messages listlengths 1 1 | ground_truth stringclasses 5 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the rank of the matrix:\n[[16, -32, 0, 0, -40, 28],\n [-36, 72, 0, 0, 90, -63],\n [-16, 32, 0, 0, 40, -28],\n [0, 0, 0, 0, 0, 0],\n [12, -24, 0, 0, -30, 21],\n [-40, 80, 0, 0, 100, -70]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-31, 156, -128, 122, 28, -126],\n [-73, 18, 106, -124, 19, -63],\n [-81, -68, 214, -232, 26, 20],\n [-5, 48, -53, 55, 23, -7],\n [-27, 28, 5, -7, 35, 9],\n [18, -54, 23, -15, 12, 92]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[20, -16, -8, -11, 0, -10],\n [52, -52, -12, -28, -12, -28],\n [-45, -3, 51, 27, -45, 15],\n [-42, 70, -14, 21, 42, 28],\n [52, 0, -56, -31, 48, -18],\n [44, 48, -88, -29, 96, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-30, -6, 6, -12, -6, 30],\n [100, 20, -20, 40, 20, -100],\n [50, 10, -10, 20, 10, -50],\n [20, 4, -4, 8, 4, -20],\n [70, 14, -14, 28, 14, -70],\n [40, 8, -8, 16, 8, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 1 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-32, -24, 12, 32, 32, 40],\n [-16, -12, 6, 16, 16, 20],\n [-80, -60, 30, 80, 80, 100],\n [8, 6, -3, -8, -8, -10],\n [-24, -18, 9, 24, 24, 30],\n [0, 0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, 40, -8, -28, -31, 37],\n [4, 8, 18, -49, -35, 41],\n [-89, -40, 20, -22, -120, 32],\n [-20, 84, -58, 34, -15, 6],\n [-2, -16, 72, -148, -116, 116],\n [41, -12, -42, -22, -54, 111]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-40, -100, -100, 90, 20, -20],\n [20, 50, 50, -45, -10, 10],\n [-4, -10, -10, 9, 2, -2],\n [-4, -10, -10, 9, 2, -2],\n [-36, -90, -90, 81, 18, -18],\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[[-36, -16, -72, -48, -32, 8],\n [-18, -6, -48, -27, -23, 2],\n [36, 36, -48, 18, -38, -28],\n [-162, -124, -12, -138, 38, 88],\n [-18, -14, 0, -15, 5, 10],\n [54, 40, 12, 48, -8, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[2, 18, 123, 59, 197, 83],\n [51, -83, -59, 76, -180, -63],\n [135, 65, 49, -73, -74, 150],\n [-67, -183, -111, 204, 5, -148],\n [-105, -33, 53, 123, 100, -80],\n [13, 16, -22, -101, 87, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[72, 0, 48, -24, -56, -40],\n [45, 0, 30, -15, -35, -25],\n [45, 0, 30, -15, -35, -25],\n [-72, 0, -48, 24, 56, 40],\n [81, 0, 54, -27, -63, -45],\n [-90, 0, -60, 30, 70, 50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 1 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[66, 111, -6, -6, -81, 24],\n [81, 125, 41, 60, -64, -50],\n [91, 143, 35, 52, -80, -38],\n [14, 33, -42, -58, -47, 72],\n [23, 18, 87, 122, 37, -138],\n [-45, -68, -29, -42, 31, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-71, 148, 79, -103, 89, -85],\n [71, -11, -11, 31, -25, -35],\n [191, 72, -63, -67, -13, -45],\n [-6, 128, -46, 44, 182, 64],\n [120, 55, -185, -11, 106, 203],\n [77, 43, -77, -100, 7, 66]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-80, 20, 106, 140, 79, -28],\n [14, -13, -10, -26, 16, 61],\n [94, -98, -118, -118, -15, 64],\n [60, -137, -148, -39, -32, -80],\n [50, 8, -54, -101, -50, 47],\n [9, -69, -102, -15, -26, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-48, 80, 2, 62, 31, -66],\n [-102, 22, 86, 77, 10, -6],\n [4, 114, -50, 22, 94, -126],\n [-72, 21, 85, 28, 92, -45],\n [36, -94, 74, -118, 136, 6],\n [-40, -97, 97, -14, -21, 87]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-26, 24, 33, -55, 