16, 32, -22],
 [0, -78, 24, -72, -60, -102, -48, -96, 66],
 [0, -65, 20, -60, -50, -85, -40, -80, 55],
 [0, 104, -32, 96, 80, 136, 64, 128, -88],
 [0, 13, -4, 12, 10, 17, 8, 16, -11],
 [0, -221, 68, -204, -170, -289, -136, -272, 187],
 [0, 208, -64, 192, 160, 272, 128, 256, -176]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-45, -106, 212, -56, 301, -102, -656, -512, 41],
 [-136, -110, 206, -25, -616, 214, 206, 114, -241],
 [-532, 81, -101, 161, -250, 95, -64, -118, -318],
 [-68, 388, -450, -74, 213, 69, 472, 376, 217],
 [151, -51, 209, 94, 74, -136, -310, -134, -1],
 [-62, 106, -75, 271, -163, -120, 92, 269, -203],
 [-278, 417, -400, 3, 62, 148, 410, 233, 99],
 [-326, -67, 46, 35, -287, -161, -386, 233, -456],
 [-259, 442, -76, 240, -6, 291, 280, -350, 190]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[343, -12, -462, -268, -95, 146, 180, -420, -480],
 [-591, 162, 307, 615, -400, 428, 77, 279, 208],
 [495, 46, 518, 89, 71, -178, -80, 372, 279],
 [73, -477, 519, 93, 171, -379, -527, -391, -306],
 [186, 346, -21, 333, -249, 67, 406, 112, 323],
 [-299, 357, -142, 295, -376, 21, 235, 95, 434],
 [-361, 323, -342, 55, 240, 870, 647, 293, -44],
 [490, 265, -392, -367, -63, -244, 200, 88, 233],
 [260, 229, -741, -93, 211, 50, 711, -348, -59]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[-64, 124, -60, -85, -62, 13, -28, -18, -58],
 [30, 240, 0, -195, 60, 105, -150, -90, -60],
 [108, -196, 100, 133, 106, -17, 40, 26, 94],
 [111, -66, 90, 30, 123, 33, -33, -18, 57],
 [74, 168, 40, -147, 104, 101, -138, -82, -24],
 [33, 158, 10, -131, 55, 76, -107, -64, -35],
 [87, -46, 70, 19, 97, 28, -29, -16, 43],
 [-37, 234, -50, -177, -19, 68, -105, -64, -81],
 [-15, 198, -30, -153, 3, 66, -99, -60, -63]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[192, 203, 9, 118, 125, -228, 100, -24, -137],
 [-246, -33, -193, 72, 119, -10, -4, 174, 334],
 [-143, -290, -178, 137, -308, 789, -156, 141, 590],
 [-438, 310, -181, 517, 248, -417, 434, -72, 177],
 [-301, -139, -231, 144, 156, 275, 268, 494, 432],
 [32, 217, -161, 461, 94, 193, 338, 200, 267],
 [206, 85, 253, -388, 49, -376, -152, -180, -523],
 [256, -6, 303, -624, -161, 19, -478, -195, -400],
 [-301, 89, -158, 296, -27, 336, 170, 129, 418]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[99, -77, 154, 99, -11, 99, 99, -55, -121],
 [72, -56, 112, 72, -8, 72, 72, -40, -88],
 [0, 0, 0, 0, 0, 0, 0, 0, 0],
 [81, -63, 126, 81, -9, 81, 81, -45, -99],
 [-81, 63, -126, -81, 9, -81, -81, 45, 99],
 [-27, 21, -42, -27, 3, -27, -27, 15, 33],
 [108, -84, 168, 108, -12, 108, 108, -60, -132],
 [-81, 63, -126, -81, 9, -81, -81, 45, 99],
 [-81, 63, -126, -81, 9, -81, -81, 45, 99]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-251, 208, 277, -144, -321, -229, -714, 358, -598],
 [-5, -255, 11, -23, -201, 409, 288, -47, -299],
 [53, 394, 16, 9, -237, -281, -461, 242, -202],
 [-118, 231, -267, 355, 25, 79, 58, -271, 354],
 [-120, 220, -179, 434, 131, 260, 175, -216, 73],
 [520, 256, 99, -16, 664, -86, 406, -124, -227],
 [-807, 273, 38, 719, 367, 229, 48, -199, 320],
 [-80, 439, -121, 250, 174, 357, 399, -590, -585],
 [-128, -6, 51, 62, 4, -339, -369, 287, 558]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-111, 116, 187, 301, -332, 407, 691, 66, 142],
 [-367, 410, 166, 143, -218, 316, 748, 259, -72],
 [-275, 14, 56, -140, -67, -278, 56, -50, 23],
 [113, -544, 333, -457, -359, -682, -59, -447, -321],
 [-590, 138, 135, -349, -270, -146, 433, -95, -22],
 [-577, 135, 16, -459, -491, -400, 413, -331, -29],
 [9, 327, -131, 648, -147, 236, 277, 120, 427],
 [69, 20, -120, 8, 397, 122, -134, 314, -163],
 [101, -405, -96, 32, -361, -542, -152, -514, 354]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-81, 356, -330, 457, 400, -324, -161, 570, -177],
 [21, 5, 14, 127, -28, 188, 80, -60, -122],
 [210, 9, 272, -267, -159, 515, 152, -189, 51],
 [-53, -309, 428, -260, -186, 172, 263, -226, 470],
 [74, 227, -356, 48, 51, -292, -294, 40, -327],
 [-71, 190, -54, 120, 232, -379, -81, 371, 223],
 [214, -100, 220, -114, -295, 768, 229, -446, -250],
 [89, 471, -240, 406, 278, -80, -107, 398, -248],
 [-273, -178, 168, 167, 156, -285, 158, 251, 457]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-200, -12, 130, 290, 124, -240, 2, 202, -36],
 [-309, 632, -250, -79, 68, 42, 304, 502, -291],
 [-262, 151, 265, 542, 103, -463, 492, 453, -470],
 [199, -57, 246, 98, -166, -74, 543, -53, -422],
 [-191, 180, 141, 318, -71, -312, -2, 156, -79],
 [-314, 394, -273, -11, 214, 117, 94, 273, -139],
 [74, -137, -397, 7, 107, -166, -639, -16, 474],
 [68, 182, -78, -4, -202, 78, -4, -294, -80],
 [-398, 196, 271, 641, 64, -468, 123, 241, -244]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[169, -136, 55, -101, 262, 29, 201, -310, 91],
 [165, -13, 107, 178, -96, -277, 252, -23, -231],
 [-314, -165, 0, 135, 73, -126, 301, 147, -17],
 [-104, 35, 303, 239, 37, -442, 316, 108, -184],
 [-171, -384, -394, 475, -224, 399, 455, 194, -172],
 [360, 404, -43, -218, -445, 204, -594, -156, 142],
 [-140, -396, -348, 844, -162, 456, 464, 500, -530],
 [672, 470, 516, -150, 30, -328, -307, -387, -76],
 [10, 13, 90, -760, 337, -448, -140, -369, 351]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[244, -288, 246, 74, 332, -14, 296, -530, -12],
 [-331, 91, -172, -271, -213, -27, -179, 219, 313],
 [33, 19, 2, 43, -1, 7, -3, 25, -59],
 [-244, 288, -246, -74, -332, 14, -296, 530, 12],
 [73, 91, -22, 123, -41, 23, -43, 137, -179],
 [-374, 54, -168, -334, -202, -38, -166, 166, 402],
 [-220, 8, -86, -210, -100, -26, -80, 58, 260],
 [201, 79, 32, 241, 23, 37, 9, 91, -323],
 [120, 14, 37, 125, 40, 17, 30, -1, -160]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[70, 233, -712, -259, -20, 9, -559, 330, -55],
 [-126, 125, -52, 356, -261, 359, -34, 58, 38],
 [134, -305, 434, 157, -218, 168, 204, -48, -296],
 [247, 150, 109, -170, 395, -304, 48, -173, -120],
 [379, 55, -160, -193, 120, -219, -186, 39, -331],
 [-139, -85, 67, -235, 19, -551, -74, -577, -78],
 [-85, 228, -110, 4, 232, 165, 1, 195, 256],
 [-173, 66, -205, 260, -277, 570, -106, 411, 152],
 [173, 96, 207, -276, 505, -496, 140, -323, -28]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-22, 44, -99, 187, -55, 143, 165, 132, 143],
 [0, 0, 0, 0, 0, 0, 0, 0, 0],
 [0, 0, 0, 0, 0, 0, 0, 0, 0],
 [12, -24, 54, -102, 30, -78, -90, -72, -78],
 [18, -36, 81, -153, 45, -117, -135, -108, -117],
 [-20, 40, -90, 170, -50, 130, 150, 120, 130],
 [-18, 36, -81, 153, -45, 117, 135, 108, 117],
 [12, -24, 54, -102, 30, -78, -90, -72, -78],
 [8, -16, 36, -68, 20, -52, -60, -48, -52]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-135, -524, -560, -295, 69, 28, 250, 337, 294],
 [-471, -326, 92, 300, 5, 185, -43, -180, 19],
 [467, 317, 12, 92, 413, 35, 236, 82, 506],
 [-497, -705, -392, -299, -111, 99, 138, 229, -40],
 [-107, 138, 306, 298, -327, 17, -112, -201, -401],
 [-344, -308, 24, 313, -200, 162, 108, -58, -121],
 [-232, -114, 136, 469, 428, 170, -142, -298, 381],
 [-217, -501, -438, -43, -99, 82, 274, 243, 194],
 [-336, -641, -580, 7, -258, -55, -34, 146, -71]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-88, 241, -77, 149, -239, -186, 259, -73, -267],
 [202, 61, 130, -296, -61, -47, -351, -43, -115],
 [4, -603, -32, -457, -246, 430, -538, 864, 112],
 [244, -196, -287, 153, 343, -292, 206, -239, 642],
 [235, -66, -121, 259, 53, 235, -260, 123, 275],
 [-119, 238, 25, 111, -35, 131, 82, -152, -152],
 [-156, 336, -240, -334, -215, -471, 488, -477, -254],
 [60, -146, -562, -348, 86, 124, 464, -209, -427],
 [162, 55, -72, 43, 216, 186, -174, -245, 149]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[342, 39, -358, 209, 141, -7, -415, -278, 139],
 [96, 17, -12, 51, 141, -41, -103, 262, -13],
 [222, 6, -166, 220, 252, 94, -276, 2, 48],
 [-180, -26, 202, -87, -36, 32, 216, 179, -82],
 [-228, 50, 124, -446, -522, -394, 318, 0, -14],
 [63, -79, -19, 372, 396, 457, -132, -143, -14],
 [-168, -50, 212, 20, 90, 166, 186, 174, -94],
 [-159, -3, 75, -170, -246, -71, 194, -157, -8],
