messages listlengths 1 1 | ground_truth stringclasses 3 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "What is the rank of the matrix:\n[[12, 9, 0, -12],\n [-25, -9, 0, 16],\n [-6, -11, 0, 12],\n [-21, -6, 0, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-2, 8, 6, -16],\n [-22, 22, -12, -8],\n [-4, 16, 12, -32],\n [-19, 21, -5, -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[[-13, 3, 2, -3],\n [17, -3, -10, 9],\n [-18, 4, 4, -5],\n [-7, 3, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[-11, 8, 0, -12],\n [-2, 2, -3, 0],\n [-1, -2, 15, -12],\n [-4, 8, -28, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-9, 1, -10, -8],\n [15, 13, 12, 13],\n [-8, 0, 15, 19],\n [-12, -16, -13, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -4, 0, 0],\n [22, 14, -6, 9],\n [20, 12, -4, 6],\n [22, 14, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[7, 12, 28, -11],\n [6, 16, 24, -8],\n [2, 4, 8, -3],\n [-1, 4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-12, -4, -12, -8],\n [6, 2, 6, 4],\n [-12, -4, -12, -8],\n [12, 4, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[5, -4, 5, -1],\n [15, -12, 15, -3],\n [14, -10, 14, -4],\n [-8, 0, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-10, -12, 6, 4],\n [22, -29, -7, 7],\n [14, -4, -18, -12],\n [-9, -4, 4, 1]]\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, -3, -12],\n [9, -3, -3, -12],\n [3, -1, -1, -4],\n [-6, 2, 2, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-6, 12, -12, 12],\n [-6, -3, -6, 0],\n [9, -8, 14, -10],\n [3, -6, 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[[-2, -1, -3, -1],\n [4, 2, 6, 2],\n [2, 1, 3, 1],\n [6, 3, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[16, 9, 8, -10],\n [6, 15, 16, 2],\n [14, 6, 8, -4],\n [-1, 9, 10, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[0, -3, -2, 1],\n [21, 21, -1, -1],\n [9, 18, -8, 4],\n [-9, 7, -7, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-3, 0, -6, 3],\n [-3, 12, 2, -13],\n [1, 0, 2, -1],\n [4, -12, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[3, -9, 3, -6],\n [1, -3, 1, -2],\n [-4, 12, -4, 8],\n [-1, 3, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[0, 6, 3, -4],\n [-2, -3, 0, 0],\n [-12, 12, 15, -20],\n [2, 3, 0, 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[[4, -4, 1, 2],\n [-8, 8, -2, -4],\n [22, -4, 4, -1],\n [-16, -8, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-14, -5, -11, 1],\n [20, 7, 16, -2],\n [-4, -2, -2, -2],\n [20, 7, 16, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -2, -6, 4],\n [-9, 27, -1, 5],\n [0, -18, 3, -6],\n [-9, -9, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-9, -3, 2, -5],\n [12, 6, -10, -3],\n [9, 3, -7, -5],\n [-12, -16, 17, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[-9, -8, 12, -14],\n [-11, -12, 3, -6],\n [6, 8, 6, -4],\n [19, 20, -9, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[9, 9, -6, -3],\n [-12, -12, 8, 4],\n [9, 9, -6, -3],\n [12, 12, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[2, 1, 7, 6],\n [-12, -4, -12, -8],\n [20, 4, -20, -24],\n [-7, -2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[7, 6, 3, 10],\n [-8, -18, -10, -18],\n [5, 15, 16, 21],\n [-18, -14, -4, -22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[8, 3, 1, -4],\n [10, 6, -5, 10],\n [-13, 2, 1, -9],\n [-12, -9, 11, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[3, 4, 2, -4],\n [-12, 0, -8, 16],\n [-21, 12, -14, 28],\n [6, 4, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[12, 12, 0, -16],\n [12, 12, 0, -16],\n [-6, -6, 0, 8],\n [6, 6, 0, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-6, 3, 6, 3],\n [2, -1, -2, -1],\n [2, -1, -2, -1],\n [4, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[12, -4, -8, 18],\n [8, -4, -8, 12],\n [2, 0, 0, 3],\n [0, 4, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[18, -4, 4, -9],\n [-8, 4, 16, 24],\n [-6, 0, -12, -9],\n [-4, 2, 8, 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[[-12, -5, 5, 3],\n [-13, 5, -12, -8],\n [14, -1, 