24, 47],\n [-25, 45, 90, -140, 30, 100],\n [13, -31, -67, 103, -18, -71],\n [-48, -20, -110, 154, 24, -74],\n [33, -29, -38, 64, -30, -56],\n [0, -38, -101, 151, -12, -95]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[38, -96, -111, 47, -22, 34],\n [-56, 180, 66, -134, 100, -76],\n [11, 16, 61, -46, 12, 17],\n [76, -18, -44, -156, 84, 62],\n [-6, 28, -15, -29, 26, -14],\n [-10, -1, -3, 25, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-26, -102, -32, -3, -15, -94],\n [16, -30, -37, -60, -32, -4],\n [24, -36, -50, -84, -44, 0],\n [-8, -84, -42, -36, -28, -64],\n [-6, -72, -37, -33, -25, -54],\n [-40, -6, 43, 96, 44, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[140, 140, -62, 7, 30, -75],\n [-59, -10, -5, 74, 31, 16],\n [37, -10, -5, -10, -17, 4],\n [-19, 120, -30, 50, 74, -58],\n [-34, 90, -33, 90, 75, -36],\n [-78, -140, 50, -21, -50, 73]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, -4, 6, 2, 4, -14],\n [-3, -2, 3, 1, 2, -7],\n [3, 2, -3, -1, -2, 7],\n [18, 12, -18, -6, -12, 42],\n [-15, -10, 15, 5, 10, -35],\n [-12, -8, 12, 4, 8, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-45, -18, 90, -81, -54, 36],\n [-30, -12, 60, -54, -36, 24],\n [-30, -12, 60, -54, -36, 24],\n [-25, -10, 50, -45, -30, 20],\n [40, 16, -80, 72, 48, -32],\n [-15, -6, 30, -27, -18, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 1 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-160, -16, -73, -2, 8, 11],\n [140, 5, 8, -14, 60, 50],\n [110, 77, 71, -26, -10, -40],\n [-20, 82, 4, -40, 12, -26],\n [140, -6, 101, 26, -60, -45],\n [-30, 14, -48, -22, 50, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[6, 34, -15, -14, 149, 26],\n [13, -37, 44, -53, -35, -33],\n [-49, 28, 90, -31, -4, -16],\n [200, -150, -192, -56, 90, -6],\n [-35, 15, 59, -13, -30, -13],\n [70, -61, -47, -38, 22, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[44, 69, 61, 105, -205, 92],\n [-78, -95, 124, 57, 22, 36],\n [-74, -62, -35, -81, 151, -84],\n [250, 130, -65, 35, -34, 74],\n [112, -102, 38, 38, -10, 144],\n [-66, 88, 83, 93, -162, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-18, -6, -8, -18, -16, 14],\n [-18, -6, -8, -18, -16, 14],\n [63, 21, 28, 63, 56, -49],\n [90, 30, 40, 90, 80, -70],\n [-54, -18, -24, -54, -48, 42],\n [27, 9, 12, 27, 24, -21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 1 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[4, 4, -6, 10, 3, -9],\n [-40, -40, 60, -100, -30, 90],\n [4, 4, -6, 10, 3, -9],\n [-24, -24, 36, -60, -18, 54],\n [24, 24, -36, 60, 18, -54],\n [20, 20, -30, 50, 15, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 1 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[84, 64, -48, -72, -60, 80],\n [-39, -61, 89, 86, -10, -85],\n [-75, -109, 5, 74, 122, -97],\n [153, 30, -76, -76, -61, 76],\n [114, -119, -33, 36, 29, -59],\n [-54, -17, -22, 5, 69, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[112, -56, -56, -11, 22, -35],\n [3, -57, 30, 0, -8, 11],\n [-107, 34, 52, -2, -34, 48],\n [-76, 140, 32, 59, 42, -41],\n [144, -72, -32, 26, 60, -78],\n [-43, -37, 102, 52, 20, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-92, 34, 59, -25, -6, -24],\n [16, -40, -104, 64, 82, -64],\n [88, -28, -44, 16, -5, 32],\n [44, -10, -11, 1, -12, 24],\n [-12, -30, -87, 57, 81, -72],\n [28, -2, 5, -7, -18, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[4, 24, 8, 36, -28, -4],\n [-6, -36, -12, -54, 42, 6],\n [-1, -6, -2, -9, 7, 1],\n [-4, -24, -8, -36, 28, 4],\n [6, 36, 12, 54, -42, -6],\n [-4, -24, -8, -36, 28, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-92, 48, -22, 66, 32, 82],\n [103, -9, 50, -111, -1, -56],\n [-54, -134, 21, 57, -81, -1],\n [-57, -15, -39, 78, -15, 15],\n [89, 73, -30, -53, 37, -60],\n [-78, -32, 66, 0, -3, 92]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[2, 25, 56, -96, -59, 43],\n [-90, -45, -36, 0, 63, -99],\n [42, 35, 49, -56, -63, 70],\n [46, 25, 23, -8, -37, 54],\n [54, 25, 17, 8, -33, 56],\n [86, 45, 39, -8, -65, 98]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[46, -55, -113, -88, 50, -68],\n [-41, 71, 78, -6, 18, 30],\n [2, -14, 41, 76, -42, 38],\n [-140, 12, 27, -10, -178, 65],\n [-19, -20, 25, 32, -52, 37],\n [-3, 68, 107, 44, 48, 39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[46, -62, 22, -28, 71, -57],\n [-154, -62, -110, -116, 145, -139],\n [132, -138, -16, 0, 116, -26],\n [-62, -47, -85, -40, 72, -50],\n [2, 36, 78, -20, -11, -5],\n [-84, 149, 31, 48, -172, 50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-8, 13, 26, 0, 41, -43],\n [-15, 20, 40, -5, 60, -55],\n [-10, 18, 36, 2, 58, -64],\n [-1, 13, 26, 13, 49, -72],\n [-19, 16, 32, -17, 40, -15],\n [-35, 28, 56, -33, 68, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-27, -44, -63, -19, 35, 11],\n [78, 58, 11, 70, -24, -45],\n [-45, -54, -60, -33, 33, 24],\n [24, 18, 17, 8, 10, -23],\n [31, 8, 28, -31, 88, -63],\n [-5, 8, -9, 31, -61, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-24, -63, 49, 20, -58, -89],\n [10, -14, -12, 3, -17, -12],\n [38, -166, 101, -26, -105, -133],\n [2, 27, 70, -52, 75, 66],\n [16, -185, 119, -8, -130, -175],\n [-44, -12, 46, 20, -14, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-246, -75, 32, -4, 35, -25],\n [57, -131, -210, 97, -200, -71],\n [-55, -99, -64, 41, 40, 23],\n [61, 71, -21, 125, -18, -154],\n [52, -168, -252, 48, -160, 62],\n [-27, -75, -86, 135, -92, -172]]\n\nPresent the answer in LaTex format: \\boxed{Your an... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-166, -2, 73, 29, 74, -82],\n [54, 0, -25, -49, 39, 71],\n [183, -43, -36, 52, 7, 118],\n [-17, 57, -41, -9, -87, -74],\n [76, 99, -53, -108, 75, 124],\n [94, -68, -89, -35, -159, -39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[16, 38, 6, 0, 38, -44],\n [-18, -15, 3, 30, -3, 30],\n [-5, 39, 16, 55, 61, -22],\n [45, 93, 12, -15, 87, -114],\n [30, 25, -5, -50, 5, -50],\n [-67, -99, -4, 65, -73, 142]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[51, -33, 27, -16, -2, -46],\n [-7, -142, -67, -10, 66, 90],\n [-131, 16, -75, 98, 50, 50],\n [-46, -70, -45, 92, 45, -52],\n [-52, 82, -71, 40, -157, -36],\n [81, 44, 84, -82, -13, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-53, 61, -108, -100, 85, -33],\n [-103, -9, 36, -4, -73, -123],\n [17, 81, -93, -19, 102, 40],\n [-40, -27, 32, 148, -53, -78],\n [49, 80, 16, -4, 42, 31],\n [9, 22, 125, 181, -79, -69]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[5, 30, -30, 52, 11, -45],\n [-1, -41, -20, 59, -39, -72],\n [-14, -74, 46, 39, -43, -78],\n [-22, -2, 128, -34, 38, -4],\n [-13, -58, 54, 0, -27, -31],\n [0, -75, -32, 42, -67, -55]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-108, 62, -82, 142, -12, 82],\n [-38, 27, -47, 57, 8, 27],\n [-32, 22, -37, 47, 5, 23],\n [32, -22, 37, -47, -5, -23],\n [-36, -12, 87, 3, -81, 39],\n [44, 10, -90, -10, 88, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-54, -92, 0, 56, -50, -66],\n [-27, -43, -82, -44, -17, 50],\n [-24, -30, -68, -42, -8, 46],\n [-36, -67, -38, 10, -36, -11],\n [42, 125, 18, -74, 86, 75],\n [99, 171, 74, -42, 89, 50]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-15, -88, 11, -87, -111, 4],\n [-54, 78, 9, 22, -12, 27],\n [68, -64, -4, 0, 42, -34],\n [-28, 52, -2, 22, 9, 15],\n [-16, 42, -39, 28, 42, 13],\n [21, 66, -24, 75, 108, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-6, 4, -103, -46, 29, 64],\n [-2, -7, 94, 43, -27, -62],\n [44, 24, -66, -36, 22, 64],\n [-76, -36, 30, 24, -14, -56],\n [-26, -6, -87, -36, 23, 44],\n [-96, -46, 46, 34, -20, -76]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-26, 55, -23, -67, 13, -18],\n [-18, 52, -48, -86, 26, -68],\n [7, -9, 85, 40, -34, -4],\n [10, -4, 82, 24, -30, -44],\n [2, -24, -83, 7, 28, 60],\n [-16, 53, -23, -81, 17, -82]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-65, 17, -31, -87, -12, -100],\n [116, -17, 48, 70, -66, 108],\n [17, 124, -135, -125, 22, -135],\n [-31, -5, -23, -59, -48, -39],\n [72, -87, 112, 100, -92, 143],\n [-113, -61, 35, -5, 20, -23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[69, 19, -9, 1, 33, 31],\n [15, -101, -20, -23, 32, -98],\n [85, 42, -66, 53, 56, -18],\n [51, -64, -64, 15, 62, -108],\n [-125, -100, 78, -73, -72, -30],\n [-48, -137, -29, -68, 59, -125]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-21, -53, -28, 39, -91, 119],\n [7, 40, 20, -19, 75, -70],\n [11, -107, -36, 55, -201, 100],\n [-10, 21, 8, 4, 48, -5],\n [40, 9, 40, 38, 36, -148],\n [17, -47, 12, 85, -57, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-8, 36, 8, 1, -21, 2],\n [-68, 27, -25, -38, -39, 79],\n [-4, 171, 55, 26, -87, -33],\n [32, 108, 52, 38, -42, -64],\n [-48, 72, 0, -18, -54, 44],\n [28, -99, -19, 1, 60, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-57, -154, -87, 52, 27, 38],\n [56, -118, 1, -82, -33, 26],\n [148, -30, -18, -140, -120, 15],\n [53, -70, -129, -38, -15, -19],\n [10, -98, -69, -27, -22, 34],\n [6, 90, 72, -17, 23, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-149, -22, -65, -67, -163, -19],\n [37, -19, 104, 1, 218, 48],\n [119, 54, 79, 72, 13, -74],\n [-96, 79, -81, -89, -9, 83],\n [-118, -168, -5, -40, -75, -43],\n [138, 24, 33, 60, 143, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-32, 90, 6, 91, -97, 90],\n [-65, -121, 43, 27, -56, 25],\n [-67, -35, 72, 118, -143, 160],\n [16, 20, 55, -1, -15, 129],\n [-4, 79, 22, 97, -109, 86],\n [176, 60, 74, -147, 93, 46]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[18, 63, 10, 36, -5, -71],\n [73, 24, 30, -33, 5, -26],\n [209, -21, -38, -21, -142, -171],\n [9, -74, -33, -24, -37, 29],\n [142, -40, -33, -27, -102, -97],\n [-60, -78, -65, 27, -50, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-18, 26, 10, 26, 64, 48],\n [3, -31, -35, 119, 46, -18],\n [-16, 24, 10, 19, 55, 43],\n [-26, 34, 10, 54, 100, 68],\n [16, -24, -10, -19, -55, -43],\n [26, -66, -50, 94, -32, -80]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-63, 17, 47, -57, -3, -7],\n [68, -110, -8, 86, 56, -44],\n [6, -98, 61, 31, 24, -56],\n [-94, 88, 46, -124, -2, 2],\n [36, -50, 28, 12, 34, -54],\n [55, 11, -55, 70, -66, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[10, 50, 0, 25, 20, 50],\n [-10, -50, 0, -25, -20, -50],\n [6, 30, 0, 15, 12, 30],\n [14, 70, 0, 35, 28, 70],\n [2, 10, 0, 5, 4, 