 [-162, 4, 128, -191, -204, -114, 208, 49, -38]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-2, -78, 437, 99, -202, 64, -10, 64, -213],
 [3, -108, 357, 114, -222, 54, -60, -21, -168],
 [-3, -72, 453, 96, -198, 66, 0, 81, -222],
 [-36, 324, 90, -234, 396, 0, 396, 576, -90],
 [16, -168, 68, 132, -232, 16, -184, -248, -12],
 [20, -210, 85, 165, -290, 20, -230, -310, -15],
 [34, -300, -112, 214, -360, -4, -372, -546, 98],
 [6, -24, -150, 4, 4, -20, -56, -106, 80],
 [12, -60, -246, 22, -20, -32, -116, -208, 134]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[0, 225, -45, 45, 195, -255, -30, 60, -105],
 [0, -255, 51, -51, -221, 289, 34, -68, 119],
 [0, 270, -54, 54, 234, -306, -36, 72, -126],
 [0, -240, 48, -48, -208, 272, 32, -64, 112],
 [0, -225, 45, -45, -195, 255, 30, -60, 105],
 [0, 255, -51, 51, 221, -289, -34, 68, -119],
 [0, 120, -24, 24, 104, -136, -16, 32, -56],
 [0, -225, 45, -45, -195, 255, 30, -60, 105],
 [0, 255, -51, 51, 221, -289, -34, 68, -119]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[84, 30, 21, 27, 147, 315, 9, 468, -162],
 [-399, -300, -286, 212, -184, -281, 24, 13, 229],
 [304, 0, -68, -55, 215, 348, -135, 265, -313],
 [-188, 262, 73, -37, 179, -9, 181, 380, -6],
 [-191, 162, -213, -68, 238, -206, 54, 146, -78],
 [342, 42, 209, -59, 27, 349, -68, 57, -152],
 [161, 98, -193, -90, 344, 198, -90, 342, -336],
 [-42, 76, 120, -68, -142, -270, 39, -463, 172],
 [152, -172, 402, 128, -376, 278, 26, -96, 206]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[308, 152, -100, -228, -103, 547, -215, 115, -48],
 [-208, -28, 158, 160, 193, -306, 209, -28, -2],
 [-331, -107, 126, 309, 233, -388, 278, -95, 78],
 [295, 116, -152, -196, -125, 590, -216, 178, 17],
 [-195, 69, 164, 273, 310, -138, 147, -723, -168],
 [-355, 137, 442, 349, 650, -249, 491, -64, -74],
 [35, -241, -330, -41, -459, -204, -280, -361, 58],
 [260, -117, -332, -269, -458, 275, -296, 488, 187],
 [-62, -243, -188, -31, -381, -500, -169, -341, -1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-10, 133, 82, -393, -223, 319, -21, 263, -115],
 [-45, 4, 199, -260, -198, 222, -14, 24, -126],
 [56, -188, -49, -5, 140, -379, 121, 202, 17],
 [105, 204, 188, 4, 218, -220, 231, -211, 205],
 [88, 383, -229, -236, 180, -55, 215, 4, -80],
 [8, 36, -120, -332, -129, 117, -9, 443, -124],
 [210, 149, 553, -47, -212, 612, -89, -19, 268],
 [629, -784, 347, 723, 171, 80, -103, 68, 194],
 [199, 132, 59, -156, 278, -390, 318, 180, 170]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[-63, -152, -166, 294, -81, 58, -128, 149, -554],
 [-222, 34, 380, 316, -42, -166, -28, -320, 51],
 [-153, 239, 266, 363, 232, -223, 19, -235, -156],
 [691, 839, -74, 105, 561, 602, -241, 487, -32],
 [335, 254, -338, -40, 28, 33, 104, 367, 135],
 [151, -81, -252, -22, 327, 150, -216, 184, -263],
 [353, -200, -95, -116, 457, 962, -218, 562, -33],
 [18, 284, 22, -213, 521, 162, 55, 17, -399],
 [408, 20, 45, -126, 245, 201, -488, -33, 716]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-291, 190, 137, -27, -118, -466, -225, 196, -59],
 [-20, 60, 397, -343, 25, -16, 272, -380, 148],
 [417, 62, 220, 204, -268, 265, 629, 402, -135],
 [580, -234, -241, -353, 431, 454, -233, -423, 65],
 [-134, -210, 320, -187, 373, -303, 80, 71, 595],
 [189, -1, -210, 390, -201, 426, 6, 78, -277],
 [8, 352, 223, -71, 2, -103, -391, -423, -465],
 [195, -260, 169, 322, -792, 500, 295, 381, -28],
 [394, 167, -219, -130, -305, 280, 8, 72, -370]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[5, -75, 15, -60, -5, -45, 60, 35, 35],
 [10, -150, 30, -120, -10, -90, 120, 70, 70],
 [-11, 165, -33, 132, 11, 99, -132, -77, -77],
 [-6, 90, -18, 72, 6, 54, -72, -42, -42],
 [6, -90, 18, -72, -6, -54, 72, 42, 42],
 [10, -150, 30, -120, -10, -90, 120, 70, 70],
 [5, -75, 15, -60, -5, -45, 60, 35, 35],
 [8, -120, 24, -96, -8, -72, 96, 56, 56],
 [7, -105, 21, -84, -7, -63, 84, 49, 49]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-178, -197, -106, 194, -88, 27, 29, 175, -162],
 [-356, -683, -173, -45, -128, -136, 57, -42, -79],
 [-263, 227, -148, 350, -270, -13, 4, 401, -123],
 [418, -277, 301, 527, 320, 596, 341, 472, -380],
 [79, -583, 193, 91, 58, 196, 372, 208, -18],
 [321, -143, 123, -55, 298, 218, 54, -130, -64],
 [-373, 131, -213, -317, -260, -454, -266, -308, 208],
 [372, 151, 533, 120, 181, 157, 137, 108, 7],
 [-84, -219, 221, 30, -175, -49, 287, 228, 166]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[24, -156, 48, 156, 120, 144, 72, -204, 36],
 [8, -52, 16, 52, 40, 48, 24, -68, 12],
 [-4, 26, -8, -26, -20, -24, -12, 34, -6],
 [20, -130, 40, 130, 100, 120, 60, -170, 30],
 [-34, 221, -68, -221, -170, -204, -102, 289, -51],
 [-16, 104, -32, -104, -80, -96, -48, 136, -24],
 [-6, 39, -12, -39, -30, -36, -18, 51, -9],
 [-4, 26, -8, -26, -20, -24, -12, 34, -6],
 [4, -26, 8, 26, 20, 24, 12, -34, 6]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[182, 75, 190, -82, -67, -58, 106, -446, -396],
 [-142, -305, 334, 13, -72, 126, -118, -314, 5],
 [52, 46, 32, 140, 199, -103, 81, 368, 307],
 [-184, -337, 204, -116, -100, 201, -168, -410, -22],
 [114, -318, 629, 148, 421, 53, 198, -33, -23],
 [-210, -11, -358, -24, -98, 99, -163, 290, 203],
 [-212, -182, -18, 23, -147, 204, -134, -26, -219],
 [-272, -493, 264, -138, -69, 298, -223, -446, 31],
 [390, 108, 285, 132, 554, -132, 433, 287, -202]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-198, 760, 204, 423, 68, 15, 207, -328, -131],
 [140, 65, -34, 168, -244, -176, 99, 86, 288],
 [89, -145, 358, -130, -438, -109, 192, -108, -53],
 [-183, 14, 116, -364, -46, -182, 217, -60, -19],
 [-43, 695, -316, 390, 134, -152, -30, -364, -103],
 [-225, -223, 171, -373, -502, -259, 490, 10, -150],
 [-320, 764, 6, 271, -136, -307, 495, -192, 71],
 [-208, -170, 55, -93, -312, -72, 361, 141, -98],
 [-165, 370, -215, 329, 126, 81, 19, -180, -288]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-22, 363, -109, 57, -499, -107, -811, 59, -8],
 [11, 269, 212, 161, 263, 435, 268, 21, -17],
 [113, -431, -93, 192, 156, 239, 726, -113, -329],
 [85, 330, 65, 160, -313, 471, -43, 152, -85],
 [-392, 458, 449, -422, -164, 538, 232, 44, -24],
 [617, -252, -234, 529, 399, -227, 59, 183, 621],
 [-428, 462, 419, -807, 106, 99, -355, -222, -629],
 [174, 501, 474, -219, 398, 551, 144, 6, 219],
 [-30, 233, 276, -505, 180, -65, -307, -212, 108]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-279, -140, -150, 329, 365, 86, -283, 371, 15],
 [-83, 255, -506, -304, 193, -43, 591, -422, 283],
 [129, -33, 223, -175, -250, 387, -406, 281, 212],
 [128, -145, 94, 281, -429, 189, -515, 205, -76],
 [-265, -47, -208, -79, 85, 319, -111, 383, 682],
 [326, 139, -259, 57, -493, 399, -692, 152, 77],
 [813, 52, -363, -212, -394, -328, -304, -264, -358],
 [-201, -171, 513, 146, 245, -450, 409, -74, -338],
 [-372, 88, 131, 615, -227, 346, -158, -86, -284]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[72, 29, -47, -53, 7, 53, 232, -67, -178],
 [0, 345, -207, -193, 225, -272, -91, -36, -106],
 [-78, -155, 113, 129, -79, 92, -117, 46, 164],
 [-144, -179, 101, 187, -43, 272, 121, -68, 30],
 [102, 82, -22, -112, -16, -255, -265, 127, 118],
 [171, 283, -199, -254, 125, -220, 148, -47, -261],
 [54, 335, -233, -213, 217, -165, 174, -115, -284],
 [-207, -70, 28, 165, 64, 264, 165, -133, -41],
 [-372, 98, -38, 162, 226, 100, -150, -112, 112]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-83, -44, 136, 228, -454, 49, -38, 41, -407],
 [14, 356, -106, -184, 191, 226, -4, -309, 133],
 [-156, -429, -172, 595, 764, 321, -324, 139, 711],
 [48, 51, 209, 498, -218, 218, -487, 494, 79],
 [-77, -795, 38, -164, 23, -429, 60, -448, 172],
 [-342, -101, 370, -303, -674, -327, -97, 52, -362],
 [-229, 210, 390, -56, -430, 163, -485, 32, 5],
 [442, 13, -159, 510, 308, 309, 16, -88, 233],
 [-86, -239, -68, 239, -85, -190, 195, 408, -273]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[20, -209, -165, -315, -35, 241, -68, 394, -222],
 [2, -96, 263, -185, 2, -248, -148, 86, 320],
 [330, 258, 209, -139, 51, 38, -403, 222, 389],
