messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[12, 11, 0, -28, -1],\n [-14, 16, -39, 10, -39],\n [20, 13, -17, 8, -28],\n [-20, -24, 13, 40, 17],\n [-9, 17, -36, 5, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-3, -6, 3, -1, -1],\n [-35, -10, -35, -25, 25],\n [-6, -12, 6, -2, -2],\n [16, 20, -2, 8, -2],\n [22, 14, 13, 14, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[11, 22, -12, -17, 5],\n [-29, 24, -1, -14, 34],\n [27, -10, 1, 10, -30],\n [7, -8, 8, 13, -17],\n [-23, 0, 26, 25, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[11, -2, -5, 2, -10],\n [19, -1, -11, 4, -19],\n [-9, 0, 5, -6, -5],\n [31, 9, -27, 16, -13],\n [10, 10, -16, 4, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-14, -8, -23, -1, -13],\n [2, 2, -18, 1, -29],\n [12, -4, 18, 12, 28],\n [29, 12, 7, 10, -21],\n [-4, 2, -2, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[10, -19, 18, 12, 23],\n [-6, 7, -13, -5, -16],\n [-10, 31, -12, -18, -17],\n [-6, 25, -4, -14, -7],\n [2, -1, 5, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[9, 5, 2, 27, -37],\n [-8, -3, -14, 38, -4],\n [-17, 20, 26, -15, 1],\n [15, -11, -15, 2, -1],\n [34, -25, -4, -34, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-32, 25, 12, -11, 36],\n [15, -34, -27, 30, -31],\n [28, 19, 12, -5, 24],\n [-27, 23, 6, -3, 44],\n [-26, 17, 20, -24, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[26, 8, -22, -16, -4],\n [25, 10, -5, 0, -10],\n [6, 0, -18, -16, 4],\n [-20, -8, 4, 0, 8],\n [-27, -9, 18, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[32, 30, 4, -24, 42],\n [3, 16, 30, -1, 11],\n [-34, -25, -8, 26, -35],\n [18, 19, -6, -14, 29],\n [11, 22, 21, -5, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[40, -20, 5, 15, 35],\n [-17, 16, -7, -15, -13],\n [11, 12, -10, -16, 14],\n [-4, -8, 6, 10, -6],\n [5, -20, 12, 22, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-28, -2, 0, -10, 12],\n [16, 5, -6, 1, -12],\n [-13, 1, -3, -7, 3],\n [-13, -8, 11, 4, 15],\n [-41, -1, -3, -17, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-7, -40, 28, -37, 5],\n [2, 9, -6, 8, -2],\n [-8, -19, 10, -14, 12],\n [3, 22, -16, 21, -1],\n [-2, -26, 20, -26, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[36, 14, 25, 15, 30],\n [-31, 27, -8, -15, 23],\n [41, -2, -5, 31, -9],\n [5, -8, 21, 21, 5],\n [5, 12, 47, -26, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[24, 30, -17, 21, -1],\n [-18, -15, 25, 6, 4],\n [21, 15, -37, -3, -17],\n [-31, -40, 16, -19, -11],\n [2, 5, 2, 11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[32, 15, 10, -33, -18],\n [16, 5, -1, -39, -21],\n [-19, 15, 13, -1, 5],\n [24, -25, -27, -29, -23],\n [41, 0, -11, -13, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-7, -3, -5, -26, 19],\n [8, -2, 3, 8, 0],\n [-2, 4, 1, 12, -14],\n [-11, 3, -4, -10, -1],\n [-6, 2, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[11, -7, 10, 2, -19],\n [27, -27, 4, 30, -19],\n [-15, 12, -8, -11, 15],\n [41, -51, 23, 33, -34],\n [30, -18, 19, 27, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-10, -4, 4, 29, -20],\n [3, -13, -16, 9, -7],\n [24, -13, -19, 10, -1],\n [-38, -5, -1, 0, -13],\n [26, -14, -24, -2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-14, -19, -17, 21, -7],\n [7, -35, -11, 16, -36],\n [4, -22, -14, 6, -34],\n [2, 1, 19, 9, 29],\n [4, 