10],\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[[41, 5, 43, 61, -33, 31],\n [-24, 40, -8, -56, 56, -72],\n [41, 5, 43, 61, -33, 31],\n [44, 110, 88, 16, 54, -98],\n [67, 35, 81, 87, -31, 17],\n [36, -5, 34, 58, -37, 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[[47, 28, 19, -69, -48, 47],\n [24, 58, -49, 14, -13, 3],\n [-65, -42, 19, 74, 14, -86],\n [-89, -6, -20, 155, -4, -158],\n [-51, -76, 57, 69, -50, -63],\n [-2, -82, 40, -73, 85, 81]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-40, 48, -32, 64, 32, 0],\n [5, -6, 4, -8, -4, 0],\n [-45, 54, -36, 72, 36, 0],\n [-50, 60, -40, 80, 40, 0],\n [50, -60, 40, -80, -40, 0],\n [30, -36, 24, -48, -24, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[10, 9, 34, -13, 7, 3],\n [207, 13, 60, 136, 173, 20],\n [-66, 13, 52, -9, -55, 7],\n [-38, 0, -28, 2, -26, 24],\n [-38, -32, -115, 8, -30, -23],\n [31, 10, 43, 3, 24, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[61, -78, -100, -15, 54, 27],\n [-86, 78, -34, 3, -22, 172],\n [171, 33, -77, 47, -37, -37],\n [-62, 17, -31, -14, 3, 120],\n [-87, 47, 43, 3, -9, 31],\n [19, 28, 26, 23, -12, -63]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 4 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[61, 68, -11, 30, -61, 86],\n [91, 12, 0, 59, -135, 43],\n [90, -88, -58, 86, -121, -85],\n [50, 72, -38, 26, -21, 75],\n [10, -104, -57, 35, -5, -128],\n [53, 68, 19, 20, -73, 96]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[50, -40, -45, -45, -40, 35],\n [-40, 32, 36, 36, 32, -28],\n [90, -72, -81, -81, -72, 63],\n [30, -24, -27, -27, -24, 21],\n [-20, 16, 18, 18, 16, -14],\n [40, -32, -36, -36, -32, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[62, -39, 177, -35, 75, -31],\n [-51, -92, -4, 6, 20, 5],\n [93, -40, 131, -13, 16, 59],\n [-183, 85, 48, 134, 182, 21],\n [129, -194, 33, -121, -139, -84],\n [-48, -19, 21, -35, 64, -96]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-9, -126, -105, -42, 66, 33],\n [18, -4, 20, 65, -4, 85],\n [75, -80, 45, -66, -96, -36],\n [-21, 196, 115, 79, -44, -31],\n [94, -26, 110, -19, -138, -14],\n [48, -64, 20, -70, -64, -50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[123, -74, -61, -50, -176, 44],\n [-106, 50, 64, -18, 136, -12],\n [121, 77, -78, -61, -106, 32],\n [13, -113, 26, -123, -85, 63],\n [55, 84, -57, 68, -11, -29],\n [106, -33, -51, -79, -143, 49]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[3, 6, 9, 18, 63, -48],\n [57, -54, 45, -36, 84, 54],\n [36, -40, 24, -36, 14, 68],\n [58, -60, 42, -48, 52, 84],\n [26, -20, 24, -6, 69, -2],\n [-18, 28, -6, 36, 46, -80]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-24, 12, -24, -24, 0, 18],\n [24, -12, 24, 24, 0, -18],\n [-56, 28, -56, -56, 0, 42],\n [0, 0, 0, 0, 0, 0],\n [72, -36, 72, 72, 0, -54],\n [32, -16, 32, 32, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-10, 64, 74, -63, -25, -17],\n [-68, -32, -34, -8, 40, 33],\n [116, 168, 96, -4, 47, 103],\n [13, 46, 19, -41, -104, -14],\n [-46, 165, 44, 65, 68, 41],\n [102, -7, 42, 47, -15, -95]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[52, -10, 7, 47, -60, -5],\n [-5, 24, -20, -35, 28, 14],\n [-8, -28, 16, 3, -25, -282],\n [36, -39, -99, -12, -75, -37],\n [37, 59, 202, 89, 3, 99],\n [87, 10, 6, 67, -64, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-22, 181, 44, -86, -33, -43],\n [36, 152, 18, -102, -6, 34],\n [12, 68, -79, -79, 115, -11],\n [-102, -77, -1, 89, -2, -130],\n [36, -46, -77, -17, 95, 37],\n [64, 58, 50, -42, -64, 92]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-40, 42, 52, 183, 38, 9],\n [-90, -8, 60, -62, -100, 72],\n [-16, 68, -116, 143, 60, -6],\n [-6, -30, 204, 24, 60, -84],\n [-108, -18, -16, -112, -112, 38],\n [-80, 30, 94, 2, 41, -43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-112, 70, -2, 8, -34, -26],\n [49, -55, -4, 3, 23, 39],\n [84, -15, 9, -16, 13, -23],\n [77, -5, 10, -17, 9, -31],\n [-21, 90, 15, -19, -32, -92],\n [126, -60, 6, -14, 32, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[37, 25, 5, 26, -28, 21],\n [-5, 15, -25, 70, 0, 35],\n [-29, -15, -10, -2, 21, -7],\n [-55, -39, -5, -46, 42, -35],\n [-38, -22, -10, -12, 28, -14],\n [-63, -49, 0, -70, 49, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-86, -171, 1, -95, -14, -6],\n [-73, -108, -58, -99, 79, 24],\n [-32, 14, 2, 150, -7, -11],\n [-41, -147, 36, -110, -105, -58],\n [-51, -115, -128, -184, 58, -4],\n [-103, -33, 24, 58, 31, -170]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 5 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-153, 26, 92, 31, 83, -5],\n [90, -81, 18, -74, -96, 39],\n [-32, -1, -18, 57, -35, -37],\n [61, 8, -17, -37, 18, 24],\n [-116, -77, 92, 15, -51, 33],\n [143, -94, 135, -144, -73, 68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 5 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[33, 137, 37, 66, -85, 122],\n [-39, 0, 2, 62, 27, -25],\n [133, 65, 128, 67, 84, -137],\n [13, 9, 11, 12, 53, -50],\n [119, 30, 66, -48, -25, -13],\n [-159, -34, -175, -99, -122, 224]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[64, -72, 72, 16, -64, -32],\n [-8, 9, -9, -2, 8, 4],\n [-40, 45, -45, -10, 40, 20],\n [-80, 90, -90, -20, 80, 40],\n [80, -90, 90, 20, -80, -40],\n [-80, 90, -90, -20, 80, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[15, 36, 78, -25, -6, -91],\n [22, -26, 87, -75, -75, -7],\n [-108, -64, -44, -56, 16, 24],\n [37, 106, -120, 181, 135, -27],\n [28, -98, -60, -18, -87, 200],\n [-53, -18, -59, 10, 37, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[4, 7, 8, -10, -5, -9],\n [24, 42, 48, -60, -30, -54],\n [-16, -28, -32, 40, 20, 36],\n [-8, -14, -16, 20, 10, 18],\n [-32, -56, -64, 80, 40, 72],\n [8, 14, 16, -20, -10, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[76, 142, 18, -143, -16, -58],\n [-12, 97, -75, -82, -53, -112],\n [45, 64, 57, -112, -29, -25],\n [-28, -19, 146, -79, -64, -21],\n [-74, -76, 81, -42, -91, -37],\n [-9, -2, 37, -103, -73, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-42, -56, 7, -70, 70, -14],\n [-60, -80, 10, -100, 100, -20],\n [-60, -80, 10, -100, 100, -20],\n [36, 48, -6, 60, -60, 12],\n [-30, -40, 5, -50, 50, -10],\n [-54, -72, 9, -90, 90, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 1 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[6, -4, -8, 6, -2, -2],\n [21, -14, -28, 21, -7, -7],\n [24, -16, -32, 24, -8, -8],\n [-18, 12, 24, -18, 6, 6],\n [27, -18, -36, 27, -9, -9],\n [30, -20, -40, 30, -10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-17, -48, -57, -5, -34, -36],\n [-30, 2, -10, 8, 28, -26],\n [-47, -113, -137, -10, -74, -91],\n [31, -78, -69, -23, -106, -6],\n [-61, 13, -11, 18, 66, -49],\n [-55, -108, -135, -7, -62, -96]]\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-46, -101, 0, -78, 104, 100],\n [26, -67, -64, -12, -12, -24],\n [-62, -133, -60, -27, 34, 44],\n [-148, 8, 16, -43, 