 [-262, -152, 300, 227, 246, -393, 444, -483, 145],
 [77, 486, 35, 608, -297, 5, -176, -301, -102],
 [-240, -309, -223, -80, -247, 94, 96, 177, -461],
 [-26, 94, -601, 137, -182, 384, 98, -24, -504],
 [258, 67, -437, -346, 134, 438, -111, 313, -54],
 [29, -231, -179, -423, 203, 111, 77, 214, 60]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[163, 106, 791, -46, -214, -112, 162, 321, 398],
 [423, 21, 543, 197, -403, -160, 30, 294, 74],
 [230, -79, -258, 162, -327, 168, 302, -44, 97],
 [473, 99, -113, -562, -146, 129, 168, -305, 229],
 [82, 241, 149, -2, -431, -174, -79, -265, 88],
 [-11, 97, -476, 90, 79, 52, -259, -182, -592],
 [461, 349, -250, -805, -157, 233, 140, -547, 96],
 [198, 48, -391, -255, 230, 210, -24, -88, -339],
 [15, 365, -408, -80, -362, 300, 61, -456, -338]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[322, 43, -76, 543, -97, -151, 256, -230, 319],
 [394, -27, -104, 342, -473, -323, 141, -781, -209],
 [-89, 47, 101, 7, 10, 249, 194, -509, -334],
 [-104, -46, 348, -548, 257, 279, 65, -315, -556],
 [-385, -81, -90, 158, -219, 294, -137, 486, 232],
 [116, 406, 284, 349, 168, -83, 10, -160, -176],
 [-399, 129, 276, -140, -281, -321, -582, 390, -61],
 [328, 38, 424, -49, 93, 167, 338, -842, -610],
 [46, -3, -255, 136, -406, -513, -132, -373, 74]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[-19, 261, 260, -139, -162, -338, -243, -361, 215],
 [-67, 81, 169, -213, 318, 275, 418, 430, -286],
 [15, -227, -316, 239, -106, 14, -133, -87, 39],
 [-194, 52, -71, -28, 8, -135, -53, -175, -41],
 [-15, 4, 105, -149, 308, 337, 424, 484, -285],
 [-415, 274, 95, -249, 128, -253, 34, -246, -145],
 [118, -328, -309, 232, 64, 323, 141, 311, -119],
 [-263, 216, 141, -229, 156, -99, 124, -48, -149],
 [-328, -139, -315, 18, 274, 191, 283, 197, -370]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[218, 408, -524, 260, 442, -34, -198, 48, -154],
 [-131, -337, 328, -137, -308, -74, -37, -92, 15],
 [112, 372, 98, -86, -286, 416, 110, 14, 154],
 [150, 96, 4, -28, -126, 146, -102, -12, -58],
 [243, 433, 6, -53, -232, 468, -153, -4, 51],
 [-79, -344, 180, -44, -146, -182, -315, -129, -107],
 [16, 292, 31, -57, -59, 299, 252, 83, 194],
 [572, -74, 163, -285, -213, 610, -569, 93, -247],
 [-267, -312, 456, -180, -440, -46, 191, -99, 163]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[33, -145, -103, 11, 170, -185, -129, -25, 152],
 [-341, 8, 203, 11, 68, -151, 109, 111, -443],
 [307, -18, -189, -9, -48, 121, -107, -101, 407],
 [301, 104, -115, -19, -196, 287, -5, -87, 307],
 [102, 30, -42, -6, -60, 90, -6, -30, 108],
 [-117, -251, -77, 25, 334, -403, -171, 13, 40],
 [-121, -82, 23, 11, 128, -171, -31, 31, -93],
 [157, 139, -11, -17, -206, 267, 67, -37, 96],
 [-85, 238, 187, -17, -272, 289, 221, 51, -289]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-215, 85, 63, 120, 225, 19, 74, 412, -436],
 [53, -68, 287, 27, 184, -408, -124, 472, 97],
 [-230, -235, 286, -533, -162, -232, 179, 207, 380],
 [-109, 444, 100, 41, -240, -132, -268, 413, 138],
 [229, -174, -18, 37, 150, 190, 0, -219, -26],
 [-154, 179, 356, 82, 27, 26, -296, 149, 356],
 [237, 31, -439, 294, 84, 274, 87, -361, -475],
 [164, -358, 396, -346, 66, -114, -50, 35, 527],
 [-177, 3, -189, -389, -407, -170, 258, -15, 81]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-254, -330, -11, 58, -133, -164, 176, 271, 179],
 [416, 3, 398, 103, -347, -106, -1, -104, -203],
 [-206, -108, -114, 93, 128, -242, 38, 267, 2],
 [165, 254, -56, -80, -54, 134, -260, -305, 319],
 [237, -32, 166, 326, -54, -62, 202, -187, -37],
 [38, 406, -256, -204, 394, 469, -154, -384, -85],
 [-415, -297, -123, -324, -122, 199, 97, 231, 188],
 [-186, 277, -323, -490, 132, 426, -359, -184, 306],
 [-171, -325, 169, -478, -510, 298, 33, 137, 137]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[14, -629, 104, -151, 209, 2, 531, -571, 253],
 [-159, -438, 531, -26, 311, -191, 189, -375, -10],
 [-192, -14, 27, -296, 98, 230, 393, -482, -63],
 [25, 267, -146, 299, -115, -178, -469, 694, -66],
 [-377, -233, -247, -6, 413, -19, 491, -152, -311],
 [725, -6, 7, 172, -754, 2, -321, 333, 494],
 [-168, -163, 249, 300, 383, -455, 372, 134, -480],
 [-198, 129, -254, 36, 425, -139, -87, 160, -41],
 [621, -8, 78, 110, -742, 70, -208, 199, 363]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[165, 498, 66, -615, 828, -494, -11, 165, 359],
 [519, 226, 466, -431, 438, -567, -244, 524, 388],
 [-391, -143, -79, -125, -243, 147, 250, 43, 89],
 [-496, 512, 117, 5, 14, -89, -62, -601, -105],
 [153, -334, -191, -158, 76, -351, 178, -3, -118],
 [-246, -156, -224, 343, -352, 1195, 41, -7, 79],
 [-17, 331, -295, 173, -75, 185, -16, -626, 49],
 [-742, 226, 35, -3, -166, 271, 133, -179, -157],
 [49, -866, 19, 354, -461, 60, 53, 0, -414]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[297, -397, -314, 426, -596, -215, 265, 300, -70],
 [-749, -350, -191, 543, -475, -94, 34, 457, 249],
 [440, 344, -81, -361, 330, 166, 198, -151, -237],
 [275, 86, 176, 152, -486, 231, -279, -177, -187],
 [223, 107, -239, -165, 272, -211, 87, -15, 553],
 [-245, 188, -608, 131, 300, 38, 215, 603, 5],
 [-275, 270, 165, -255, 1, 61, -62, -163, -391],
 [198, -74, 386, -244, -111, 186, 61, -359, -181],
 [-593, 78, 370, -200, -269, 136, 3, -209, -458]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[-349, 304, -329, -285, 90, 8, -35, -226, -197],
 [125, -89, -68, -318, 158, 70, 65, -103, 117],
 [177, 192, -76, 203, -207, -349, 229, 32, -217],
 [-443, -255, -258, 469, -312, -52, -559, -248, -38],
 [306, 19, 400, -430, 374, 306, 280, 253, 266],
 [-226, 388, -184, -156, 120, -94, 63, -28, -207],
 [307, -44, 635, 36, -184, 254, 65, 35, 476],
 [-212, 242, -361, 310, -348, -396, -73, -229, -316],
 [121, 172, -72, -94, -504, -28, 303, -386, -153]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[120, -352, 414, -431, 55, -184, -10, -89, 0],
 [191, 285, -72, -252, -54, 401, 73, 72, -401],
 [-197, 175, -15, 397, 347, 107, 331, 24, -190],
 [-114, 18, -195, 190, -496, -144, -444, -35, 567],
 [-258, -56, 431, 160, -148, -238, -433, 344, 691],
 [-2, -60, -94, -537, -53, 17, -162, -244, -223],
 [-359, -105, 179, -43, 15, -277, -61, -136, 128],
 [-172, -48, -191, 54, 23, -308, -266, 233, 254],
 [385, 68, -343, -223, -84, 367, 339, -411, -589]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[70, -49, -77, -28, 105, 63, 14, -14, -7],
 [160, -112, -176, -64, 240, 144, 32, -32, -16],
 [150, -105, -165, -60, 225, 135, 30, -30, -15],
 [-170, 119, 187, 68, -255, -153, -34, 34, 17],
 [120, -84, -132, -48, 180, 108, 24, -24, -12],
 [-140, 98, 154, 56, -210, -126, -28, 28, 14],
 [0, 0, 0, 0, 0, 0, 0, 0, 0],
 [110, -77, -121, -44, 165, 99, 22, -22, -11],
 [-20, 14, 22, 8, -30, -18, -4, 4, 2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[835, 274, 449, -277, -639, 54, -399, -183, 14],
 [-122, -41, 40, 230, -125, -105, 442, 350, -630],
 [-295, 222, 0, -220, 66, 240, -72, -208, 270],
 [-497, -596, -457, 286, 556, -225, 2, -55, 97],
 [294, 417, -155, 113, 85, -33, -193, -173, -25],
 [546, 183, 7, -104, 24, -34, -475, -442, 289],
 [292, 227, 228, -60, -315, -141, 432, 295, -367],
 [153, 55, -488, 195, 384, -206, -494, -369, 328],
 [-37, 531, 566, -411, -454, 572, 133, 154, 77]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[20, -59, 40, -304, 56, 23, 168, 101, 73],
 [135, -266, 2, -497, -186, 219, 69, 246, 24],
 [-54, 98, 19, -10, 138, -105, 93, -33, 57],
 [125, -179, -117, -363, -284, 151, -144, 244, 16],
 [69, -199, 111, -291, -4, 167, 204, 92, 0],
 [15, -32, 5, -77, -12, 24, 24, 33, 9],
 [114, -162, -110, -286, -272, 142, -156, 208, 0],
 [-17, 140, -187, 163, -140, -116, -312, 13, 5],
 [6, -85, 131, -194, 130, 58, 261, 16, 30]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[499, -157, -336, -141, 281, -171, 106, -50, -328],
 [358, 23, -217, 126, 53, -240, -64, -187, -296],
 [180, 208, -209, 283, -8, 264, 80, -138, -467],
 [-567, 309, 389, 366, -441, 147, -218, -68, 287],
 [-64, -287, 127, -384, 115, -282, -20, 169, 416],
 [102, -67, -146, -145, 191, 288, 224, 121, -173],
