messages listlengths 1 1 | ground_truth stringclasses 5
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the rank of the matrix:\n[[0, 56, 40, 80, -72, -40],\n [0, -28, -20, -40, 36, 20],\n [0, 35, 25, 50, -45, -25],\n [0, -42, -30, -60, 54, 30],\n [0, -7, -5, -10, 9, 5],\n [0, -63, -45, -90, 81, 45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[70, -40, 44, -6, 16, -4],\n [-25, 30, 22, -34, -1, -19],\n [95, -100, -50, 97, 8, 54],\n [30, -40, -36, 50, 0, 28],\n [-120, 90, -24, -39, -21, -21],\n [-70, 50, -20, -17, -13, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[70, 21, -14, 49, 21, 56],\n [-40, -12, 8, -28, -12, -32],\n [-80, -24, 16, -56, -24, -64],\n [20, 6, -4, 14, 6, 16],\n [0, 0, 0, 0, 0, 0],\n [30, 9, -6, 21, 9, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[14, 6, 4, 12, -18, -14],\n [63, 27, 18, 54, -81, -63],\n [63, 27, 18, 54, -81, -63],\n [-14, -6, -4, -12, 18, 14],\n [-28, -12, -8, -24, 36, 28],\n [-7, -3, -2, -6, 9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[0, -40, 24, 16, 36, -20],\n [-20, -54, 42, 38, 46, -30],\n [10, 37, -27, -23, -32, 20],\n [-10, 13, -3, 3, -13, 5],\n [20, -86, 42, 18, 80, -40],\n [0, -20, 12, 8, 18, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-6, 49, -62, -56, 14, -14],\n [14, 45, -146, -172, 63, 80],\n [43, -32, -4, 55, -89, -11],\n [3, 16, -152, -17, -40, 31],\n [46, -17, -84, -40, -43, 50],\n [1, -9, 75, -37, 55, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[51, 47, -188, -26, -92, 87],\n [-45, -82, -9, -12, 22, 69],\n [-115, -22, 174, -77, 135, 90],\n [15, -60, -33, 66, 28, 27],\n [131, 3, -70, 132, -117, -39],\n [-66, -7, -97, -118, 0, 183]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-40, -38, -12, -6, 142, -28],\n [-72, 9, 59, 192, 90, -81],\n [-44, -38, -40, 33, -42, -55],\n [-103, -65, -11, 191, 242, -128],\n [35, 6, -26, -90, -64, 42],\n [116, 157, 100, -160, -143, 179]]\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-19, 67, -61, 37, -8, 10],\n [26, -12, -64, 102, -72, 38],\n [-7, -14, -107, 63, -101, -57],\n [-18, -40, -68, 58, -101, -2],\n [61, 43, -12, -19, 62, -102],\n [164, 96, -113, 148, 31, -76]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[6, -51, -25, -26, 103, -140],\n [-16, -110, -9, -65, -2, 8],\n [31, -45, -54, -3, 35, -57],\n [-50, 31, 79, 15, -86, 115],\n [-22, -44, 19, 14, 67, -113],\n [-16, -103, -15, -143, 50, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[36, 27, -143, 33, 84, -28],\n [-32, 110, 8, -74, -30, -124],\n [24, -33, -50, 39, 39, 38],\n [20, 1, -67, 23, 42, 0],\n [8, -104, 66, 44, -18, 116],\n [24, -114, 22, 66, 12, 128]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[18, -9, 24, 30, -30, -18],\n [-54, 27, -72, -90, 90, 54],\n [-42, 21, -56, -70, 70, 42],\n [48, -24, 64, 80, -80, -48],\n [-30, 15, -40, -50, 50, 30],\n [-60, 30, -80, -100, 100, 60]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-78, -23, -115, 10, 58, 87],\n [-16, 33, -51, 39, 43, -42],\n [6, 36, -5, 61, 7, 59],\n [46, 2, 81, -5, -51, 19],\n [-18, -23, -25, -44, 16, -75],\n [-98, -21, -148, 26, 76, 121]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[45, 45, 12, -20, -16, 95],\n [-71, 40, -93, -113, 58, -47],\n [173, -5, 104, 85, -15, 38],\n [-79, 4, 33, 51, -54, 53],\n [25, -14, 98, 112, -13, -46],\n [1, -44, -59, -42, 