messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the rank of the following matrix:\n[[10, 26, -17, -1, -28],\n [-11, -13, -1, -5, 0],\n [-5, 17, 6, 18, 4],\n [-1, 33, -12, 12, -24],\n [-12, 0, 4, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-13, -14, -20, 5, 16],\n [13, 16, 21, -2, 4],\n [-7, -10, -12, -1, -16],\n [22, 26, 35, -5, -4],\n [8, 10, 13, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[6, 3, 29, -13, -33],\n [8, 12, 20, -20, -20],\n [-1, 0, -6, 2, 7],\n [1, 6, -8, -4, 11],\n [6, 15, 1, -17, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-2, 1, 10, 20, 6],\n [-3, 7, 4, 16, -4],\n [-8, 8, 5, 6, 17],\n [-7, 0, 1, -18, 33],\n [-4, -2, 0, -16, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[12, 1, -9, -9, -11],\n [0, 5, 15, -15, 5],\n [8, 3, 1, -13, -5],\n [-4, -1, 1, 5, 3],\n [-4, -3, -5, 11, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-2, -1, 16, 8, -11],\n [11, -16, 24, -5, -28],\n [11, -10, 7, 7, -20],\n [-8, -2, 21, 24, 6],\n [10, 9, -41, -36, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-18, 14, -11, 3, -31],\n [30, -29, -15, -24, 27],\n [24, -13, 22, -15, 8],\n [-12, -7, 5, -11, 14],\n [-28, 8, 8, 12, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-5, 16, -8, -17, 15],\n [25, -40, 30, 35, -35],\n [10, 12, 5, -21, 14],\n [25, -12, 23, 0, -7],\n [-5, -12, -1, 18, -13]]\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, 18, 29, 8, -12],\n [31, -2, 7, 17, 9],\n [-11, 13, -20, 19, -14],\n [-10, -18, -7, -18, 14],\n [-20, -13, 1, -28, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[5, 19, 29, 6, 16],\n [21, 5, 7, 0, 9],\n [14, -11, -17, -5, -5],\n [-15, -17, -15, -10, -12],\n [-4, -27, -37, -11, -20]]\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, 31, -32, -13, 22],\n [19, -5, -8, 35, 14],\n [-13, 11, -4, -23, -2],\n [11, -29, 28, 17, -18],\n [15, -25, 20, 25, -10]]\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, 12, -20, -17, 9],\n [-30, 16, 18, 28, 20],\n [5, -28, 1, 12, -32],\n [-15, -6, 23, -26, 4],\n [-20, 16, 20, 42, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[1, -10, -11, 13, 16],\n [-5, 6, -11, 23, 30],\n [2, -6, -1, -2, -3],\n [5, -14, -1, -7, -10],\n [5, -8, 8, -19, -25]]\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, -12, -6, -32, 29],\n [25, -25, -29, 5, 20],\n [6, -17, -32, 17, 3],\n [6, 8, 20, -32, 12],\n [12, -15, -30, -9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[0, 18, -16, 8, -6],\n [0, -18, 16, -8, 6],\n [0, 9, -8, 4, -3],\n [14, -15, 4, -2, -9],\n [12, 0, -8, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[14, 2, 1, -8, -6],\n [0, -16, 20, -8, -8],\n [0, -5, 22, -10, 1],\n [4, -16, 3, -2, -14],\n [7, -12, 1, -3, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[12, -10, 4, -4, 9],\n [6, 2, 1, -7, 6],\n [16, -10, 12, -8, -1],\n [8, 0, -9, -7, 28],\n [4, 2, -3, -5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[10, 6, 8, 2, -4],\n [15, 9, 12, 3, -6],\n [30, 31, -12, 27, -9],\n [19, 14, 8, 8, -7],\n [-12, -2, -24, 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[[20, 14, -22, -7, 16],\n [-25, -14, -3, 17, 16],\n [-15, -25, 31, 27, -12],\n [25, 27, -19, -32, -4],\n [-5, -14, 25, 13, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[33, 30, -3, -26, -28],\n [-15, -12, -3, 18, 6],\n [31, 25, 1, -22, -31],\n [16, 1, 