 [-388, 237, 300, 317, -369, -42, -244, -113, 235],
 [-48, 135, 63, 222, -171, -126, -156, -141, -6],
 [-286, -60, 249, -103, -108, -114, -100, 88, 397]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-102, -371, -142, -754, 517, 6, -33, -451, 480],
 [39, 434, -237, 328, -101, 108, 106, 200, -363],
 [-142, -467, 108, 412, 91, -134, 558, 276, 90],
 [140, 239, -55, 83, 28, 237, 301, 224, 416],
 [528, -2, -124, -632, 367, 326, -265, -28, -160],
 [259, -22, 105, 95, -153, 202, 377, 256, -412],
 [-277, 17, -181, 52, 131, -10, 365, 98, 293],
 [-10, 62, -32, 72, -23, -84, 22, -248, 33],
 [-124, 345, -54, 547, -316, -137, -66, 73, -353]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-21, -30, -186, 114, 320, 86, 175, 156, 142],
 [-75, 191, 256, -384, -184, -263, 47, -322, -89],
 [108, -169, 184, 219, -619, 109, -553, -85, -230],
 [-25, 27, -198, 9, 413, 33, 298, 179, 154],
 [184, -88, -14, 63, -217, 84, -157, 255, -179],
 [28, 64, -178, -99, 381, -12, 341, 245, 87],
 [221, -129, -168, 156, -12, 169, -45, 458, -117],
 [54, -88, 166, 99, -449, 36, -375, -121, -163],
 [153, -183, -240, 318, 106, 247, -55, 420, -1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-489, -49, 352, 251, -530, -176, -387, 228, 210],
 [503, -53, -363, -335, 441, 91, 309, -259, -306],
 [91, 61, -184, -133, -218, -212, -227, -206, -180],
 [662, -68, -494, -466, 386, 34, 342, -92, -278],
 [324, 102, -323, -194, 383, 36, 87, -721, -467],
 [-436, 72, 303, 302, -319, -61, -270, 75, 194],
 [-301, -30, 309, 239, -235, 53, 3, 642, 473],
 [90, 1, 3, 14, 221, 165, 250, 204, 141],
 [-256, -209, 215, 36, -255, -138, -253, -76, -108]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[157, -39, -72, 17, -532, -23, -195, -183, -338],
 [-156, -69, 367, -226, 160, -5, -486, -61, -160],
 [148, -100, 256, -222, -56, -146, -520, -62, -312],
 [150, 149, 101, -263, -227, -36, -469, -136, -190],
 [20, -100, -6, -115, -39, -365, -59, -63, 18],
 [24, 478, 176, -471, 222, 329, -203, 234, 142],
 [-104, -157, -183, 424, -386, 197, 193, -204, -170],
 [-281, 86, -159, 395, 97, 276, 150, -250, 280],
 [84, 204, -139, -22, 377, 155, 508, 386, 356]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[-7, 3, -5, -13, 13, -11, -4, 0, -6],
 [-126, 54, -90, -234, 234, -198, -72, 0, -108],
 [-49, 21, -35, -91, 91, -77, -28, 0, -42],
 [-126, 54, -90, -234, 234, -198, -72, 0, -108],
 [63, -27, 45, 117, -117, 99, 36, 0, 54],
 [35, -15, 25, 65, -65, 55, 20, 0, 30],
 [0, 0, 0, 0, 0, 0, 0, 0, 0],
 [-35, 15, -25, -65, 65, -55, -20, 0, -30],
 [-35, 15, -25, -65, 65, -55, -20, 0, -30]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-387, 53, 188, 243, 149, 99, -371, -321, -353],
 [-29, -140, -142, 192, -290, 131, -178, -20, 45],
 [345, -113, -218, -153, -299, -39, 251, 261, 353],
 [287, 20, -47, -273, -25, -134, 322, 200, 240],
 [-280, 149, 316, -3, 257, -44, -185, -313, -294],
 [199, -93, -117, -84, -284, -12, 95, 101, 228],
 [-33, -168, -309, 333, -159, 204, -138, 156, 18],
 [16, -4, -52, 24, 48, 12, 36, 68, 4],
 [71, -72, 50, -84, -366, -17, -78, -136, 137]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[22, -92, 190, -178, 56, 70, -22, -544, -276],
 [-148, -117, -246, 232, -164, -253, -285, 587, -175],
 [655, 355, 191, 498, -238, 230, 86, 694, 297],
 [10, -118, 49, -247, -536, 52, -381, -428, -32],
 [459, -635, -482, -78, -18, -150, 317, -185, 155],
 [-265, -278, 73, 36, 436, -597, 395, -115, -230],
 [261, -7, -143, 286, 215, 32, 192, 460, 12],
 [-486, -279, -143, -172, 82, -422, -59, -163, -194],
 [21, -730, -654, -218, -46, -363, 156, -170, 126]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[70, -50, 94, -125, 199, -141, 305, 132, 421],
 [500, -46, -633, 101, -202, 25, 274, 58, 350],
 [-302, 433, 18, -181, -65, -66, -892, -492, -815],
 [193, 162, -221, -212, -10, -23, -287, -190, -336],
 [197, -27, 173, -481, 406, 50, -73, 199, -187],
 [322, 133, -108, 210, 255, -346, 131, 42, -47],
 [-385, 386, -307, 495, -818, 252, -266, -513, 95],
 [-213, -788, 644, -75, 450, 49, 272, 598, -116],
 [112, -550, 51, 399, 37, -283, 785, 324, 901]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[69, -93, 152, -84, 78, -170, -256, 365, 35],
 [79, 134, -77, 28, 96, -5, -118, -103, 138],
 [-194, -299, -95, 264, 324, -81, -144, 218, -249],
 [239, 248, 1, -84, 132, -107, -346, 21, 332],
 [38, 122, 52, -144, -282, 112, 254, -192, 44],
 [-379, -489, -144, 388, 324, -18, 42, 203, -491],
 [-336, -356, -250, 436, 381, 26, 19, 17, -391],
 [-273, -345, -182, 372, 390, -40, -92, 139, -329],
 [16, -28, 164, -176, -252, 12, 156, 84, -32]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-59, -60, 192, -160, 2, -185, -66, 260, 266],
 [-186, -27, -195, -155, 461, -109, -67, -384, -317],
 [110, 107, -18, 154, -406, 183, -53, 81, 46],
 [-81, 217, -37, 115, -127, -322, 217, -376, 427],
 [-264, -319, -172, 270, 154, -319, 242, -343, -588],
 [70, 480, -334, -297, -67, 88, -328, -314, 19],
 [-79, -194, 272, 275, 31, -173, 366, -4, 357],
 [-350, -564, 298, 380, -198, -66, -2, 209, -236],
 [77, 247, -77, 161, -605, -418, 223, -32, 341]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[492, 255, -216, 139, 18, -175, 338, -388, 104],
 [-175, -341, -95, 13, 217, 2, 154, -315, 330],
 [135, 61, 24, -343, 43, -439, 16, -24, 258],
 [129, -214, -251, -10, 137, -74, 21, 32, -4],
 [275, 299, -176, 21, 175, -208, 299, -729, 364],
 [-499, 146, 253, 22, -136, 405, -308, 332, -472],
 [364, 625, -195, 78, 66, -113, 269, -623, -10],
 [-282, -370, 219, 512, -214, 600, 85, 224, -166],
 [-1, 191, -274, -75, 209, 41, -216, -134, -194]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[193, 434, -182, 76, 89, 169, 156, 208, 283],
 [-136, -95, 326, -22, 232, -46, 576, 89, 308],
 [-71, 148, 16, 128, -59, 151, 188, -52, 39],
 [344, 201, -355, 32, 256, 70, -35, 286, 267],
 [-95, -220, 57, 114, 125, 47, 259, -57, 44],
 [-136, -257, 259, -118, 54, -167, 110, -36, -8],
 [325, 149, 55, -318, 459, -258, 200, 518, 561],
 [65, 76, 112, -282, -73, -232, -279, 98, -28],
 [56, 235, -304, 218, -200, 254, -198, -115, -166]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-112, 126, 49, -98, 7, -77, 63, 70, -119],
 [-176, 198, 77, -154, 11, -121, 99, 110, -187],
 [32, -36, -14, 28, -2, 22, -18, -20, 34],
 [-160, 180, 70, -140, 10, -110, 90, 100, -170],
 [272, -306, -119, 238, -17, 187, -153, -170, 289],
 [-240, 270, 105, -210, 15, -165, 135, 150, -255],
 [112, -126, -49, 98, -7, 77, -63, -70, 119],
 [-32, 36, 14, -28, 2, -22, 18, 20, -34],
 [-128, 144, 56, -112, 8, -88, 72, 80, -136]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[334, 148, 75, -1009, -247, -633, 297, 283, 18],
 [-34, -380, -354, 162, 476, -177, 483, -222, -65],
 [64, 40, -492, -605, -344, -793, 556, 164, 291],
 [-96, 11, -226, -8, 443, -419, 475, -12, 305],
 [-338, 170, 219, -12, 351, 45, -200, -71, -73],
 [16, 3, -519, 225, -54, 44, 508, -283, 304],
 [700, -238, 541, 108, 451, 166, -47, 24, -722],
 [314, 39, 594, 43, -301, 416, -621, 271, -221],
 [-397, -161, -629, 157, 232, -78, 107, -310, 24]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[603, 203, 118, 352, -211, -442, -573, -69, -499],
 [-223, -46, 161, -109, 273, -415, -88, -196, -69],
 [-25, -322, -254, -71, -96, 169, 383, -214, 63],
 [-68, 40, -272, -105, 4, 93, -137, -279, -245],
 [257, 36, -131, 9, -77, 200, -171, -166, -570],
 [-425, 196, 258, -348, 212, 203, 188, 697, 670],
 [-238, -190, -48, -201, 160, -116, 115, -127, 23],
 [-411, 116, 261, -27, 223, -38, 93, 254, 514],
 [-177, -612, -524, 200, -176, -207, -9, -425, 121]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-95, 240, 180, 67, 278, -191, -89, 46, 76],
 [-15, 303, 141, -33, 309, -219, -54, -69, 150],
 [-160, -199, 47, 212, -135, 108, -59, 251, -186],
 [-230, 120, 240, 238, 212, -134, -146, 244, -56],
 [220, -64, -208, -236, -152, 92, 132, -248, 80],
 [30, 270, 90, -78, 258, -186, -24, -114, 156],
 [225, 200, -100, -285, 110, -95, 95, -330, 220],
 [-160, -272, 16, 224, -208, 160, -48, 272, -224],