31, -68]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-9, 2, -9, -1, -8, -9],\n [-45, 10, -45, -5, -40, -45],\n [0, 0, 0, 0, 0, 0],\n [-36, 8, -36, -4, -32, -36],\n [36, -8, 36, 4, 32, 36],\n [-45, 10, -45, -5, -40, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[40, -32, 8, 16, 80, -40],\n [-20, 16, -4, -8, -40, 20],\n [45, -36, 9, 18, 90, -45],\n [-50, 40, -10, -20, -100, 50],\n [45, -36, 9, 18, 90, -45],\n [40, -32, 8, 16, 80, -40]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-47, 62, 57, -51, 49, -11],\n [-104, 143, 93, -55, 82, -11],\n [38, -56, -81, 105, -64, 2],\n [87, -113, -49, -7, -49, 18],\n [-63, 9, 12, 64, 39, -138],\n [-58, 80, -28, 112, -14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-21, -26, 43, 63, 19, 61],\n [24, 18, -55, -31, 31, -58],\n [-30, -58, 51, 163, 121, 108],\n [-12, -24, 20, 68, 52, 44],\n [6, 22, -5, -69, -71, -32],\n [-18, -40, 28, 116, 96, 70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[50, -60, 98, 0, -34, 108],\n [30, -33, 63, 3, -21, 69],\n [-25, 40, -35, 10, 15, -40],\n [15, -69, -42, -51, 0, -39],\n [-35, 56, -49, 14, 21, -56],\n [50, -120, 14, -60, -22, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-77, 75, 106, 16, 58, -44],\n [1, -9, -57, -45, -41, -2],\n [22, 46, 18, 17, 67, -75],\n [-8, 142, 92, -130, -8, -40],\n [116, -41, -72, -96, -109, 93],\n [58, 55, 94, -59, -20, 56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-85, 21, -80, -93, 40, -44],\n [-56, -92, -16, 36, -70, 12],\n [96, 131, 47, -14, 89, -80],\n [3, -103, 32, 114, -99, -8],\n [-9, 68, -53, -104, 74, 72],\n [20, 1, -1, 54, -14, -102]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[25, 72, 31, -19, 25, -44],\n [-5, 18, -1, 10, 47, -52],\n [115, 104, 37, -6, 39, -50],\n [-38, -55, -5, -21, -90, 97],\n [-95, -91, -48, 34, 29, -15],\n [44, 10, -10, 27, 48, -40]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[12, -42, -100, -136, 60, -44],\n [-64, 20, 148, 170, -82, 8],\n [-66, -21, 74, 62, -36, -38],\n [-16, 14, 54, 67, -31, 12],\n [-28, -52, -50, -91, 35, -64],\n [38, -31, -124, -153, 71, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-164, -32, 8, -40, -72, -80],\n [68, 54, 26, -2, 0, -22],\n [176, 0, -108, 38, 232, 92],\n [22, -2, -78, 6, 136, -10],\n [25, 14, 66, -4, -96, 20],\n [129, 15, -53, 64, 124, 77]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[63, -14, -14, -28, -63, 7],\n [-36, 8, 8, 16, 36, -4],\n [-81, 18, 18, 36, 81, -9],\n [-54, 12, 12, 24, 54, -6],\n [-18, 4, 4, 8, 18, -2],\n [-63, 14, 14, 28, 63, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-41, 10, -138, -15, 104, -66],\n [-49, 26, -96, 55, 47, -61],\n [5, 33, 11, 20, 45, -59],\n [48, -52, 60, -98, 32, 8],\n [-47, 7, -33, 70, -93, 115],\n [47, 48, -41, -83, 81, -137]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-8, -5, -8, -10, 2, 10],\n [-64, -40, -64, -80, 16, 80],\n [-56, -35, -56, -70, 14, 70],\n [-48, -30, -48, -60, 12, 60],\n [40, 25, 40, 50, -10, -50],\n [-32, -20, -32, -40, 8, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-30, 17, 23, -46, -1, -42],\n [66, -43, -47, 102, 5, 94],\n [30, 11, -41, 42, -13, 34],\n [-84, 70, 50, -132, -14, -124],\n [18, 71, -66, 16, -40, 2],\n [-24, -90, 85, -22, 51, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-48, 60, 117, 93, 16, 92],\n [32, 5, -6, 14, -78, 43],\n [-84, -75, 