4, -5, -11, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-8, 10, -4, 10, -8],\n [-33, 20, -19, 15, -8],\n [8, -10, 4, -10, 8],\n [-33, 20, -19, 15, -8],\n [-37, 25, -21, 20, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[11, -39, -20, -22, -17],\n [-6, 8, -2, 4, 4],\n [-12, 33, 13, 20, 21],\n [-21, -1, -7, -15, 6],\n [-35, 23, -11, 1, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[17, -21, -8, -33, 23],\n [-4, 15, 4, 4, 37],\n [-13, 36, 13, 43, -2],\n [-38, 11, -3, 14, 3],\n [-25, 10, 0, 5, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-12, -4, -9, 11, -17],\n [-12, 11, -18, -1, -14],\n [0, 15, -9, -12, 3],\n [-20, -5, -16, 17, -28],\n [0, 20, -12, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[30, 6, 9, -7, -20],\n [-16, -4, -2, 6, 12],\n [-7, -4, 7, 9, 9],\n [0, -6, 21, 17, 10],\n [-17, -2, -10, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[7, -13, -15, 35, 13],\n [-12, 12, 16, -40, -16],\n [-12, -6, -1, -5, -5],\n [26, 16, 5, 5, 9],\n [13, -1, -6, 20, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-2, -17, 35, 6, 6],\n [4, -4, 18, 25, 10],\n [5, -10, 11, -1, -5],\n [-15, 30, -4, 16, -16],\n [-21, 10, -15, -15, 33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[15, -20, -24, 3, -13],\n [11, -4, -12, 27, -21],\n [30, 5, 9, -10, -4],\n [-16, -21, -17, -22, 40],\n [-25, 8, 8, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[5, 0, 0, 1, 3],\n [20, 0, 0, 4, 12],\n [-10, 0, 0, -2, -6],\n [-21, -20, -20, -5, -11],\n [3, -15, -15, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-2, 5, -14, -3, 5],\n [10, -11, 0, -13, 17],\n [4, -9, 23, 4, -7],\n [-2, 1, 6, 5, -7],\n [-8, 9, -1, 10, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-13, -31, -39, -42, -32],\n [-7, -33, -33, -43, -20],\n [5, 18, 16, 18, 9],\n [-13, 5, 5, 32, -4],\n [13, 13, 17, 5, 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, -2, -16, 34, 4],\n [-20, 4, -28, -8, 22],\n [4, -22, -24, 18, 10],\n [14, 7, 36, 3, -25],\n [-18, 8, 2, 28, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[26, -16, -8, -22, 25],\n [12, -3, -1, -7, 15],\n [-25, 29, 8, 30, -14],\n [-22, 9, 1, 15, -25],\n [-2, 6, -6, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-6, 28, -40, 28, 37],\n [-34, -15, 8, -19, -5],\n [4, -13, 12, -29, -29],\n [-22, -22, 4, -4, -6],\n [-3, 0, 2, -16, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-18, -20, 10, -14, -20],\n [-35, 15, -5, 25, 27],\n [11, 8, -11, 1, -23],\n [-10, -27, 14, -22, -26],\n [17, 15, -19, 2, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0, 0],\n [11, 4, 1, -12, 19],\n [-12, -12, -3, 1, -8],\n [17, 16, 4, -3, 13],\n [0, -12, -3, -19, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-8, 38, 7, -16, -6],\n [0, -14, -11, 8, 0],\n [-26, 18, -1, -4, 5],\n [7, -63, -14, 29, 11],\n [-24, 0, -12, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-9, -11, 12, -1, 15],\n [-2, 4, 34, -16, -14],\n [-12, -20, 4, 8, 32],\n [1, -7, -3, 10, 14],\n [12, -7, 11, 19, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[4, 3, -4, -2, 6],\n [16, 12, -10, -14, 12],\n [-16, -12, 13, 11, -18],\n [-20, -15, 19, 11, -28],\n [4, 3, -6, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-2, 7, 9, -3, 12],\n [-9, 23, 32, -5, 20],\n [-4, 11, 15, -3, 12],\n [-1, 4, 5, -2, 8],\n [-1, 5, 6, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-25, 