 [-20, -399, -153, 88, -391, 280, 49, 139, -218]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-857, -25, 248, -229, -157, -490, -167, 323, -370],
 [-96, 270, -520, -147, -190, -306, 138, 8, 476],
 [-161, 50, -20, 65, 176, -321, 12, 336, 386],
 [115, 113, 114, 759, 437, 129, -265, -42, 516],
 [-541, 36, 91, -82, 3, -426, -91, 329, -24],
 [-659, -153, 415, -127, -66, -330, -138, 301, -182],
 [-239, 73, -76, -8, -315, 20, -61, -291, 130],
 [-226, 159, -65, 169, 214, -244, -146, 224, -114],
 [-498, -201, 318, -410, -395, -66, -37, -44, -550]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[-238, -152, 154, -329, 70, 152, -429, 182, -355],
 [124, 55, 3, 195, -31, -63, 149, 46, 174],
 [86, 120, -13, 140, -69, -98, 202, -151, 66],
 [66, 206, 490, 103, -150, -130, -157, 240, -181],
 [78, -51, -436, 39, 70, 9, 307, -293, 314],
 [-168, -168, -333, -195, 107, 126, 41, -273, -79],
 [90, 38, -49, 298, -41, -64, 282, -55, 122],
 [38, 31, -204, 67, -6, -37, 239, -255, 104],
 [62, -100, -119, 354, 29, 18, 266, 85, 180]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[304, 95, -15, 3, 166, 28, -138, 123, -1],
 [228, -114, 190, 369, 159, 199, -93, -97, 40],
 [69, 95, 138, -39, -352, -203, 429, 366, 667],
 [243, 97, -315, -325, -19, 5, 17, 270, 50],
 [326, 98, -12, -25, 28, 8, -3, 233, 195],
 [-147, -94, 234, 154, -467, -87, 519, 163, 667],
 [-21, 125, -144, -306, -226, -131, 132, 237, 166],
 [-217, 56, -384, -495, -198, -150, 182, 142, -33],
 [57, -96, -171, -43, 25, 116, 34, -8, -42]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[81, 237, 40, 140, -116, -420, 138, 59, 283],
 [117, 442, 214, -214, -55, 93, 6, -197, 87],
 [237, 256, -19, -38, -264, 144, 105, -420, -326],
 [206, 476, 55, 123, -311, -270, 205, -203, 101],
 [-57, -88, -185, 299, -218, 73, 93, 2, -178],
 [217, -94, 76, -281, 221, -348, -34, -97, 65],
 [41, -276, -218, 207, -95, -124, 76, -23, -209],
 [39, -363, -194, 134, 24, -214, 36, 39, -137],
 [-69, 172, -170, 494, -411, -59, 210, 45, -15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[157, 339, 114, 278, -303, -38, -92, 247, -76],
 [138, 63, -216, -19, -37, 80, -123, -260, 115],
 [-170, -147, 72, -97, 153, -80, 199, 76, -103],
 [-324, -123, -148, -219, 334, -302, 703, -46, -392],
 [-211, -120, -154, -189, 258, -178, 453, -115, -225],
 [-72, 216, 96, 140, -85, -214, 318, 280, -305],
 [118, 171, 176, 201, -226, 42, -205, 224, 38],
 [43, -114, -14, -57, 27, 124, -201, -113, 174],
 [51, 84, -310, -71, 50, -46, 151, -293, -51]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[260, 34, -329, 97, 157, -69, 93, 239, 113],
 [-82, 133, 7, 168, 105, 364, 138, 178, -211],
 [368, -62, -13, -197, -453, -88, 397, 166, 323],
 [-269, 646, -93, -748, -513, 253, 38, -613, -196],
 [-186, 472, -314, -862, -182, 163, 102, -518, -120],
 [-155, -307, 536, 206, -138, 73, -198, -165, 115],
 [25, -535, 425, -96, 195, 245, -276, -151, 20],
 [-306, 528, 64, -397, -679, 648, 429, -268, -268],
 [222, 87, -190, -258, -130, -305, 202, 53, 234]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-313, 161, -185, -606, 49, -465, -714, -127, -308],
 [289, -180, 168, -68, -153, 17, 13, 407, 235],
 [427, 93, 1028, 195, -696, 540, 170, -351, -726],
 [275, 685, 89, -619, 88, 78, -513, -448, -796],
 [390, 31, 291, 142, 12, -129, 629, 350, 556],
 [123, -508, 128, 367, -296, -385, 264, 537, 546],
 [-288, -299, -486, -196, -198, 6, -353, -104, -523],
 [-457, -941, -87, 232, 74, 222, 128, -20, 181],
 [248, -551, 437, 132, -197, 499, 246, 62, -70]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-26, 97, 110, 61, -198, -146, 41, 199, -59],
 [224, -40, 60, 126, 90, -157, -249, -102, 157],
 [207, -317, 134, -109, 18, -255, 405, 298, -426],
 [195, -2, 200, 106, -86, -542, 69, 161, -214],
 [179, -221, -19, 107, 167, 339, 63, -198, 227],
 [396, -135, 60, 32, -38, -140, -225, -126, 493],
 [-200, 137, -218, -367, -221, 110, 125, -159, 360],
 [-170, 76, 144, 250, -165, 180, 416, 168, -227],
 [407, -101, -78, 78, 268, -29, -651, -449, 648]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[-78, -125, 260, -36, -106, 60, -52, 42, 9],
 [30, 35, -80, 60, 40, -30, 70, 30, -15],
 [72, 186, -348, -216, 102, -18, -222, -288, 54],
 [62, 112, -226, -16, 85, -41, -7, -78, 4],
 [-70, -8, 74, -400, -89, 109, -445, -330, 100],
 [-128, -206, 428, -56, -174, 98, -82, 72, 14],
 [-98, -120, 270, -176, -131, 95, -207, -78, 44],
 [68, 51, -138, 236, 89, -83, 267, 168, -59],
 [78, 6, -78, 456, 99, -123, 507, 378, -114]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[1, 80, 55, 316, -30, 113, -104, 198, -8],
 [577, 176, -30, 597, 183, 360, -49, 165, 155],
 [-31, -288, -116, 183, -362, 228, -159, 282, -396],
 [-112, -186, 81, 147, -603, 344, -207, 477, -251],
 [542, -106, -172, 542, 141, 425, 14, 269, -223],
 [280, 210, 71, 11, 204, 44, 99, -106, 318],
 [-757, 208, 292, -103, 302, -384, 131, 162, -24],
 [767, -204, -394, 448, 505, 305, 179, -33, -301],
 [510, 232, -60, 112, -148, 62, -226, -388, 540]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-306, 132, -342, -270, -27, 9, -324, -144, -51],
 [190, 144, -107, 51, -31, 95, 33, 191, 76],
 [-313, -93, 31, -141, -30, -113, -100, -243, -179],
 [406, 90, 51, 213, 4, 116, 203, 307, 159],
 [75, -17, -103, 9, 146, 63, -106, 23, 247],
 [269, 117, -49, 111, -8, 103, 90, 229, 119],
 [-56, 286, -367, -165, -117, 95, -185, 99, -50],
 [-104, 4, -73, -75, 12, -10, -95, -69, -5],
 [27, 249, -148, -54, -217, 48, 35, 152, -211]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[501, 600, 595, 46, -49, -280, 93, 32, 123],
 [68, 334, -410, -272, 112, -59, -758, -235, -219],
 [-153, 50, -131, 89, 139, -29, -332, 249, -381],
 [32, -13, -155, -152, -275, -128, 350, -297, 263],
 [165, 126, 307, -410, 163, -82, -293, -91, 480],
 [-169, -547, 74, -269, 348, 353, -120, 37, 293],
 [131, -431, 71, -363, 249, 349, 189, -259, 339],
 [-256, -256, 274, 300, -186, 98, 182, 130, 486],
 [-228, -431, -202, -364, 230, 196, -201, -61, 191]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[50, 368, -169, 190, 25, 235, 35, 304, 55],
 [84, 506, -142, 216, -44, 196, 136, 248, 30],
 [-264, 107, -98, 174, 27, 329, -171, 456, 60],
 [166, -6, 135, -301, 0, -351, 339, -718, -60],
 [-94, 291, 29, -158, 26, -20, 324, -396, 1],
 [188, -576, -134, 40, 190, 38, -473, 378, 66],
 [-226, 535, 263, -170, -252, -206, 606, -692, -117],
 [-292, 287, 300, -50, -319, -177, 342, -378, -134],
 [598, -87, -81, 158, -54, -216, -93, 146, -33]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[117, -88, 327, -22, 37, -268, 34, 135, 76],
 [178, 28, 2, -136, 426, 252, -12, -274, 172],
 [594, 398, 130, -355, 545, -25, -278, 215, 475],
 [-17, -306, 277, 85, 156, 77, 304, -192, 65],
 [-422, -139, -255, 246, -483, 55, 125, -26, -333],
 [-137, 203, -320, -185, -29, -170, -581, -314, -378],
 [-475, -226, -223, 274, -473, 72, 174, -123, -376],
 [-421, -133, -226, 218, -488, -36, 50, -38, -376],
 [-462, -118, -400, 216, -390, 215, 75, -223, -377]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[26, -76, 54, -320, -42, -112, -56, 70, 48],
 [38, -220, 20, -118, -256, 82, -310, 300, 98],
 [-121, 315, -44, 266, 373, -59, 450, -464, -148],
 [153, -21, -38, -2, -33, 61, -66, 158, -16],
 [-321, 103, 161, -54, 56, -339, 190, -452, 75],
 [-462, -141, -99, -216, 228, 345, 108, -123, -78],
 [-283, -212, 144, -36, -320, -98, -276, 1, 193],
 [24, -133, 176, -14, -395, -269, -310, 109, 209],
 [-57, -113, 15, -430, 42, -11, -18, 68, 13]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[117, 108, -99, -126, 108, -108, -45, 54, 18],
 [-234, -216, 198, 252, -216, 216, 90, -108, -36],
 [26, 24, -22, -28, 24, -24, -10, 12, 4],
 [104, 96, -88, -112, 96, -96, -40, 48, 16],
 [39, 36, -33, -42, 36, -36, -15, 18, 6],
 [-104, -96, 88, 112, -96, 96, 40, -48, -16],
 [-130, -120, 110, 140, -120, 120, 50, -60, -20],
 [-117, -108, 99, 126, -108, 108, 45, -54, -18],
 [156, 144, -132, -168, 144, -144, -60, 72, 24]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[447, 293, 297, 231, -134, 427, -590, -513, 199],
 [-341, -287, -350, -368, 59, -203, 137, -576, -290],
 [65, 230, -53, 139, 384, 89, 403, -92, 121],