16, -6, -29],\n [-9, 4, -20, 17, 2]]\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, 0, -13, 1, -10],\n [-20, -4, -23, 7, -16],\n [5, -18, 20, 22, 23],\n [-25, -10, -25, 15, -15],\n [-5, -22, 10, 28, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[11, -20, -14, 13, 21],\n [4, -20, -16, 16, 16],\n [-12, 11, 30, 21, 5],\n [-6, -15, -6, 25, 13],\n [-12, 8, 24, 20, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-19, 31, 19, 19, -12],\n [-17, 15, 17, -5, 2],\n [9, -6, -9, 6, -3],\n [8, -9, -8, -1, 1],\n [-8, 9, 8, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-2, -7, -1, 1, -3],\n [1, -22, -4, 7, -15],\n [0, -17, -3, 5, -11],\n [-28, 4, 4, -16, 24],\n [-5, -9, -1, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[23, -41, -12, -39, -10],\n [-8, 34, -18, 12, -35],\n [0, 15, 0, 10, -25],\n [8, 4, 0, 10, 1],\n [-16, -7, 2, -20, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[25, 2, 3, -25, 15],\n [-10, -12, -12, -20, -18],\n [-15, -15, -14, -20, -23],\n [7, -8, 1, -15, 1],\n [-34, -27, -10, 0, -34]]\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, 12, 4, 0, 12],\n [6, -3, 3, -4, 3],\n [-17, -9, -5, 2, -12],\n [7, -6, 4, -6, 3],\n [28, 6, 10, -8, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-4, -16, 25, -8, -10],\n [-32, -14, 10, -7, -23],\n [-20, 4, -15, 2, -8],\n [-16, 2, -10, 1, -7],\n [-8, 16, -30, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[20, -20, -16, 16, -8],\n [25, -20, -13, 18, -8],\n [15, -20, -19, 14, -8],\n [5, -10, -11, 6, -4],\n [-5, 0, -3, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[10, 14, 0, 19, 6],\n [0, -8, -8, -5, 0],\n [-6, 16, 16, 1, 6],\n [-9, -16, 12, -14, -23],\n [17, -28, -28, 8, -17]]\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, 9, 4, 2, 15],\n [22, 16, -1, 10, -16],\n [-27, -36, 10, 0, 6],\n [-32, -7, -22, -2, 1],\n [6, 12, 10, -27, 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[[-25, 41, 32, 27, 17],\n [31, -5, -5, -12, 46],\n [2, -2, -1, -6, 19],\n [-12, -28, 5, -17, 29],\n [10, 11, 1, 9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-4, 17, 21, -11, -33],\n [15, -5, -28, 18, 20],\n [-6, -22, 4, 0, 4],\n [8, 26, -11, 2, -10],\n [-4, 9, -2, -5, 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[[-21, 29, 36, -27, 15],\n [-1, 9, 20, -15, 3],\n [-17, 13, 4, -3, 9],\n [6, -14, -24, 18, -6],\n [24, -16, 0, 0, -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[[15, -15, -50, -15, 15],\n [-5, -1, 20, 13, -11],\n [-3, 30, -5, -33, 24],\n [-1, 16, -5, -19, 14],\n [-6, 6, 20, 6, -6]]\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, 19, 36, -32, 9],\n [-11, -38, -18, 11, 12],\n [2, 9, -17, 18, 5],\n [8, -4, -3, 6, 6],\n [5, 19, 7, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-5, 23, 7, -26, 8],\n [-6, 29, 10, -33, 9],\n [-9, 19, -13, -18, 24],\n [4, -3, 12, 1, -13],\n [-8, 13, -16, -11, 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[[33, -9, -15, 18, -8],\n [36, 0, -9, 18, -3],\n [-10, 14, 13, -18, -15],\n [19, 25, 14, 4, 10],\n [-20, -8, -1, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-5, -3, 12, -8, 2],\n [-20, -6, 36, -17, 8],\n [0, -8, 16, -20, 0],\n [-10, 6, 0, 14, 4],\n [10, 2, -16, 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[[13, -1, -6, 10, 2],\n [-17, -7, 12, -8, 2],\n [9, 9, -9, 1, -4],\n [40, -10, -15, 35, 10],\n [-4, 