15, 9],\n [12, 7, 14, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 4, 12, 4],\n [-9, 3, 9, 3],\n [9, -3, -9, -3],\n [-3, 1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[9, 8, 15, -16],\n [0, 8, 18, -18],\n [-24, -6, -3, 5],\n [-3, 22, 3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-10, -4, 12, 24],\n [20, -8, -6, 8],\n [18, -34, 2, -4],\n [-2, 10, 0, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, 3, 6, 6],\n [4, -2, -4, -4],\n [2, -1, -2, -2],\n [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[[29, -5, 19, -1],\n [-7, -5, -7, 3],\n [5, -17, -4, 7],\n [-5, -10, -9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-2, 4, -2, 0],\n [-1, 2, -1, 0],\n [0, 0, 0, 0],\n [-2, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-11, 5, -8, -5],\n [10, -1, 10, 4],\n [-7, -11, -16, -1],\n [4, -3, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-36, 8, -5, -11],\n [16, -21, -3, 19],\n [16, -13, -6, 14],\n [14, 4, -5, 1]]\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, 6, -12],\n [-2, 18, 2, -16],\n [7, -7, -3, 8],\n [9, -11, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[4, 12, -8, 16],\n [-4, -12, 8, -16],\n [1, 3, -2, 4],\n [2, 6, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-3, 8, -5, -2],\n [-11, 6, 5, 16],\n [9, -10, 1, -8],\n [-24, -26, 10, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, 0, -12, 3],\n [8, -4, 12, 12],\n [-6, 3, -1, -11],\n [14, -7, 9, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[8, -2, -8, -8],\n [12, -3, -12, -12],\n [0, 0, 0, 0],\n [4, -1, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-1, 4, 2, 2],\n [2, 16, 2, 8],\n [9, -12, -12, -6],\n [3, 12, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[0, -16, -2, 17],\n [-21, -12, 21, 3],\n [7, 26, 2, -30],\n [9, 24, 3, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-24, 10, -4, -4],\n [3, 20, -32, 22],\n [21, -8, 8, 2],\n [-8, 14, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[13, 5, -8, 4],\n [-2, 14, -6, -6],\n [7, -13, -1, 11],\n [-5, -1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-8, 0, 2, 8],\n [0, 0, 0, 0],\n [-8, 0, 2, 8],\n [-4, 0, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[20, -16, -10, 0],\n [-13, 11, 7, -1],\n [-20, 16, 10, 0],\n [-20, 16, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-9, -12, 18, -3],\n [-10, 6, 11, 6],\n [-14, -4, -12, 6],\n [-17, -3, -23, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-2, -6, -8, -4],\n [-7, -14, -18, -5],\n [-12, -8, -8, 12],\n [9, 13, 16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[0, -4, -8, -4],\n [0, -16, -22, -12],\n [0, 6, 12, 6],\n [0, -4, -13, -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[[-1, 0, 2, 3],\n [3, 0, -6, -9],\n [2, 0, -4, -6],\n [-4, 0, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[9, 9, -9, 0],\n [-9, -9, 10, 0],\n [-6, -6, 0, 0],\n [-3, -3, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-3, 2, 1, 4],\n [-6, 4, 2, 8],\n [4, 0, 4, -16],\n [12, -8, -4, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[8, 8, -4, 4],\n [-16, -16, 8, -8],\n [-8, -8, 4, -4],\n [8, 8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-4, 6, 0, -2],\n [2, 9, 8, -15],\n [-14, 12, -6, 5],\n [0, 3, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-4, -10, 6, 4],\n [10, -10, 22, -12],\n [8, 16, -10, -6],\n [11, 10, 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[[6, 6, 0, -6],\n [-2, -9, 1, 6],\n [-14, 0, -2, 6],\n [-4, 3, -1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[6, 7, -5, -12],\n [12, -10, -16, 12],\n [-12, 2, 14, 0],\n [-12, 10, 16, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[1, -4, 1, -4],\n [4, -16, 4, -16],\n [1, -4, 1, -4],\n [1, -4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[2, 0, 0, -5],\n [-20, -8, 16, 6],\n [13, 5, -10, -5],\n [-8, -2, 4, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-9, 12, 12, 12],\n [3, -4, -4, -4],\n [3, -4, -4, -4],\n [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[[-5, -14, -25, -13],\n [5, 14, 25, 13],\n [-6, 12, 2, 14],\n [-8, -8, -24, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-2, 6, 6, 8],\n [-4, 12, 12, 16],\n [-1, 3, 3, 4],\n [4, -12, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-8, -12, 12, -4],\n [4, 6, -6, 2],\n [6, 9, -9, 3],\n [8, 12, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-16, 4, 16, -16],\n [16, -4, -16, 16],\n [8, -2, -8, 8],\n [4, -1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[6, -4, -8, 4],\n [0, 0, 0, 0],\n [-9, 6, 12, -6],\n [3, -2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[24, 0, 6, -3],\n [0, -12, -6, 3],\n [8, -8, -2, 1],\n [-4, -10, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[3, 0, 0, -1],\n [6, 0, 0, -2],\n [3, 0, 0, -1],\n [9, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[22, -14, -10, -8],\n [-24, 23, 1, 10],\n [-21, 5, 1, -2],\n [-16, -2, 14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-8, 8, 2, -2],\n [-16, 16, 4, -4],\n [-16, 16, 4, -4],\n [-16, 16, 4, -4]]\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, 0, 0, 0],\n [-1, 3, 2, 1],\n [-3, 9, 6, 3],\n [2, -6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-4, -8, 0, -4],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [2, 4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[3, 0, -6, -9],\n [0, 0, 0, 0],\n [-4, 0, 8, 12],\n [1, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[2, 0, 5, -9],\n [-2, -2, -4, 12],\n [-1, 3, -4, 0],\n [-2, 4, -7, 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[[-23, 5, -13, -20],\n [-12, 23, -15, -8],\n [-15, -6, -4, -14],\n [17, -13, 10, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[2, 6, 6, -8],\n [-1, -3, -3, 4],\n [1, 3, 3, -4],\n [4, 12, 12, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-3, -9, 3, 12],\n [-13, -19, -15, 4],\n [10, 15, 11, -4],\n [-8, -9, -13, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[8, -3, 4, 8],\n [-4, 14, 7, 12],\n [17, 4, 4, -5],\n [-4, -9, -5, -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[[-1, 1, -2, -4],\n [-3, 3, -6, -12],\n [-3, 3, -6, -12],\n [-3, 3, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, 2, -2, -12],\n [-14, 10, -10, -4],\n [-8, 4, -4, -12],\n [17, -9, 9, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-4, 2, 3, 1],\n [12, -6, -9, -3],\n [-4, 2, 3, 1],\n [-4, 2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, -9, -9, -6],\n [0, -12, -12, -8],\n [0, 12, 12, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[0, -6, 6, -3],\n [0, -2, 2, -1],\n [0, 4, -4, 2],\n [0, -2, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-1, -2, -5, -3],\n [-9, 12, 3, 9],\n [-10, 15, 6, 12],\n [8, -14, -8, -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[[-12, -8, 16, 4],\n [-9, -6, 12, 3],\n [-6, -4, 8, 2],\n [-6, -4, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[14, 10, 10, 20],\n [1, -4, 9, 7],\n [8, 0, -19, -10],\n [3, 0, -21, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-14, 0, -18, 11],\n [-10, -4, -14, 12],\n [-14, 14, -10, -4],\n [1, -3, 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[[9, 15, 8, 0],\n [-18, -24, -14, 9],\n [13, 17, 10, -7],\n [-1, 1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[9, -6, -12, -12],\n [6, -4, -8, -8],\n [-6, 4, 8, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 16, 17, -19],\n [4, 11, 6, -10],\n [8, 1, -3, 1],\n [4, 4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-2, -8, 28, -4],\n [-2, 4, -4, -4],\n [-12, 15, 0, -24],\n [-4, -4, 24, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, -12, -5, 2],\n [-6, 18, -3, 3],\n [-28, 4, 11, -6],\n [12, 0, -7, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[12, 12, 4, 4],\n [3, 3, 1, 1],\n [-3, -3, -1, -1],\n [-9, -9, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[1, 12, 1, 0],\n [0, 4, 0, -1],\n [-2, 8, -2, -8],\n [4, -32, 4, 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, -8, 4, 8],\n [12, -12, 6, 12],\n [8, -8, 4, 8],\n [-8, 8, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
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