 [339, 306, 267, 252, -80, 369, -326, -303, 77],
 [-223, -88, -9, -135, -64, -216, -38, 31, -225],
 [-182, 77, 146, 134, -272, 9, -600, 86, -598],
 [-225, -141, -83, -215, 33, -270, 238, 30, -78],
 [-59, -443, -237, -180, -301, -21, 178, 364, 46],
 [256, -270, 4, 28, -473, 253, -404, 235, 187]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[262, -91, 309, -296, -21, -79, 11, 152, -206],
 [66, 99, 76, 46, 93, -68, -100, -81, -121],
 [-337, -288, -269, -192, -324, 195, 252, 348, 476],
 [-276, 60, -59, -98, -60, -47, -145, 195, 197],
 [182, -168, -39, 50, -48, 125, 253, -99, -45],
 [-12, -63, -234, 258, -9, 150, 192, -207, 81],
 [334, 257, 243, 196, 303, -169, -211, -346, -452],
 [287, -50, 273, -184, 30, -71, 10, 40, -244],
 [-33, -207, 42, -288, -189, 54, 135, 288, 138]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[390, 408, -346, 48, -70, 168, 170, 52, -394],
 [60, -18, 41, 317, 245, -28, -270, 183, -101],
 [60, 138, -141, -281, -249, 76, 302, -155, -23],
 [60, 54, -43, 41, 17, 20, -6, 27, -65],
 [60, 102, -99, -143, -135, 52, 170, -77, -41],
 [60, -24, 48, 340, 264, -32, -292, 196, -104],
 [0, 102, -119, -391, -323, 68, 374, -221, 51],
 [-15, -108, 121, 352, 295, -68, -345, 198, -31],
 [-345, -336, 277, -138, -17, -132, -59, -100, 361]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-237, 234, 107, -83, -338, -486, 612, -453, -11],
 [39, -67, 5, 190, -177, 239, -200, 392, -149],
 [-76, 78, -90, 150, -110, 111, -3, 78, -73],
 [183, 75, 37, 34, -78, -212, 245, -327, 128],
 [563, -24, 327, 361, -256, 114, -90, 375, 98],
 [334, 102, 70, 246, 257, 267, -225, 189, 237],
 [-364, 286, -100, -16, -159, -253, 439, -389, -27],
 [453, -24, 355, 281, -440, -77, 107, 243, 20],
 [-705, 0, 155, -517, -5, -347, 239, -24, -197]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[304, 21, 340, -534, 534, -137, -172, 86, 22],
 [456, 488, -183, 11, 299, 308, 148, 333, -474],
 [-192, 377, 596, 373, -163, 192, -90, 124, -221],
 [-463, 86, -233, -587, -448, -367, -643, -406, 393],
 [-44, 463, 193, -88, -9, 281, -454, 370, -375],
 [-571, 218, 347, -111, -326, -111, 72, 108, -315],
 [-86, 347, 10, 119, 48, 233, 224, 413, -571],
 [220, 588, 227, -2, 369, 489, -20, 652, -804],
 [19, 58, -151, 715, -390, 308, 392, -22, -173]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-125, 214, -180, -63, 250, -268, 15, 169, 171],
 [369, 294, -163, 607, 481, -201, -162, 25, 200],
 [-69, -203, 90, -190, -409, 426, 357, -42, -141],
 [-306, -301, 104, -278, -2, 201, 18, -302, -110],
 [-430, 210, 72, -131, -124, 102, 88, 621, -305],
 [-69, 315, -335, 169, -174, -128, 782, 552, -45],
 [-452, -149, 110, 58, 121, -376, -286, -164, -3],
 [573, -32, -228, 276, 244, -338, 15, -410, 206],
 [5, -156, 53, 365, -78, -296, -79, -283, 116]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[124, -94, 114, -179, -124, 107, 109, -102, -249],
 [-100, 70, -87, 140, 100, -86, -85, 84, 204],
 [24, -284, 248, -234, -24, 34, 154, 60, 98],
 [124, -74, 97, -164, -124, 106, 99, -108, -260],
 [-16, -264, 220, -184, 16, 0, 124, 96, 184],
 [-52, -98, 69, -28, 52, -38, 23, 84, 180],
 [80, 40, -12, -40, -80, 64, 20, -96, -216],
 [16, 164, -135, 109, -16, 5, -74, -66, -129],
 [-60, 70, -76, 105, 60, -53, -65, 42, 107]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-424, 164, 419, -31, -437, -300, 322, 157, 190],
 [-192, -66, 99, -49, -82, -194, 21, 94, 149],
 [147, 198, 206, 236, -247, 93, 270, -95, -106],
 [395, -71, -210, 336, 5, 210, -232, 42, 89],
 [-1, -161, 30, 188, -21, -442, 119, -98, -272],
 [-342, -141, 345, -23, -292, -389, 114, 167, 505],
 [-294, 36, 122, -206, -114, -268, 72, 14, 94],
 [-564, 160, -3, -713, 197, 136, -46, 143, 70],
 [229, 306, 86, 100, -171, 213, 201, -223, -181]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[381, -53, -83, -416, 147, -152, 521, -508, -28],
 [-96, -161, 80, 68, -292, -369, 79, -77, -428],
 [142, -387, 16, -8, 197, 411, 424, -369, 93],
 [-152, 764, -498, 553, -262, 162, -306, -138, -521],
 [451, -176, 2, -389, 263, 209, 387, -422, 590],
 [187, -335, 43, -311, -68, -90, -42, -94, 203],
 [117, 24, -321, 371, -346, -283, -488, 366, 66],
 [-105, -285, 119, -325, -311, -27, -281, 61, -18],
 [138, 552, -343, 435, -617, -274, -485, -220, 60]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-135, 56, 46, -139, 308, -135, -7, -156, -16],
 [-111, 389, 245, -534, 346, -73, -172, -183, 198],
 [335, -684, -176, 520, -221, 141, 149, 57, 210],
 [572, -55, 526, 267, 312, 372, -170, -91, -6],
 [-54, -392, -251, 174, -52, 504, -567, 512, 436],
 [325, -368, 77, 313, 430, 413, -93, 318, 376],
 [-425, 341, -211, -391, -167, -413, 220, -108, -140],
 [54, 280, 160, -56, 220, -378, 586, -271, -322],
 [556, -354, 186, 384, -60, 432, -90, 163, 266]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[17, -237, -19, 50, -248, 17, -34, -177, -374],
 [-42, 250, 6, -106, 258, -42, 230, 94, 456],
 [127, -259, 185, -255, -295, 127, 277, -113, 24],
 [-110, 294, -98, 10, 314, -110, 178, 42, 344],
 [-18, 62, -46, 123, 75, -18, -241, 96, -82],
 [38, 190, 104, -152, 190, 38, 100, 202, 460],
 [-162, 16, -193, 28, 21, -162, 462, -370, -64],
 [80, -288, 24, 144, -296, 80, -416, -16, -544],
 [99, -275, 99, -55, -297, 99, -55, -77, -264]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[101, -803, -267, -110, 132, -112, 26, 127, -98],
 [154, -102, 499, -164, 402, 90, -92, -91, 433],
 [310, -447, 95, 60, 58, 10, -361, -175, -108],
 [294, -80, 481, 74, 90, 286, -651, -277, -116],
 [-114, -260, -358, 55, -23, 261, 448, 365, 12],
 [-201, 31, -663, 339, -284, 25, 622, 103, 190],
 [-183, 678, 134, 154, -100, 480, 56, -222, 379],
 [-268, 984, 427, 456, -145, 632, -74, -44, 147],
 [-495, 379, 120, 102, 19, -74, -221, -299, 214]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-140, -224, -182, -238, 168, 126, -210, -196, -98],
 [100, 160, 130, 170, -120, -90, 150, 140, 70],
 [-130, -208, -169, -221, 156, 117, -195, -182, -91],
 [140, 224, 182, 238, -168, -126, 210, 196, 98],
 [100, 160, 130, 170, -120, -90, 150, 140, 70],
 [-90, -144, -117, -153, 108, 81, -135, -126, -63],
 [130, 208, 169, 221, -156, -117, 195, 182, 91],
 [60, 96, 78, 102, -72, -54, 90, 84, 42],
 [90, 144, 117, 153, -108, -81, 135, 126, 63]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[75, -93, -244, -35, -30, -260, -239, -140, -92],
 [-93, 223, 36, 605, -330, -236, -39, -200, -312],
 [204, -13, -364, 14, -483, -168, -134, -363, -227],
 [-48, 35, -55, 242, -24, -249, -155, -84, -140],
 [121, -34, -74, -227, -161, 190, 111, -51, 53],
 [49, -117, 18, -365, 190, 198, 73, 140, 204],
 [42, 3, -98, 44, -123, -82, -58, -103, -79],
 [94, -158, -89, -406, 157, 117, -9, 77, 173],
 [131, 15, -262, 93, -376, -170, -117, -286, -206]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[264, -27, -120, 117, -114, 87, 201, 63, -162],
 [-152, -56, 2, 139, 63, -55, -244, 369, 131],
 [-114, 172, 42, -188, 146, -90, -104, 18, 41],
 [372, 38, -168, 88, -118, 100, 286, 76, -244],
 [-284, -73, 146, -60, 55, -56, -185, -160, 189],
 [-88, -304, -20, 390, -106, 42, -184, 362, 138],
 [234, 234, -114, -134, 50, -4, 166, 80, -193],
 [100, 370, -40, -340, 170, -80, 90, -40, -140],
 [-210, -97, 66, 83, 40, -45, -217, 135, 163]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-679, -31, -199, 206, -358, 90, -68, 311, 358],
 [-296, -115, -555, 304, 175, 14, -269, 36, -154],
 [294, 129, 664, -61, -332, -14, 131, -171, 84],
 [-81, 28, 79, -364, 116, -550, 374, -231, 573],
 [-459, 96, 331, -130, -514, -171, 219, 101, 651],
 [106, -123, -172, -184, 189, -17, -116, -107, -398],
 [-293, 128, 410, 41, -523, -247, 37, -164, 431],
 [-369, 338, -163, -101, -152, -171, -218, 84, 274],
 [-21, 9, 155, 608, -372, 521, -299, 201, -276]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[82, 273, 353, 229, 138, 451, 241, -22, -126],
 [716, -293, 430, -371, -359, 430, 162, -334, -17],
 [-499, 10, -782, -358, -140, -47, -325, 462, -18],
 [-228, -327, 58, 4, -643, -62, 201, 101, 135],
 [585, -421, 565, -143, -405, 493, 338, -351, 72],