10, -3, -9, -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[[-7, -1, -20, 5, 12],\n [9, 5, 28, 5, -6],\n [-10, -19, 3, -27, 12],\n [-8, 7, -25, -1, 4],\n [7, 8, 25, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-19, -5, -18, -3, -11],\n [-5, 1, -5, 0, -2],\n [1, -7, 3, 12, 8],\n [-2, 11, -3, 6, 5],\n [9, 7, 8, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[5, -3, -1, 2, 5],\n [0, 8, -12, 16, -4],\n [25, -13, -8, 14, 24],\n [25, -5, -20, 30, 20],\n [-15, 9, 3, -6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[0, 15, 10, 0, -25],\n [-8, -6, -4, 4, -14],\n [10, 24, 16, -5, -10],\n [-4, 9, 6, 2, -27],\n [4, 21, 14, -2, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-14, -6, -2, -7, -5],\n [22, 3, 11, 1, 15],\n [14, 24, -20, 35, -15],\n [6, -9, 15, -15, 15],\n [18, 18, -10, 25, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[34, 23, 43, 19, 2],\n [-1, -50, -16, -15, -49],\n [29, 25, 6, 4, 15],\n [22, -2, -1, -5, -9],\n [-3, -42, 5, -8, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[6, -5, 8, 13, 3],\n [-6, -17, -8, -4, 16],\n [-24, -15, -28, 19, 28],\n [22, -5, 26, -16, -12],\n [-6, 48, -9, 13, -25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[0, 0, 6, -12, -15],\n [15, 20, -11, 34, 46],\n [-12, 1, 13, -22, -15],\n [9, 13, 0, 8, 13],\n [-9, -13, -6, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[18, -1, 26, -9, 20],\n [-5, 8, 3, -25, 16],\n [-20, 4, 8, -51, 39],\n [-25, -6, -25, -6, -7],\n [5, 12, -31, 41, -50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[27, -26, 7, 16, -26],\n [8, 12, -28, 12, 12],\n [-16, -5, 27, -17, -5],\n [17, -22, 13, 8, -22],\n [3, 14, -25, 8, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[12, 16, -2, -15, 3],\n [24, 24, 0, -32, -12],\n [-3, 17, -3, 2, 29],\n [-12, -16, -6, 23, 17],\n [-3, 9, -5, 6, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, -7, -8, 25, 6],\n [1, -30, -5, -28, -44],\n [7, -14, -24, -11, -34],\n [3, -6, 23, -26, -10],\n [18, -12, 9, 3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-16, 24, 10, 39, 4],\n [-4, -17, -11, 23, -2],\n [12, 6, 4, -27, -8],\n [-13, 5, 3, 19, 12],\n [-1, 1, -1, 11, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[45, -8, 27, -22, -4],\n [37, 11, 30, -17, -13],\n [-40, 20, -24, 10, 6],\n [-2, -29, -11, 5, 11],\n [10, 0, 26, 30, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-6, -20, -6, 25, -23],\n [0, 2, 2, -3, 3],\n [-12, -16, 12, 14, -10],\n [-15, -19, 16, 16, -11],\n [6, 2, -12, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[35, 0, 4, 15, -33],\n [-27, 3, -5, -11, 27],\n [-19, 14, 0, -6, 16],\n [-3, -2, 8, -2, -4],\n [0, -11, 5, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[6, -5, 28, -33, -2],\n [16, 6, 23, -28, 1],\n [6, -7, 41, -40, -4],\n [13, 18, 34, 12, -4],\n [23, 4, 3, -22, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[2, -5, -5, -3, 0],\n [-2, -31, -31, 3, -4],\n [18, 0, 0, -27, 5],\n [8, -2, -2, -12, 2],\n [6, -15, -15, -9, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-2, -28, -14, -1, -2],\n [21, -7, 22, 36, 20],\n [13, 22, 27, 34, 2],\n [-8, 12, -5, 10, -12],\n [13, 10, 20, 26, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[4, 15, -5, -2, -6],\n [0, 10, -6, -12, 4],\n [2, 0, 0, -5, -5],\n [-19, -30, 9, 25, 40],\n [19, 40, -13, -24, -37]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[39, 