34, 31, -45, 17],\n [-10, 35, 5, -44, 39],\n [-11, 10, -20, 2, 6],\n [-4, 3, 12, -7, -2],\n [22, -23, -27, 30, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-13, 19, 38, 29, -2],\n [7, -14, -2, -1, 41],\n [41, 27, -16, -15, -8],\n [-44, -27, 15, 15, -3],\n [7, 9, -15, -20, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-24, -40, 32, 0, -5],\n [-56, -17, 42, 21, -4],\n [45, 42, -46, 3, 13],\n [-23, 17, 4, 36, 40],\n [23, -22, -2, -35, -38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-5, 15, -25, 0, -30],\n [13, -3, -25, 24, 0],\n [-10, 12, -5, -12, -21],\n [-21, 15, 15, -32, -22],\n [3, 3, -15, 8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-4, 38, -2, 10, 2],\n [39, 21, 38, 41, -25],\n [17, -25, 30, -3, -29],\n [-23, 14, -33, -10, 32],\n [29, 3, 13, 33, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[4, 0, -2, -21, -12],\n [5, 36, 2, 0, 12],\n [4, -16, 16, -16, -24],\n [4, 20, 1, -6, 3],\n [5, -4, 26, -5, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-6, -32, 4, -14, -10],\n [-9, -7, 14, 0, 6],\n [-18, -24, 3, -5, 2],\n [24, 9, -30, -5, -19],\n [-6, 13, 22, 9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[6, -8, -12, -3, -1],\n [13, 35, -5, 11, 38],\n [36, 13, -9, 15, -13],\n [24, 1, -13, 4, 6],\n [16, 39, -11, 14, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-23, -14, -4, 8, -4],\n [22, 18, -8, -4, 2],\n [9, 6, 4, 2, -1],\n [4, 9, -16, 4, -2],\n [-9, -13, 20, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[22, -39, -49, -13, -5],\n [-17, -14, 1, 19, 29],\n [-19, -23, -24, 22, 6],\n [-8, 7, 27, 11, 23],\n [-23, 4, -15, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-1, 3, 0, -3, 4],\n [-20, -11, 45, 25, -21],\n [16, -4, 0, 8, -8],\n [28, -8, -35, -1, -7],\n [22, 4, -25, -9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[40, -6, 18, 3, 29],\n [-6, -4, -2, 9, 3],\n [-4, -12, 0, 24, 16],\n [-6, -4, -2, 9, 3],\n [-1, -3, 0, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[0, 2, -7, 3, -2],\n [-4, 4, 8, 0, 10],\n [14, -20, -7, -9, -29],\n [-12, 18, 3, 9, 24],\n [-6, 14, -16, 12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[9, -6, -22, -20, -3],\n [1, 5, -2, 1, -3],\n [5, 2, 16, -15, -20],\n [11, 41, 6, -4, -43],\n [-8, -24, -2, 9, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-1, -9, -8, -3, -6],\n [-24, 9, 6, -18, 0],\n [14, -24, -20, 6, -12],\n [14, -24, -20, 6, -12],\n [-35, 10, 6, -27, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[37, 7, 9, 31, -4],\n [14, 8, 5, 22, 3],\n [6, 1, -12, 2, -9],\n [14, -12, -5, 17, -22],\n [-26, -9, -17, -10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-8, 35, -13, -34, 13],\n [-29, -65, 16, 2, 6],\n [-8, -35, 1, 8, 6],\n [-18, -35, -1, -6, 13],\n [1, -5, 10, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-3, 7, 1, 2, 16],\n [1, 8, 1, 23, 12],\n [14, -6, -14, -8, -20],\n [3, -32, 1, 19, 18],\n [9, -1, -13, -28, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[7, -13, -16, -7, -13],\n [15, -20, -30, -15, -20],\n [-2, 21, 14, 2, 21],\n [-13, 21, 28, 13, 21],\n [-6, -25, -6, 6, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-23, 11, 15, -11, 17],\n [-9, 4, 5, -5, 6],\n [17, -13, -25, -3, -23],\n [12, -10, -20, -4, -18],\n [6, 2, 10, 14, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-7, -5, -6, -1, 19],\n [28, 25, -6, 24, 10],\n [-13, -11, 2, -11, -3],\n [-31, -18, 0, -29, -3],\n [-13, -1, -8, -11, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[20, -4, 8, -8, -8],\n [-9, -15, -30, 10, -6],\n [-26, 22, 16, 4, 20],\n [-24, 9, -3, 8, 12],\n [-15, 3, -6, 6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-7, -15, -25, -14, -5],\n [-8, -12, -23, -13, -7],\n [-6, 6, -1, -1, -9],\n [20, 0, 25, 15, 25],\n [2, -6, -4, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-25, -3, -20, 15, 20],\n [-13, -7, -12, 24, 22],\n [-6, -16, -16, 12, 11],\n [0, -25, -40, 13, 10],\n [-6, -32, -56, 11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[13, -6, -6, -5, 9],\n [-27, 4, 14, 15, -26],\n [5, 18, -6, -13, 21],\n [29, -10, -14, -13, 23],\n [3, -20, 2, 9, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[1, -20, -3, 31, -1],\n [-5, -17, 2, 14, -8],\n [-7, -31, 2, 30, -12],\n [-7, -4, 5, -9, -9],\n [-8, -11, 5, -1, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[22, 21, -16, 21, -20],\n [-2, -9, -4, -9, 16],\n [-16, -7, 18, -7, -2],\n [24, 17, -22, 17, -10],\n [-11, -17, 3, -17, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[0, -20, 8, -8, 8],\n [-18, 13, 45, -31, 26],\n [-4, -10, 37, -25, 15],\n [-2, 19, -23, 21, -9],\n [-21, 20, 51, -32, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-5, 4, -31, -4, 32],\n [17, 14, -15, 6, 12],\n [-8, -29, 17, -57, -11],\n [14, 10, -33, -5, 40],\n [-28, -36, 49, -29, -43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-1, -30, -15, -3, -1],\n [23, -11, 11, 3, -11],\n [6, -30, -25, -17, -9],\n [27, -23, -3, -10, -20],\n [-9, 27, 23, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[20, -11, 3, -13, 14],\n [-25, 8, 10, -1, 16],\n [3, 13, -19, 20, -30],\n [40, 43, -43, 17, 10],\n [-7, 4, -4, 21, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-5, 8, -14, -10, -15],\n [-17, 5, 4, -5, -3],\n [1, -4, 40, -20, -21],\n [-27, 12, -21, 1, 3],\n [-33, 5, 18, -3, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-2, -32, -29, 29, -10],\n [-26, 1, 26, -21, -3],\n [-32, 9, -1, 10, 3],\n [-30, 10, 22, -15, 1],\n [-24, 27, 4, 4, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[9, 3, 6, 5, 11],\n [-12, -14, 2, 8, 7],\n [-3, -10, -4, 8, 7],\n [15, -15, -10, 8, 25],\n [10, 27, 4, -18, -21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[6, -6, -8, -12, -12],\n [-7, 11, 13, 22, 23],\n [-14, -2, 4, -4, -8],\n [-4, -4, -2, -8, -10],\n [11, 5, 0, 10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-1, 18, 15, 27, -3],\n [5, -1, 9, 31, -20],\n [-6, 15, 22, 36, -19],\n [17, 8, -5, -17, 47],\n [26, -9, -26, -12, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[0, 10, 10, 36, 7],\n [-16, 8, 8, -32, -20],\n [9, -14, 22, 9, 1],\n [8, -2, -8, 19, 12],\n [1, 2, 32, 32, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-10, -2, 8, -8, -6],\n [-20, 15, 40, -25, 0],\n [-11, 13, 28, -16, 3],\n [-25, -24, -4, -11, -27],\n [-8, -13, -8, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[26, 2, 11, 8, 3],\n [-13, -19, 1, 7, 18],\n [40, -1, -10, -8, -9],\n [-20, 7, 35, 26, 18],\n [24, -2, -23, -18, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[0, -18, -39, -8, 21],\n [-19, 33, 4, -9, -22],\n [-4, -18, 1, 0, 5],\n [34, -10, 16, 18, 12],\n [-12, -26, -5, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[13, 41, -30, 