 [-504, -6, -287, 28, -82, -56, -21, 311, 111],
 [-230, 69, -390, -199, 345, -208, -282, 178, 133],
 [-465, 120, -483, -299, 91, 533, -97, 487, 55],
 [285, -364, 450, 298, -374, -60, 301, -352, 8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[43, -514, 157, -200, 457, 270, -90, -56, 228],
 [-191, -198, -177, -60, 217, -228, 220, 10, 254],
 [37, -272, 101, 386, -314, -221, 201, -249, -147],
 [215, 210, 1, -289, 197, 436, -428, 100, 14],
 [191, -218, -17, 444, -416, -140, 36, -357, -149],
 [-96, 260, -48, -160, 32, 86, -54, 168, 52],
 [642, 76, 230, 296, -257, 1, -307, -237, -681],
 [-262, -441, 187, 221, -97, -180, 381, -112, 99],
 [227, 24, 217, 59, -82, 152, -166, -45, -269]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-7, -64, 306, 282, -569, -338, 23, -303, 52],
 [-66, 19, 305, -34, -393, -157, 427, -327, 456],
 [-165, 40, -339, -524, 661, 276, 252, 180, 241],
 [74, 22, -46, -16, -172, 120, 346, 164, 256],
 [18, -69, 159, -198, -330, -243, 153, -402, 315],
 [-73, -150, -297, -96, 163, -156, -264, 62, -223],
 [-176, 153, 162, 580, 201, 172, -97, 326, -377],
 [245, -89, 151, 76, -781, -207, 250, -177, 309],
 [-165, 111, 332, 50, -77, -11, 339, -218, 298]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-265, -5, -346, -213, -18, 97, 46, -260, -30],
 [104, -44, 308, 153, -18, -221, 76, 397, 201],
 [119, 230, 53, 288, 124, -192, -40, -157, -193],
 [360, 394, 166, 267, -126, 153, -396, -273, -317],
 [-540, -105, -326, -419, -103, 143, 88, 92, -7],
 [-494, -39, -208, -326, -245, -34, 118, 233, 272],
 [132, 87, 91, -274, -605, 466, -381, 56, 292],
 [87, 152, 34, 290, 272, -210, 29, -146, -305],
 [147, -237, -322, -406, -128, 646, -178, -521, 13]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[34, -22, 44, -436, 77, 296, -236, -190, -280],
 [264, -479, -400, 118, -156, -39, -188, 17, 232],
 [-22, -52, -100, 340, -635, 328, -432, 78, 496],
 [150, -89, -84, -324, 185, 14, -42, -78, -236],
 [148, -71, -239, 55, -79, -433, -51, 501, -102],
 [-97, -329, -123, 258, -503, 343, -475, -23, 336],
 [-175, 186, 292, -175, 148, 328, 64, -364, -94],
 [328, -94, -434, 352, -368, -443, -96, 579, 328],
 [225, -240, -301, 156, -133, -154, -61, 136, 208]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[-51, 155, -152, -62, -2, -16, 104, 95, 58],
 [-9, -83, 44, 134, 26, -44, -50, -101, 2],
 [35, 159, -66, -306, -62, 110, 93, 218, -20],
 [-18, 102, -84, -84, -12, 12, 66, 84, 24],
 [-34, -120, 42, 252, 52, -94, -69, -175, 22],
 [-155, 253, -322, 98, 46, -130, 181, 56, 160],
 [-66, -162, 36, 396, 84, -156, -90, -264, 48],
 [29, 59, -8, -158, -34, 64, 32, 103, -22],
 [-144, 146, -242, 208, 64, -154, 113, -43, 142]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[-203, -238, 263, -96, -189, 215, 190, 80, -150],
 [-670, -275, 191, -345, 49, 575, -127, 150, -142],
 [92, 147, -187, -51, -98, -19, 20, 181, 388],
 [-452, -227, 191, -189, 84, 359, -98, 9, -256],
 [-186, 129, -221, -117, 259, 115, -321, 20, 134],
 [-65, 80, -111, 30, 322, -39, -293, -179, -160],
 [-469, -299, 284, -183, 28, 380, -25, 0, -340],
 [-12, -42, 44, -54, -175, 68, 141, 133, 130],
 [314, 344, -382, 108, 154, -286, -184, -16, 348]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-218, -23, -33, -3, 43, 88, 121, 44, -37],
 [-356, -146, -16, 68, 90, 356, 140, 74, -92],
 [-18, -33, 22, 38, 39, 28, -12, -17, -34],
 [288, 84, -47, -122, -221, -13, -103, 51, 178],
 [300, 48, 30, -19, -83, -125, -154, -46, 71],
 [-402, -189, 143, 284, 434, 7, 85, -150, -352],
 [414, 195, 29, -72, -68, -519, -157, -116, 84],
 [302, 185, 32, -49, -2, -537, -102, -125, 33],
 [-190, -193, -20, 49, -42, 565, 34, 121, -1]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[224, 655, 49, 147, 347, 2, 39, -277, 530],
 [28, -173, 315, -101, 123, -310, 179, -178, -110],
 [-83, -93, -366, -88, -72, 174, -470, 81, -296],
 [52, 81, -329, -141, -419, 61, -432, 278, -178],
 [124, -97, 102, 31, 303, -64, -18, -119, 190],
 [-129, -56, -163, 51, 102, 149, 14, -71, 0],
 [-261, -387, -347, 48, -64, 340, -119, 162, -212],
 [90, -362, 110, -66, 213, -168, -12, -80, 58],
 [-281, -318, -264, -93, -531, 243, -267, 411, -654]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[-234, -126, -198, -108, -180, 18, -162, 144, -270],
 [169, 91, 143, 78, 130, -13, 117, -104, 195],
 [-117, -63, -99, -54, -90, 9, -81, 72, -135],
 [117, 63, 99, 54, 90, -9, 81, -72, 135],
 [208, 112, 176, 96, 160, -16, 144, -128, 240],
 [91, 49, 77, 42, 70, -7, 63, -56, 105],
 [-221, -119, -187, -102, -170, 17, -153, 136, -255],
 [104, 56, 88, 48, 80, -8, 72, -64, 120],
 [130, 70, 110, 60, 100, -10, 90, -80, 150]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[27, 99, -63, 126, 126, -45, 45, 126, -153],
 [51, 91, -115, 78, 110, -97, 97, 158, -209],
 [-111, -167, 249, -118, -198, 215, -215, -318, 429],
 [51, 187, -119, 238, 238, -85, 85, 238, -289],
 [75, 107, -168, 70, 126, -146, 146, 210, -285],
 [-99, -171, 223, -142, -206, 189, -189, -302, 401],
 [114, 154, -255, 92, 180, -223, 223, 312, -426],
 [-9, 15, 19, 38, 22, 21, -21, -2, 11],
 [96, 88, -213, 8, 96, -193, 193, 228, -324]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[184, 167, -63, 135, -267, 153, -294, 447, -57],
 [-384, 124, 309, 685, -75, 553, -510, 386, 153],
 [154, -41, -114, -458, -14, -456, 410, -437, -186],
 [304, -219, -32, -358, -116, -300, 278, -123, -217],
 [102, -323, -230, -452, 107, -146, 442, -261, 209],
 [448, -217, -179, -427, 66, -317, 246, -23, -166],
 [14, 465, -235, -265, -354, -307, 130, -241, -129],
 [193, 239, 133, 134, -362, -86, -251, 248, -387],
 [10, 49, 4, -150, -143, -188, 152, -199, -124]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[-168, 241, 383, 172, 80, 150, 241, -258, 183],
 [54, -74, -486, -151, 263, -262, 10, -77, -119],
 [-410, -435, -484, -293, 40, 450, 401, -24, 442],
 [338, -292, 386, 601, 208, -63, 190, -200, 28],
 [-181, 183, 31, -231, -68, 74, -268, 172, -251],
 [-69, -177, -615, -294, 24, -143, 131, 33, 193],
 [-334, 289, -36, -260, 1, -122, -55, -151, -289],
 [-34, 139, 326, 161, -69, 66, 163, -496, -267],
 [306, 48, -440, -147, 0, -607, -275, 135, -266]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[128, 0, 224, -80, -256, -144, -176, 0, 208],
 [-32, 0, -56, 20, 64, 36, 44, 0, -52],
 [80, 0, 140, -50, -160, -90, -110, 0, 130],
 [-112, 0, -196, 70, 224, 126, 154, 0, -182],
 [-136, 0, -238, 85, 272, 153, 187, 0, -221],
 [56, 0, 98, -35, -112, -63, -77, 0, 91],
 [-56, 0, -98, 35, 112, 63, 77, 0, -91],
 [-144, 0, -252, 90, 288, 162, 198, 0, -234],
 [72, 0, 126, -45, -144, -81, -99, 0, 117]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[10, 72, 70, -222, -240, -36, 154, -110, 106],
 [-273, -63, -41, 6, 555, 218, 19, 325, -24],
 [96, -67, 262, -33, -305, -204, -76, -244, -13],
 [138, 239, 244, -413, 291, -260, -470, -233, 110],
 [-483, -31, -32, -121, 865, 360, 105, 499, -2],
 [-184, 401, -52, -709, 469, 142, 88, 119, 282],
 [-120, -58, 99, 564, -124, -27, -20, -75, -456],
 [-49, 406, 84, -679, 176, -35, 3, -110, 239],
 [-318, -236, 0, 361, 228, 229, 190, 293, -216]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-446, -236, -112, 583, -373, -443, -11, 186, 581],
 [-52, 168, -684, 42, 32, 230, -329, 699, 43],
 [-321, -102, -18, 293, -138, -181, -129, -43, -43],
 [446, 244, -261, -457, 135, 598, 114, 273, 93],
 [370, 272, 200, -411, 141, -41, 57, -322, -269],
 [-185, 4, 325, 161, -152, -170, 162, 60, 165],
 [80, 106, -52, -209, -198, 107, 386, 36, -449],
 [111, 254, 438, -277, 82, 509, 34, -262, -46],
 [80, -10, 197, -136, -352, -410, 544, -435, -496]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-314, 26, 988, -368, -226, 504, -518, -364, -66],
 [-65, 255, 597, -21, -119, 59, -387, -549, 323],
 [-59, -271, -195, -165, 355, 93, 330, 76, -636],
 [-391, 428, -70, 364, 191, -305, -281, -59, 451],
 [-259, 27, 538, -263, -419, 340, -183, -71, -4],
 [96, 70, -204, 134, -20, 10, -136, 143, 336],
 [92, 365, -313, 358, 149, -569, -189, -92, 145],
 [104, 285, 84, -57, -518, -107, -141, -202, 26],