52, -5, 20, 13],\n [15, 23, -7, 10, 4],\n [-2, -5, 20, 43, 30],\n [13, 10, 41, -3, 14],\n [-20, -27, 7, 36, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-6, -33, -26, 16, -13],\n [23, -27, -6, 0, -7],\n [22, -36, -8, 7, 12],\n [0, 25, 18, -10, 9],\n [-21, 12, -16, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[2, 5, -20, 4, 14],\n [14, -1, -15, 14, 2],\n [-7, 39, -24, 7, -4],\n [-19, -15, 32, 2, -16],\n [-4, -17, 11, 7, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[31, 3, -7, 6, -21],\n [-20, -4, -2, 0, 12],\n [10, -13, 16, 15, -12],\n [-17, 9, -16, -12, 15],\n [-33, 1, -9, -8, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-23, -16, -32, -3, -5],\n [-11, -10, -2, -3, 25],\n [4, 2, 10, 0, 10],\n [4, 5, -7, 2, -25],\n [6, 6, -2, 2, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[12, 5, 5, -15, -21],\n [10, 5, 4, -12, -16],\n [-12, -25, -1, 3, -15],\n [-18, -20, -5, 15, 9],\n [-2, 5, -2, 6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-3, -23, 18, -2, -10],\n [7, 9, -18, -4, 12],\n [-11, -24, 24, 5, -15],\n [10, 17, 4, -7, -3],\n [-16, -22, -6, 12, 4]]\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, 4, 12, 2, -12],\n [10, -4, -10, 9, -1],\n [28, -6, -24, 20, 8],\n [33, -4, -24, 28, 6],\n [35, 3, -20, 22, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-20, -1, -17, -5, -17],\n [20, -13, 12, -2, 19],\n [9, -13, 2, -9, 5],\n [-14, -42, -33, -37, -25],\n [18, 55, 43, 49, 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[[-11, 11, -14, -2, -10],\n [-2, -2, 26, 10, 8],\n [-11, 31, -17, 20, -9],\n [27, -19, 11, 2, 17],\n [14, -16, 8, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[13, 2, -6, 12, 2],\n [-10, -8, 12, -12, 4],\n [-1, 2, -2, 0, -2],\n [-14, -7, 12, -15, 2],\n [5, 4, -6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-16, 26, 1, -29, 10],\n [-6, -8, 7, 13, 23],\n [8, -14, 18, 12, 23],\n [24, -16, 2, 10, -22],\n [43, -12, 28, -11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-4, 3, 0, 7, -5],\n [-3, -3, 6, 9, -12],\n [18, -31, 20, -19, -5],\n [1, 8, -10, -8, 15],\n [5, -16, 14, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-37, 0, -4, 16, 16],\n [31, 13, -6, -26, 11],\n [4, -18, 20, 11, 3],\n [-28, -22, 27, 43, 2],\n [-9, -7, -5, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[3, -12, 17, 9, -28],\n [7, 5, -29, -11, 20],\n [-10, -2, -15, 12, 22],\n [-8, 23, -3, 2, 18],\n [24, 10, -2, -8, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-14, -17, -25, -12, 25],\n [11, -7, -14, 30, -10],\n [0, 17, 11, -1, -5],\n [3, -17, -4, 0, 0],\n [-8, -23, -5, -23, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-1, 2, 5, 3, 4],\n [3, 2, 7, 10, 11],\n [23, -14, -27, 7, 0],\n [-20, 0, -10, -35, -35],\n [-18, 12, 24, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[8, 11, -8, -7, -12],\n [1, -10, -1, 0, 9],\n [-12, 16, 12, 8, -12],\n [13, 0, -13, -10, -3],\n [0, 0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[2, 7, -13, -1, 19],\n [0, 12, -16, -4, 32],\n [-6, 12, -5, -8, 31],\n [6, -9, 1, 7, -23],\n [-12, 9, 10, -11, 22]]\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, 9, 6, 21, 9],\n [-8, -12, -6, -32, -14],\n [-8, -12, -8, -28, -12],\n [6, 9, 14, 5, 1],\n [8, 12, 10, 24, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[14, -28, 20, 4, 17],\n [-4, 8, -8, 0, -10],\n [-4, 8, -20, 6, -37],\n [-4, 8, -20, 6, -37],\n [18, -36, 16, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-10, 2, 9, -3, 0],\n [-20, -20, -5, 20, -54],\n [14, 11, 6, -3, -21],\n [4, -29, -6, 1, -14],\n [44, 0, 0, -11, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-20, -30, 20, -6, 4],\n [-12, -15, 12, 3, 6],\n [2, 5, -2, 5, 2],\n [-13, -20, 13, -5, 2],\n [-27, -40, 27, -7, 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[[17, -27, -5, -22, -5],\n [3, -9, 1, 3, 2],\n [29, -51, 2, -7, -6],\n [-17, 11, 1, 18, 17],\n [-21, 35, -4, -1, 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[[10, 29, -5, -4, -18],\n [-11, 44, 0, 5, -19],\n [38, 4, -26, 4, -10],\n [-2, -4, -11, 17, 6],\n [-3, 24, -2, 3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-9, -8, 25, 12, -16],\n [4, 17, -5, 2, 1],\n [7, 5, -20, -10, 13],\n [-3, -32, -5, -12, 8],\n [-1, -18, -5, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[1, 18, 16, 0, 20],\n [-11, -22, -8, 8, -28],\n [-18, 6, 27, 15, 0],\n [15, 28, 9, -11, 36],\n [16, 2, -17, -13, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-2, 20, -49, 14, 7],\n [-4, -4, -18, -5, 17],\n [18, 24, -3, 27, -16],\n [-10, -36, 41, -32, 12],\n [-8, 0, -2, -4, -7]]\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, -45, 4, 15, 6],\n [5, 11, 30, 7, -8],\n [5, 11, 30, 7, -8],\n [-11, 12, 29, -2, -10],\n [-47, -5, -6, -25, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-4, 4, 0, 12, 20],\n [-14, 4, -8, 14, 26],\n [10, -5, 4, -16, -28],\n [-11, -4, -12, -9, -11],\n [-18, -2, -16, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-5, 2, -5, -39, -6],\n [6, 19, -10, -7, 15],\n [15, -11, -25, -24, 5],\n [8, 12, 0, 36, 16],\n [4, -2, -10, -18, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[15, 0, 20, -15, -30],\n [-21, -27, 29, 30, -3],\n [12, 9, -3, -15, -9],\n [7, 3, 3, -8, -9],\n [1, 3, -5, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[21, 17, 4, 10, -18],\n [4, -5, -5, 13, 7],\n [5, 1, 12, 24, 26],\n [-6, -15, -8, 9, 21],\n [17, 14, 14, 23, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[25, -15, 4, -19, -10],\n [-10, 0, -6, -4, -10],\n [17, 12, 19, 30, 45],\n [-5, 15, 8, 27, 30],\n [-5, 15, 8, 27, 30]]\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, 4, -16, -6, 6],\n [5, 5, -25, -15, 0],\n [-2, -3, 17, 12, 3],\n [3, 4, -22, -15, -3],\n [-1, 4, -30, -27, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[54, -25, -38, -7, -33],\n [28, -13, -24, 9, 9],\n [37, -47, -13, -13, -34],\n [-1, 2, 0, -7, 2],\n [-20, -6, 22, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[17, 14, 2, -9, 7],\n [-27, -20, -11, 2, 9],\n [-28, -22, -7, 9, -2],\n [20, 14, 11, 3, -14],\n [15, 10, 10, 5, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[10, -25, -36, 49, 23],\n [-2, -11, -22, 26, 12],\n [0, -16, -18, 19, 11],\n [16, -8, -14, 29, 11],\n [8, -12, -18, 27, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[5, -20, -19, 2, 11],\n [0, -5, -11, -2, 9],\n [7, -20, -9, 6, 1],\n [-5, 20, 19, -2, -11],\n [-7, 20, 9, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-40, -20, -40, -25, 20],\n [11, -8, 7, 2, 7],\n [-7, -2, -14, 4, -15],\n [-12, -8, 0, -12, 36],\n [53, 40, 74, 21, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
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