57, 133, -44, -27],\n [48, 35, 4, -48, -61, 73],\n [12, 110, 85, 37, 11, 128],\n [-52, -95, 4, 72, -60, -55]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-10, 29, -97, -53, -66, 81],\n [-70, 17, -121, 1, -90, 71],\n [0, 24, -72, -48, -48, 64],\n [-10, -28, 74, 61, 48, -71],\n [90, 9, 63, -63, 54, -9],\n [80, 23, 11, -86, 18, 32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[63, 0, 90, 9, -54, -18],\n [-35, 0, -50, -5, 30, 10],\n [21, 0, 30, 3, -18, -6],\n [0, 0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 0],\n [49, 0, 70, 7, -42, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-6, -48, -93, -85, 25, -36],\n [24, -8, 133, 91, -29, 78],\n [-66, 52, 34, 21, 70, 18],\n [6, 33, -9, 48, 53, -42],\n [54, -58, -212, -135, -36, -126],\n [-18, 7, -50, -63, -34, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-69, -1, 35, 50, -72, 19],\n [25, -22, 133, 13, -9, 87],\n [11, 3, 43, -42, 36, 203],\n [40, -9, 43, -32, 39, 84],\n [7, -101, 42, -93, 45, 70],\n [-7, -73, -31, -116, 66, 121]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-24, -15, 42, -3, 6, -9],\n [9, 12, 24, -37, -19, 3],\n [39, 72, -84, -103, -31, -39],\n [71, 79, -134, -68, -33, -6],\n [60, 49, -74, -59, -38, -35],\n [-46, -4, -10, -8, 30, -41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[96, -89, -4, 0, -153, -126],\n [33, 14, 22, -61, -15, -1],\n [8, -38, -11, 143, 32, -45],\n [84, -82, 37, 14, -59, -90],\n [-68, -11, -12, 7, 30, 41],\n [73, 21, -2, 53, -14, -53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[79, 86, 18, -56, -5, 95],\n [11, -54, -8, -54, -83, -88],\n [60, 4, -2, 74, 67, 22],\n [137, 34, -72, 74, 110, -20],\n [-112, -40, 100, -180, -223, 7],\n [53, 30, -24, -18, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[54, 15, 9, -54, -6, -51],\n [72, -97, 77, -98, 44, -55],\n [36, 10, 6, -36, -4, -34],\n [81, -9, 31, -88, 5, -73],\n [9, -92, 54, -30, 41, 2],\n [81, 72, -14, -70, -31, -82]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[34, -10, -46, 90, -112, -96],\n [-3, 15, -3, -15, 48, 24],\n [9, -5, -11, 25, -36, -28],\n [40, 0, -60, 100, -100, -100],\n [15, 5, -25, 35, -24, -32],\n [-32, 0, 48, -80, 80, 80]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-41, -38, 93, 121, -55, 69],\n [-102, -24, -86, 70, 20, -24],\n [-15, 109, -94, -117, 87, -90],\n [66, -69, 55, -5, 5, -3],\n [-49, -24, -93, -23, 110, -124],\n [-26, 93, -71, -51, 18, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-72, 45, 54, 36, -72, 9],\n [24, -15, -18, -12, 24, -3],\n [8, -5, -6, -4, 8, -1],\n [-64, 40, 48, 32, -64, 8],\n [64, -40, -48, -32, 64, -8],\n [48, -30, -36, -24, 48, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-18, -2, 14, -10, -10, 20],\n [90, 10, -70, 50, 50, -100],\n [9, 1, -7, 5, 5, -10],\n [36, 4, -28, 20, 20, -40],\n [-81, -9, 63, -45, -45, 90],\n [63, 7, -49, 35, 35, -70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-21, -39, -126, -27, -101, -26],\n [150, 41, 160, 43, 37, 43],\n [-21, -22, 103, -41, -100, -61],\n [184, -12, 11, 147, -16, 57],\n [-72, -25, 40, 51, 3, -94],\n [81, -14, -1, 97, 4, 60]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[90, 0, 103, -164, 23, 65],\n [33, -131, 162, -62, 115, -5],\n [-51, 91, -1, -58, -93, -1],\n [103, 48, -36, -10, 53, 61],\n [-47, 3, 13, 20, 15, -21],\n [-36, 50, 