82, 68],\n [80, -73, 54, 1, 16, 66],\n [-26, -104, 0, -1, 22, 62]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[7, -2, -42, -21, 39, -14],\n [4, -8, -12, -6, 6, 4],\n [-5, 22, -6, -3, 21, -26],\n [24, -88, -2, -1, -59, 94],\n [13, -22, -46, -23, 29, 6],\n [-9, 22, 20, 10, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-117, 84, 28, -69, 50, -18],\n [153, -85, 73, 164, -65, -9],\n [-1, -55, 37, -101, 66, 2],\n [-24, 103, 111, 172, -50, -42],\n [47, 26, 38, 148, -52, -34],\n [-3, -24, 26, -180, 151, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-73, -149, 28, 66, 39, 114],\n [-23, 69, -34, 17, 27, 22],\n [19, -5, 195, 7, -99, -7],\n [-40, -72, -9, 34, 37, 59],\n [-103, -195, 52, 100, 87, 158],\n [1, -39, 151, 23, -23, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[52, -60, 65, -193, 2, 98],\n [-42, 98, 20, 48, 20, -33],\n [4, -76, -39, -101, -54, 105],\n [-22, 6, 43, -21, -124, -116],\n [-102, -118, -111, 208, -130, -147],\n [16, 20, -51, 18, -22, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 5 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-52, -61, 78, -45, -25, 25],\n [20, 65, -86, 24, 36, 2],\n [-32, 103, -34, -33, 39, 25],\n [17, -70, 62, 9, -38, -24],\n [50, -49, 66, 27, -43, -53],\n [30, -96, 12, 36, -30, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-20, 58, 74, 32, 112, 56],\n [40, 20, 39, 38, 31, 24],\n [146, -16, 39, 70, -31, 4],\n [-20, -105, -55, -100, -80, -80],\n [16, 84, 44, 80, 64, 64],\n [4, 69, 77, 56, 106, 64]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[127, 47, 64, 8, 103, -66],\n [-71, 30, -27, -12, 31, -26],\n [41, -14, 20, 34, -43, 42],\n [-23, -118, -104, -27, -92, 24],\n [-8, 147, 76, 73, 54, -10],\n [86, 63, 47, 43, 15, -26]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 5 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[27, -54, 81, 9, -45, 45],\n [-6, 12, -18, -2, 10, -10],\n [-24, 48, -72, -8, 40, -40],\n [15, -30, 45, 5, -25, 25],\n [-15, 30, -45, -5, 25, -25],\n [27, -54, 81, 9, -45, 45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[18, -144, -54, -144, -9, -81],\n [12, 52, 28, 44, 0, 16],\n [58, -94, -14, -114, -14, -86],\n [56, -78, -8, -98, -13, -77],\n [-62, -22, -38, 6, 10, 34],\n [-132, 20, -52, 76, 24, 104]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-88, 27, -66, -25, -16, -63],\n [82, -45, 34, -71, 54, 103],\n [34, -63, -24, -83, 34, 63],\n [107, -52, 63, 2, 27, 88],\n [-19, -50, -56, -31, -9, -9],\n [46, 27, 66, 37, 10, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 3 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[58, -82, 114, -96, -43, -112],\n [-85, 11, -57, 54, 26, 56],\n [100, 66, 52, 10, -127, 50],\n [21, -64, -41, -17, 58, -57],\n [35, -82, 132, -7, 8, -181],\n [-60, -2, -86, -2, 87, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 5 | MATH |
[
{
"content": "Compute the rank of the given 6x6 matrix:\n[[-45, 38, 31, -13, -15, -84],\n [17, 41, -7, 32, 41, 113],\n [-18, 34, 14, 4, 6, -6],\n [-10, 45, 10, 15, 20, 35],\n [-69, 146, 55, 23, 33, 0],\n [18, -34, -14, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[60, -57, 61, -36, 28, 95],\n [-160, 67, -91, 16, 32, -45],\n [72, -48, 56, -24, 8, 64],\n [-34, 34, -36, 22, -18, -58],\n [-100, 61, -73, 28, -4, -75],\n [-26, 23, -25, 14, -10, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 2 | MATH |
End of preview. Expand
in Data Studio
No dataset card yet
- Downloads last month
- 5