 [128, -405, 318, -195, 0, 523, -435, 505, 96]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[18, -110, -752, 163, 119, -539, -491, 28, -695],
 [88, -81, 167, -401, -190, 104, 42, 421, -6],
 [740, -35, 500, 203, 546, 187, -423, 473, 19],
 [-80, 82, 104, -345, -50, 172, 364, 88, 763],
 [-17, -257, -34, 211, 228, 161, -394, 171, -49],
 [-224, 81, 347, 732, 215, 289, 243, 106, 782],
 [30, 192, -243, -224, -1, -178, 137, 260, 472],
 [-168, 196, 110, 767, 298, 26, 274, 124, 171],
 [759, -337, 263, 188, 290, -232, -287, 862, 34]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[0, 0, 0, 0, 0, 0, 0, 0, 0],
 [22, 24, 24, -20, 32, 6, 12, 2, 12],
 [-198, -216, -216, 180, -288, -54, -108, -18, -108],
 [143, 156, 156, -130, 208, 39, 78, 13, 78],
 [-33, -36, -36, 30, -48, -9, -18, -3, -18],
 [22, 24, 24, -20, 32, 6, 12, 2, 12],
 [-11, -12, -12, 10, -16, -3, -6, -1, -6],
 [-77, -84, -84, 70, -112, -21, -42, -7, -42],
 [-99, -108, -108, 90, -144, -27, -54, -9, -54]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-117, 339, 57, -6, -426, 160, -151, -470, 152],
 [-882, 507, 171, 709, 211, 250, 487, 519, 70],
 [404, -203, 63, -78, 48, -188, 377, 133, 191],
 [-383, 127, 251, 99, -69, -176, -259, -346, -613],
 [-431, -123, -3, 194, -622, 26, -16, -616, -13],
 [97, 241, 273, 209, 99, -164, 449, 298, 267],
 [438, -510, -144, -180, 315, -286, 151, 206, -50],
 [-408, 506, -264, 642, -94, 480, 441, 334, 417],
 [-139, 19, -398, -391, 160, 512, -718, -207, -553]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-284, 9, -106, -108, -113, -575, -132, 156, 26],
 [-386, -193, -205, -105, -176, 236, 450, -201, -143],
 [168, -529, -101, -162, 139, -783, -258, 296, 430],
 [611, -86, 115, -41, -23, -220, -716, 305, 601],
 [-132, 122, -201, -124, -114, -270, 473, -40, -394],
 [353, 160, -53, 448, 213, 61, -510, 307, -522],
 [-78, -236, 250, -276, 109, 398, -319, -196, 592],
 [413, 603, -173, 79, 64, -169, -14, -23, 7],
 [-245, 3, -27, -318, -37, -696, 291, 8, 52]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[91, -142, 229, -65, -175, 187, 412, -214, 108],
 [-22, -43, -215, 222, -130, -243, -606, 194, 32],
 [-303, 423, 101, -207, 314, -279, -198, 293, -132],
 [215, -289, -147, 244, -304, -23, -140, -32, 186],
 [207, -290, 64, 21, -160, 384, 468, -363, 40],
 [35, -53, -24, 28, -29, 46, 16, -43, 2],
 [-100, 211, 332, -221, 21, -194, 280, 142, 146],
 [102, -284, -34, 190, -314, 130, -152, -176, 56],
 [-44, 95, 4, -132, 235, 174, 234, -97, -160]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-123, -154, -50, 257, 191, 0, -234, 253, 162],
 [308, 134, 90, -21, 391, -90, -101, 32, -7],
 [5, 244, 228, 76, 2, -302, 61, -231, -129],
 [-182, 82, 156, 267, 17, -264, -79, -50, -5],
 [298, 256, 179, -73, 262, -191, 17, -146, -109],
 [175, -44, -138, -318, -106, 252, 149, -29, -41],
 [140, 252, 154, -180, -110, -146, 208, -308, -192],
 [266, -46, -108, -189, 193, 192, -23, 110, 35],
 [-331, -118, -110, -101, -583, 140, 232, -139, -56]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[73, 196, -321, -465, -91, -41, -45, -6, -280],
 [343, -581, 177, 232, -137, -304, -47, 112, 307],
 [-617, -276, 462, -135, 69, 328, 201, 403, -113],
 [-397, -212, -166, -283, 291, 148, 173, -82, -464],
 [-646, 216, 81, 189, -35, 352, -75, -152, 49],
 [-99, 170, -12, 178, -227, -30, -71, -135, 283],
 [171, -227, 139, 372, 82, -293, 306, -111, 357],
 [332, 47, 481, 217, -219, 51, -221, 435, 353],
 [-284, 84, 204, 228, 60, 274, -102, 19, 43]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[-220, -307, 28, -95, 409, 101, 12, 491, -46],
 [34, -216, 332, -375, -231, -189, 383, -316, -329],
 [341, -105, 140, 158, -28, -285, -91, -393, 271],
 [76, 70, -404, -102, 300, 122, -160, 216, 8],
 [-194, -77, -147, 99, 89, 48, -32, 254, 14],
 [-160, 44, -96, -29, 88, 164, -203, 378, -79],
 [-9, 393, -511, 170, 231, 327, -427, 384, 159],
 [-357, -46, 179, 232, -228, -41, 205, -79, -121],
 [-259, 477, -215, 90, -54, 299, 46, -86, -290]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[146, -313, -230, 67, -24, -131, 336, 107, -244],
 [341, 316, -547, -240, -21, -162, 143, -102, -111],
 [395, 370, 10, -297, 373, 161, -487, -201, 293],
 [30, -292, -686, 7, -226, -27, 489, 30, -408],
 [502, 442, 88, -202, 306, -186, -216, -266, 362],
 [-74, 268, 210, -30, 0, -155, -68, 2, 96],
 [-2, 240, -145, -152, -6, 322, -353, -121, 138],
 [51, 651, -84, -250, -3, 164, -431, -271, 327],
 [240, -232, 114, -33, 196, 348, -397, 239, -12]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[74, 23, -19, 150, 14, 54, -44, -20, 58],
 [116, -82, -54, 52, 84, 68, -72, 8, 44],
 [216, -150, -100, 101, 155, 127, -134, 14, 83],
 [-236, 148, 106, -135, -161, -141, 146, -10, -97],
 [-88, -40, 20, -198, -10, -66, 52, 28, -74],
 [232, -320, -140, -138, 250, 114, -148, 68, 26],
 [148, 46, -38, 300, 28, 108, -88, -40, 116],
 [-90, 225, 75, 210, -150, -30, 60, -60, 30],
 [194, -199, -103, -9, 173, 105, -122, 34, 49]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the rank of the matrix:
[[-169, -134, 88, -3, -86, 0, 172, 24, 131],
 [-264, 13, -15, -3, -55, 8, 184, 66, 152],
 [-264, 85, -292, -212, 96, -253, -207, -54, -138],
 [267, -45, 182, -179, 29, -22, -197, 124, -359],
 [-106, -27, 241, 189, -154, 253, 432, 156, 318],
 [-114, -50, 334, -124, -128, 122, 260, 336, -50],
 [47, -143, 23, 386, -92, 167, 268, -236, 475],
 [-56, -151, 156, 218, -131, 156, 321, -36, 342],
 [-81, 201, -76, -149, 61, -36, -85, 156, -179]]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[-144, -369, 9, 270, 198, 234, 180, -261, 63],
 [37, 159, -21, -110, -137, -13, -69, 141, 61],
 [130, 343, -11, -250, -192, -204, -166, 247, -45],
 [17, -149, 55, 90, 235, -169, 47, -191, -239],
 [-91, -327, 33, 230, 251, 79, 147, -273, -73],
 [53, -37, 47, 10, 159, -213, -5, -103, -231],
 [117, 285, -3, -210, -141, -201, -141, 195, -69],
 [74, 160, 4, -120, -62, -142, -82, 100, -68],
 [115, 191, 23, -150, -19, -263, -107, 89, -175]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the rank of the following matrix:
[[244, 405, 333, -588, -38, 257, 174, -68, 46],
 [-82, 256, 12, -150, 67, -320, 217, 6, -116],
 [-258, -293, -91, -146, 69, 278, -141, -149, 322],
 [-259, 134, 152, 183, 231, -187, -194, 259, 243],
 [-41, 137, 52, -355, 195, 331, 249, -60, -22],
 [-86, 121, -492, -54, 48, 449, 327, -76, -643],
 [-102, -220, -61, -33, -601, 49, -240, 226, 155],
 [-262, -255, -153, 223, -219, 333, -79, 103, -94],
 [413, 54, -102, 65, -274, 277, 167, -273, -556]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the rank of the matrix:
[[8, -248, 151, -159, -85, -119, 19, -247, -79],
 [-105, 348, 11, -25, 227, 125, -63, 120, 120],
 [6, 0, 159, -43, 235, 73, -33, -257, 63],
 [100, 62, -296, 315, -118, 69, 38, 333, 4],
 [137, 208, -131, 399, 377, 301, -29, 26, 176],
 [-204, 456, -94, -118, 2, 26, -54, 414, 66],
 [55, -250, -95, 10, -329, -154, 65, 77, -134],
 [-147, -120, 87, -359, -349, -265, 21, 56, -150],
 [-51, 228, 17, 13, 201, 111, -45, 40, 96]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the rank of matrix A where A =
[[112, -288, 16, 144, 208, -160, -160, -160, 160],
 [-35, 90, -5, -45, -65, 50, 50, 50, -50],
 [-49, 126, -7, -63, -91, 70, 70, 70, -70],
 [28, -72, 4, 36, 52, -40, -40, -40, 40],
 [-84, 216, -12, -108, -156, 120, 120, 120, -120],
 [-14, 36, -2, -18, -26, 20, 20, 20, -20],
 [-14, 36, -2, -18, -26, 20, 20, 20, -20],
 [-14, 36, -2, -18, -26, 20, 20, 20, -20],
 [-42, 108, -6, -54, -78, 60, 60, 60, -60]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute the rank of the given 9x9 matrix:
[[195, 187, 35, 41, -294, 419, 100, 136, -324],
 [-61, -160, -270, 157, -602, -302, -181, -6, 31],
 [-105, 196, 64, -77, 319, 357, -194, -230, 12],
 [-507, 84, -187, -502, 8, -199, -134, 112, 121],
 [360, 39, -88, 323, -422, -68, 81, -99, -585],
 [392, 515, 348, 123, 117, 145, 236, -479, -24],
 [-69, 500, -116, -309, -92, -129, 169, -422, -347],
 [393, -18, 467, 334, 482, 157, 79, -45, 173],
 [-24, -338, 120, 262, 255, -576, -208, -131, 555]]

Present the answer in LaTex format: \boxed{Your answer}