3, 7],\n [-2, 11, 38, -23, 60],\n [1, 11, 4, -3, 34],\n [2, -30, -15, 19, -50],\n [-13, -7, -21, 16, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[11, 7, 20, -8, 5],\n [-36, 8, -20, 8, -20],\n [-22, 3, -15, 6, -12],\n [-16, -4, -20, 8, -8],\n [-14, 5, -5, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-5, 25, -7, 4, -16],\n [35, -9, 23, 5, 33],\n [-20, -25, -11, 15, 0],\n [-5, 5, -7, 29, -1],\n [-5, -23, 1, -10, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[7, 29, 18, 2, -12],\n [-6, -21, -11, 5, 16],\n [-13, -25, 4, 10, 21],\n [-9, -26, -9, 7, 20],\n [-5, -10, 3, -13, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[1, 1, 3, -5, -2],\n [33, -16, -15, 29, 21],\n [-9, 15, 3, -22, -28],\n [-33, -8, 45, -7, 30],\n [6, -4, 24, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-25, -3, -10, -17, 26],\n [3, 9, 10, 7, -10],\n [1, -1, -4, 3, -4],\n [18, -16, -6, -3, 2],\n [-8, -14, -34, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[7, 15, 1, 6, -5],\n [-20, -40, 0, -4, 8],\n [14, 30, 2, 12, -10],\n [-17, -35, -1, -8, 9],\n [-18, -35, 1, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-18, 1, -33, -10, -24],\n [16, -2, -18, -30, 12],\n [19, -29, 2, -3, 8],\n [-10, -16, -29, 3, 1],\n [-12, -23, -3, 20, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[15, 4, -16, 8, -8],\n [-3, -6, -2, 14, -14],\n [3, 4, 0, -8, 8],\n [0, -4, -4, 12, -12],\n [0, 0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-8, -17, -29, 19, 20],\n [26, -57, -16, -25, -1],\n [-2, 12, 1, 1, -5],\n [-28, 11, -17, 31, 0],\n [11, 12, 27, -8, 26]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[7, -39, -39, -55, -12],\n [-31, -3, -20, -21, 10],\n [32, -21, -11, -21, -26],\n [-12, -10, -13, -16, 10],\n [1, -45, -47, -65, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-15, 10, 23, 5, -12],\n [2, 5, 15, -23, 14],\n [3, 10, 5, 8, -9],\n [-4, 6, 2, 18, -16],\n [1, -28, -31, -5, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[16, -16, -22, -8, 26],\n [0, 4, 3, -2, 6],\n [15, -15, -24, -6, 27],\n [-11, 31, 56, -16, -8],\n [-12, 0, -6, 18, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-3, -4, 6, 14, -11],\n [2, -8, 8, 16, -6],\n [-11, 20, -17, -31, 3],\n [0, 0, 0, 0, 0],\n [-1, -4, 5, 11, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-6, -6, -2, -4, 2],\n [-16, 0, -6, -8, -22],\n [0, 30, -11, -1, -37],\n [12, 10, 3, 7, 1],\n [-5, 27, -16, -6, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, -19, 14, -10, 9],\n [-3, -9, 9, -3, 6],\n [-15, 31, -11, 25, -6],\n [29, -8, -17, -21, -13],\n [10, 11, -16, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[20, -42, 21, 3, 14],\n [-24, -8, 16, -23, -13],\n [-18, 24, -6, 3, -3],\n [-12, -22, 23, -10, 1],\n [1, -18, 8, -19, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-9, -1, -6, 4, 1],\n [-12, -9, 21, 11, 6],\n [-11, -2, -19, 5, -17],\n [-22, -3, -11, 11, -8],\n [-7, 10, -6, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[12, 2, -8, 13, -17],\n [21, 20, 27, -4, 13],\n [9, 29, 9, 2, 19],\n [-23, 28, 6, 15, -6],\n [-55, -3, -17, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-3, -11, -28, 30, -2],\n [9, -7, 20, 2, 26],\n [-3, -30, 12, 0, -9],\n [2, -5, -16, 24, 11],\n [7, 18, 4, -1, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
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