messages
listlengths 1
1
| ground_truth
stringclasses 3
values | dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the rank of the matrix:\n[[-4, -3, 1, -4],\n [2, 3, 1, 2],\n [2, 3, 1, 2],\n [2, -3, -5, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[-14, 4, 6, 3],\n [10, 3, -2, -2],\n [32, 6, 8, -10],\n [4, 1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[12, -8, -16, -16],\n [-6, 4, 8, 8],\n [9, -6, -12, -12],\n [-3, 2, 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, 2, -2, -6],\n [-8, -4, 4, 12],\n [-6, -3, 3, 9],\n [8, 4, -4, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-6, 6, 0, -6],\n [6, -6, 0, 6],\n [-2, 2, 0, -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, -6, -3, 6],\n [-12, 6, 3, -6],\n [-4, 2, 1, -2],\n [12, -6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[-20, 6, 0, -8],\n [-17, 2, 2, -6],\n [24, 11, -14, 4],\n [-2, 10, -8, -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[[4, -16, -16, 8],\n [0, 0, 0, 0],\n [-1, 4, 4, -2],\n [-2, 8, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[-6, 2, 6, -8],\n [-2, -1, 7, 2],\n [2, 4, -3, 0],\n [-4, -2, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[12, 8, -12, 8],\n [6, 4, -6, 4],\n [-12, -8, 12, -8],\n [-3, -2, 3, -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[[7, 10, 16, -8],\n [-12, -8, -6, 5],\n [1, 3, 4, -1],\n [-12, -15, -6, -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[[4, -12, -16, -8],\n [-3, 9, 12, 6],\n [1, -3, -4, -2],\n [3, -9, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[-10, -8, 20, 8],\n [8, 4, -24, -8],\n [-15, -18, 10, 8],\n [-3, 0, 14, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[17, -6, -8, -2],\n [13, 16, 12, -4],\n [-8, 19, 18, -1],\n [-15, -5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[2, -6, -22, 6],\n [14, 0, 0, -8],\n [-2, 12, 5, -2],\n [5, 9, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[-14, -20, -22, 8],\n [5, -1, 2, 0],\n [-2, 11, 5, -6],\n [2, 23, 13, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 2, -3, -2],\n [-9, 9, -9, -7],\n [0, 0, 18, 8],\n [12, -12, 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[[13, -10, 15, 0],\n [-5, 6, -9, -7],\n [-3, 2, -3, 1],\n [-9, 10, -15, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[12, -3, 3, -3],\n [8, -2, 2, -2],\n [12, -3, 3, -3],\n [-16, 4, -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[[9, 0, 3, 12],\n [6, 0, 2, 8],\n [9, 0, 3, 12],\n [9, 0, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[-17, -9, -9, -2],\n [13, 21, 21, 10],\n [5, 0, 0, -1],\n [-14, -18, -18, -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, 9, 3, 0],\n [-4, -3, -1, 0],\n [8, 6, 2, 0],\n [-12, -9, -3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "What is the rank of the matrix:\n[[17, 6, 17, 1],\n [10, 2, 10, 0],\n [-4, 7, -4, 3],\n [-12, -5, -12, -1]]?\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, -3, -3, 7],\n [9, -16, -9, -7],\n [-9, 11, 9, -13],\n [0, 4, 0, 16]]\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, -5, 8, 17],\n [13, -3, 1, 22],\n [-15, -2, -3, -6],\n [28, 10, -17, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [12, -6, 3, 12],\n [16, -8, 4, 16],\n [4, -2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-4, 16, 12, -10],\n [4, 0, 2, -3],\n [-15, -12, -18, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Calculate the rank of matrix A where A =\n[[-3, 1, -8, 2],\n [0, 8, -22, 15],\n [-10, -4, 6, -15],\n [-6, 8, -10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[-4, 8, 4, -2],\n [-1, 6, 8, 0],\n [15, -18, 6, 9],\n [12, -8, 16, 8]]\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, -7, 5, 2],\n [4, -4, -22, 6],\n [-4, 0, 14, -14],\n [-2, 12, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-6, 6, -12, 12],\n [-8, 8, -16, 16],\n [8, -8, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[8, -2, -8, -4],\n [0, 0, 0, 0],\n [-16, 4, 16, 8],\n [-12, 3, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[-8, 4, -16, 0],\n [8, 8, -2, -6],\n [-14, -13, 2, 10],\n [0, -8, 12, 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[[-2, 0, 2, 0],\n [-2, 0, 2, 0],\n [-8, 0, 8, 0],\n [2, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "What is the rank of the matrix:\n[[-14, 0, 7, -16],\n [-6, 0, -5, -16],\n [-7, 20, 12, 11],\n [-10, 0, 8, -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[[8, -8, 16, 22],\n [48, -48, 12, 4],\n [-12, 12, -14, -25],\n [36, -36, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[4, 10, 4, -14],\n [-24, -3, 3, -15],\n [16, 8, 4, -2],\n [28, 6, 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[[-13, 21, 21, -9],\n [16, -4, 25, 2],\n [9, -4, 13, -1],\n [16, -4, 25, 2]]?\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, -8, -8, -16],\n [-6, 4, 4, 8],\n [-3, 2, 2, 4],\n [-6, 4, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "What is the rank of the matrix:\n[[1, -10, -18, 13],\n [-23, 3, 7, -9],\n [7, 0, 16, -12],\n [14, 1, -3, 5]]?