11, -74, -87, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[17, -14, -5, 31, -46, -27],\n [-90, 44, -30, -38, 44, 94],\n [-104, 48, -40, -32, 32, 104],\n [103, -50, 35, 42, -48, -107],\n [-83, 42, -25, -41, 50, 89],\n [27, -10, 15, -2, 8, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-38, -56, 13, -61, -25, 63],\n [8, 117, -97, 15, 92, -23],\n [62, -37, 27, 71, 27, -37],\n [24, -140, -23, 78, 56, 15],\n [-49, -67, 39, -29, -75, 17],\n [52, -47, 16, 72, -88, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-12, -18, -14, 84, 18, -60],\n [22, 4, -13, 20, -62, -6],\n [36, 12, -14, 0, -96, 12],\n [-28, -1, 22, -50, 83, 24],\n [-4, -4, -2, 16, 8, -12],\n [18, 15, 5, -54, -39, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-13, 1, 36, 2, 105, 148],\n [30, 25, 43, 38, -43, 39],\n [-131, 22, -38, -66, 150, 81],\n [-90, -41, -81, -79, 124, -62],\n [128, -2, 116, 90, -34, 156],\n [-108, -30, -93, -93, 111, -61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-42, 26, -33, 132, 136, -8],\n [54, -30, -45, -36, -24, -24],\n [29, -18, 24, -93, -96, 6],\n [-23, 12, 39, -15, -24, 18],\n [-11, 8, -39, 81, 88, -14],\n [-5, 2, 24, -27, -32, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[7, 9, -5, -7, 6, 7],\n [-70, -90, 50, 70, -60, -70],\n [42, 54, -30, -42, 36, 42],\n [-63, -81, 45, 63, -54, -63],\n [-63, -81, 45, 63, -54, -63],\n [35, 45, -25, -35, 30, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 1 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[48, 88, -26, -66, 74, 64],\n [-64, -54, 41, 31, -67, -22],\n [-28, -63, 14, 49, -49, -49],\n [108, 153, -63, -108, 144, 99],\n [4, -31, -6, 29, -13, -33],\n [-32, -52, 18, 38, -46, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-7, 165, 3, -68, 8, 35],\n [-69, -58, 10, -58, 91, -21],\n [39, -102, -66, 35, 83, 42],\n [-113, 112, 100, 34, -4, -79],\n [137, -70, -100, 33, -65, 78],\n [64, 25, 31, 65, -177, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[92, -101, -3, 49, -126, 3],\n [81, -63, 135, -124, 24, 244],\n [-41, 133, 7, -21, 92, -70],\n [-41, 76, -86, 52, 8, -143],\n [24, -86, -122, -26, -35, -5],\n [28, 54, 124, -1, 13, 41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-25, -13, -82, 97, -85, 38],\n [-121, -64, 0, -53, 38, -67],\n [86, 91, 130, -112, 71, -29],\n [56, 53, 92, -128, 86, -49],\n [-22, 9, -12, 138, -100, 69],\n [41, 9, -10, -53, 35, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-95, 139, -65, 58, 73, 92],\n [56, -149, 59, -36, -56, -66],\n [-47, 61, 97, 106, 34, 11],\n [-13, 33, -61, 13, 21, 44],\n [124, 79, 73, -59, -35, -25],\n [-42, -188, 80, 2, -44, -118]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-33, -83, -81, -94, -84, 63],\n [-13, -42, -43, -9, 17, 39],\n [-2, -28, -16, -46, -78, 18],\n [64, -123, -37, 67, -51, 126],\n [-40, -65, -76, -85, -49, 48],\n [29, -51, -12, 22, -38, 51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[4, 12, 16, 36, -4, 36],\n [28, 0, -24, 16, -12, 0],\n [35, -21, -64, -39, -11, -63],\n [9, -15, -32, -37, -1, -45],\n [-6, 3, 10, 5, 2, 9],\n [-118, 24, 140, 0, 46, 72]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[22, 6, -16, -20, 4, 12],\n [-56, 35, 21, 63, 14, 28],\n [-8, 84, -28, 28, 40, 96],\n [59, -106, 5, -83, -48, -110],\n [-15, 39, -6, 24, 18, 42],\n [82, 8, -54, -78, 8, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-27, -161, 10, 16, -79, -85],\n [-33, 26, -35, 33, 69, -100],\n [-32, 4, -29, 43, -8, 61],\n [53, -107, 92, -108, -53, -169],\n [151, 124, 119, -188, 42, -35],\n [10, 69, -49, 49, 40, 105]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[106, -30, -38, -20, 83, -61],\n [44, -9, 46, 22, -99, 0],\n [-34, 0, 92, 41, -143, 55],\n [64, 66, -144, -42, -50, -104],\n [68, 9, -42, -12, -25, -52],\n [-68, 4, 86, 37, -112, 68]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[88, 60, -50, 99, 74, -61],\n [-111, -63, 63, -95, -95, 90],\n [37, 15, -34, 55, 52, -15],\n [-5, 87, 79, -13, -131, -28],\n [-23, 33, 43, 2, -71, 17],\n [-86, -120, -1, -97, 11, 78]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[4, -16, 32, 20, -4, -16],\n [-4, 16, -32, -20, 4, 16],\n [4, -16, 32, 20, -4, -16],\n [-4, 16, -32, -20, 4, 16],\n [8, -32, 64, 40, -8, -32],\n [-8, 32, -64, -40, 8, 32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-12, 113, -21, -122, -23, -40],\n [-14, 194, 122, -36, 9, -26],\n [47, -89, -30, -23, -14, -19],\n [52, -20, -44, -45, -48, -52],\n [-44, -24, 44, 50, 86, 68],\n [18, -88, -102, 23, -55, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-72, -27, -45, 45, 45, -36],\n [80, 30, 50, -50, -50, 40],\n [56, 21, 35, -35, -35, 28],\n [-24, -9, -15, 15, 15, -12],\n [72, 27, 45, -45, -45, 36],\n [-40, -15, -25, 25, 25, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[86, 45, -123, -94, 116, 33],\n [47, 24, -87, -159, -63, 90],\n [113, 28, -55, -107, 85, 31],\n [16, 65, 31, -58, 40, 27],\n [69, -98, -107, -42, -51, -99],\n [-38, 93, -27, -34, 54, 71]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[120, -52, -112, 16, 11, 40],\n [1, 26, -190, -18, -11, 86],\n [169, -18, 8, -98, -143, -137],\n [108, -8, -91, -119, -27, 21],\n [71, 38, -110, -204, -66, 7],\n [86, 4, -117, -80, -53, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[48, -60, -54, 30, 6, -18],\n [-37, 45, 91, -70, 41, 2],\n [-16, 18, 97, -85, 71, -13],\n [99, -125, -62, 15, 58, -49],\n [50, -62, -76, 50, -12, -14],\n [-87, 109, 88, -45, -20, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-18, -14, -18, 4, -8, 14],\n [45, 35, 45, -10, 20, -35],\n [0, 0, 0, 0, 0, 0],\n [-36, -28, -36, 8, -16, 28],\n [-9, -7, -9, 2, -4, 7],\n [-9, -7, -9, 2, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[21, -19, -14, 11, -28, 13],\n [22, -69, -31, 28, -108, 18],\n [-3, 63, 30, -29, 86, -31],\n [33, -3, 6, -9, -36, -39],\n [-151, -31, 23, -3, -27, -13],\n [28, -61, -21, 18, -112, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-4, 48, -5, 33, 7, 36],\n [-12, 24, -11, -1, 1, 4],\n [64, -18, 55, 97, 13, 74],\n [-80, 90, -71, -65, -5, -34],\n [-32, 54, -29, -11, 1, 2],\n [86, -87, 76, 78, 7, 45]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[15, -50, 74, 80, 161, -90],\n [-108, -28, -77, -40, 89, 17],\n [-98, 47, 96, -24, -1, -124],\n [-67, 94, 13, -95, -63, -84],\n [-98, -20, -87, -33, 76, 39],\n [-50, -70, -128, -13, 31, 137]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[112, 17, -57, 61, -100, -30],\n [-48, -122, -115, -3, -161, -103],\n [60, -25, -94, -59, -130, -25],\n [-31, -90, -48, 76, 51, 15],\n [112, -40, -23, 194, -105, -74],\n [-21, -1, -67, -36, 24, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-70, 40, 50, -30, 30, 90],\n [-63, 36, 45, -27, 27, 81],\n [28, -16, -20, 12, -12, -36],\n [7, -4, -5, 3, -3, -9],\n [21, -12, -15, 9, -9, -27],\n [-63, 36, 45, -27, 27, 81]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-114, -78, -15, -39, -6, -18],\n [-11, -55, 124, -146, -134, -84],\n [8, -20, -101, -1, 74, 66],\n [-9, -5, 90, -40, -78, -60],\n [9, 49, 85, 47, -48, -51],\n [161, 109, 42, 44, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-4, -45, 151, -56, 23, -5],\n [-50, 15, 23, 26, 7, 53],\n [-105, 35, 37, 59, 13, 112],\n [22, -50, 130, -66, 18, -32],\n [-20, -50, 190, -60, 30, 10],\n [-14, -35, 133, -42, 21, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-8, -2, 12, 8, 14, 16],\n [-28, -7, 42, 28, 49, 56],\n [-8, -2, 12, 8, 14, 16],\n [-24, -6, 36, 24, 42, 48],\n [24, 6, -36, -24, -42, -48],\n [0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-120, -186, 33, 41, 112, 28],\n [-142, 83, -136, -94, 130, 128],\n [91, -104, 193, -10, -69, -120],\n [127, 77, 18, 13, -83, -96],\n [26, 38, 65, -73, -22, 8],\n [6, -5, -70, 142, 24, 82]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[24, -86, 70, -2, 34, 48],\n [35, 105, -10, -40, 105, -185],\n [-13, 30, 6, -15, -17, -5],\n [-30, -68, 49, 4, -77, 138],\n [22, -10, 6, 0, 44, -34],\n [35, 6, 17, -13, 78, -77]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[100, 112, -34, 4, 145, 193],\n [-37, -64, 39, -73, -43, -24],\n [159, 60, -19, 37, 152, -4],\n [161, -4, -7, -4, 183, -1],\n [10, 48, 88, 146, -53, -188],\n [-121, -110, 77, 15, -130, -147]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[34, 11, -24, -42, 124, 64],\n [94, 76, 1, 48, -26, 54],\n [2, 28, -38, 52, 28, 84],\n [-27, 25, -27, 100, -70, 50],\n [-57, 8, -53, 90, -6, 86],\n [51, -30, 71, -130, 10, -130]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[38, 26, -17, -41, -9, 20],\n [45, -52, 70, 60, 43, 67],\n [14, -114, 125, 125, 97, 80],\n [78, 18, 10, 5, -35, 44],\n [46, 42, -26, -23, -55, 4],\n [63, 48, -23, -4, -83, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-58, 48, -43, 22, 39, -1],\n [53, -32, -59, 69, -45, 37],\n [44, -95, -54, 63, 57, 92],\n [21, -27, 38, 0, -51, -44],\n [-31, 102, -21, -35, -9, -2],\n [-64, -57, 27, -5, 126, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[10, 5, -7, -3, -9, -1],\n [-100, -50, 70, 30, 90, 10],\n [20, 10, -14, -6, -18, -2],\n [30, 15, -21, -9, -27, -3],\n [-90, -45, 63, 27, 81, 9],\n [10, 5, -7, -3, -9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-42, -12, 12, -28, 34, 40],\n [-166, -36, 149, -149, -123, 52],\n [-19, -14, 36, -36, -83, -20],\n [-102, -152, -17, -183, -53, 68],\n [-67, -13, 151, -41, -120, -16],\n [-9, -106, 38, -22, 21, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, 40, 24, 8, 64, -24],\n [0, 25, 15, 5, 40, -15],\n [0, -30, -18, -6, -48, 18],\n [0, -50, -30, -10, -80, 30],\n [0, 15, 9, 3, 24, -9],\n [0, -50, -30, -10, -80, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[3, -40, 3, 37, -27, 23],\n [-43, 38, -13, -25, 41, -33],\n [3, 70, 30, -100, 51, -62],\n [48, 34, -36, 2, -6, 28],\n [67, -157, 79, 78, -116, 67],\n [43, -15, 70, -55, -14, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[1, 103, 13, 29, -48, 14],\n [-13, -65, -92, -106, -39, 45],\n [-39, -146, -3, 26, 64, -31],\n [63, 70, 8, -61, -7, 12],\n [-15, -26, 6, 23, 13, -10],\n [26, -115, 60, 25, 122, -63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-5, 140, -72, -29, -76, -184],\n [-128, -212, 147, -29, 90, 224],\n [-72, 22, 15, -67, 75, -58],\n [118, 62, -9, -77, -45, -90],\n [-65, -55, 0, 82, 51, 93],\n [-127, 87, -96, 110, -7, -77]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-5, -83, 24, 18, -66, -23],\n [-80, -75, -93, 32, -56, -43],\n [-26, -53, 98, -1, 47, -4],\n [-91, -18, -71, -28, 192, -18],\n [42, 121, 63, -8, 8, 47],\n [34, -67, -68, 1, -63, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[28, 35, -49, 70, -35, -70],\n [16, 20, -28, 40, -20, -40],\n [-4, -5, 7, -10, 5, 10],\n [-16, -20, 28, -40, 20, 40],\n [-12, -15, 21, -30, 15, 30],\n [-32, -40, 56, -80, 40, 80]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-14, -14, -42, 28, 21, -14],\n [0, 0, 0, 0, 0, 0],\n [2, 2, 6, -4, -3, 2],\n [-12, -12, -36, 24, 18, -12],\n [20, 20, 60, -40, -30, 20],\n [10, 10, 30, -20, -15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-23, -102, -139, -90, 122, -12],\n [-85, -43, -10, 37, 43, 92],\n [-227, 26, -6, 35, 125, 162],\n [10, 83, 23, -2, -42, -3],\n [-27, -44, -62, -43, 65, -4],\n [50, -21, 51, 44, -85, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[95, -12, 121, 2, -21, -20],\n [45, 34, 38, -47, 33, -32],\n [-49, -28, -83, 44, -15, 26],\n [-47, -2, -20, 5, -9, 18],\n [2, 84, 14, -107, 75, -43],\n [110, -20, 50, 19, -3, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[135, -13, -43, -70, -39, 2],\n [59, -4, -67, -27, -116, -19],\n [64, 22, -6, 49, 73, -20],\n [107, -11, -75, -74, -164, -16],\n [-39, -7, 34, -132, -106, 80],\n [19, 144, 159, -63, -54, 109]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[96, 147, 72, 54, -191, -46],\n [-9, 118, 174, -40, -75, 47],\n [71, 34, -40, -24, -41, 93],\n [33, -28, -159, 66, 20, -122],\n [52, 87, 10, 66, -109, -108],\n [-44, -47, -170, -4, 159, -92]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-6, -16, 4, -10, 4, 18],\n [24, 64, -16, 40, -16, -72],\n [3, 8, -2, 5, -2, -9],\n [-30, -80, 20, -50, 20, 90],\n [24, 64, -16, 40, -16, -72],\n [6, 16, -4, 10, -4, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[4, 81, 0, 40, 18, -80],\n [-11, -21, 108, -134, -111, 136],\n [49, -21, 118, -118, -122, 71],\n [-64, 74, 20, -16, -2, 30],\n [137, -50, -18, 58, 4, -141],\n [10, 44, -46, 76, 55, -97]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-10, -74, -44, 51, -62, 58],\n [-30, -70, 48, 47, 28, -62],\n [152, -20, 22, -95, -67, 94],\n [94, 12, -28, -64, -67, 100],\n [-46, 64, 28, -6, 73, -80],\n [-104, 90, -58, 34, 40, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[7, 28, -36, 57, -34, 9],\n [-44, 59, -49, 11, -28, 24],\n [-37, 17, -3, -42, 10, 9],\n [-63, 98, -86, 37, -54, 39],\n [2, -17, 19, -23, 16, -6],\n [75, -95, 77, -10, 42, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-49, -7, 91, -47, -77, -66],\n [88, 8, -41, -8, -58, 70],\n [-60, -26, 77, -28, -63, -59],\n [12, 4, 29, -28, -58, -6],\n [-38, 12, 42, -18, 7, -47],\n [43, 5, -11, -11, -41, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-11, 3, -28, 45, -113, 10],\n [-26, 22, -112, -108, 16, -80],\n [-28, 90, -52, 24, 102, 80],\n [37, 87, -88, -72, -41, -122],\n [-41, 26, -138, -104, -5, -72],\n [58, 42, 100, 33, 120, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
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