\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, 2, -2],\n [8, -6, -5, 5],\n [10, -13, 13, -13],\n [24, -20, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[-6, -17, 8, -22],\n [-14, -11, 12, -30],\n [-15, 6, 15, -21],\n [-22, 15, 17, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "What is the rank of the matrix:\n[[-1, -4, 6, -3],\n [-8, -8, -6, 6],\n [6, 4, 9, -7],\n [-6, -8, 0, 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[[-13, 24, -15, 19],\n [13, -28, 16, -20],\n [0, -12, 3, -3],\n [1, 2, -15, 7]]\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, -15, 13, -6],\n [-14, -2, 12, -14],\n [10, 6, -12, -2],\n [13, 2, -13, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "What is the rank of the matrix:\n[[-18, -4, -16, -6],\n [-9, -12, -12, 9],\n [-12, -16, -16, 12],\n [6, -12, 0, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[4, -6, 2, 0],\n [10, -6, -6, 14],\n [-24, 15, 1, -20],\n [4, 0, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[4, -4, 4, 2],\n [8, -8, 8, 4],\n [-4, 4, -4, -2],\n [8, -8, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[-14, 4, -2, -6],\n [24, -4, 6, 10],\n [-1, -8, -13, -2],\n [-14, 4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[0, 0, 1, 0],\n [0, 0, -3, 0],\n [0, 0, -2, 0],\n [0, 0, -1, 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[[-2, 6, -4, 0],\n [2, -6, 4, 0],\n [-2, 6, -4, 0],\n [4, -12, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Calculate the rank of matrix A where A =\n[[-6, 10, -32, 14],\n [2, 1, -27, 23],\n [6, -3, 9, 3],\n [-2, -18, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -7, -7, -28],\n [-25, -4, -24, 6],\n [14, 13, 17, 17],\n [-2, 3, -1, 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[[0, 0, 0, 0],\n [0, 4, 4, -1],\n [0, -12, -12, 3],\n [0, -12, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Calculate the rank of matrix A where A =\n[[-7, 22, -3, 4],\n [8, -26, 2, -4],\n [-6, 0, 6, 3],\n [24, 13, 11, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[4, 2, -12, 6],\n [0, 12, -32, 12],\n [4, -4, 4, 0],\n [-4, 13, -28, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Calculate the rank of matrix A where A =\n[[-12, -12, 9, -12],\n [12, 12, -9, 12],\n [12, 12, -9, 12],\n [12, 12, -9, 12]]\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, 0, -6, 0],\n [1, 0, 2, 0],\n [-3, 0, -6, 0],\n [4, 0, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "What is the rank of the matrix:\n[[5, 4, -1, -6],\n [-4, -10, -24, 8],\n [2, 6, 14, -2],\n [-1, -6, -19, 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[[-12, 11, 0, 8],\n [20, -6, -22, 4],\n [-22, 11, 21, 2],\n [-19, 15, 20, 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[[-6, -6, -2, 2],\n [3, 3, 1, -1],\n [3, 3, 1, -1],\n [-6, -6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[2, 6, 2, -8],\n [4, 12, 4, -16],\n [2, 6, 2, -8],\n [1, 3, 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[[0, 0, 0, 0],\n [0, -6, 0, 9],\n [0, -4, 0, 6],\n [0, 8, 0, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "What is the rank of the matrix:\n[[7, -3, 4, -1],\n [9, -6, 0, -3],\n [12, -3, 12, 0],\n [8, -7, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[2, 4, 0, 0],\n [-1, 0, -2, 2],\n [12, 10, -9, -14],\n [28, 30, -27, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "What is the rank of the matrix:\n[[0, -9, 8, -18],\n [-18, 12, -8, -12],\n [8, -6, 6, 4],\n [-18, 26, -21, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [4, 8, -6, -6],\n [-8, -16, 12, 12],\n [-4, -8, 6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[-20, 2, 11, 13],\n [16, -2, 3, -11],\n [20, -8, 4, -16],\n [8, -12, -25, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[6, 4, -4, 8],\n [-15, -6, 12, -12],\n [-11, -4, 9, -8],\n [6, 4, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[-3, 5, -2, 8],\n [-6, -11, 3, -12],\n [6, -1, 1, -4],\n [9, 18, -5, 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[[1, 4, 4, 4],\n [-1, 13, 11, 10],\n [-4, 1, -1, -2],\n [-6, -7, -9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [12, 4, -12, 12],\n [12, 4, -12, 12],\n [12, 4, -12, 12]]\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, -15, 3, 10],\n [-7, 0, 3, -10],\n [13, 15, 0, -6],\n [11, 3, -18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
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MATH
|
[
{
"content": "Calculate the rank of matrix A where A =\n[[-16, 12, -12, -8],\n [8, -6, 6, 4],\n [12, -9, 9, 6],\n [-12, 9, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
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MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[2, 0, -6, 4],\n [-3, 0, 9, -6],\n [3, 0, -9, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
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MATH
|
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[-1, 8, 10, -13],\n [4, -6, -14, 13],\n [-3, -2, 4, 0],\n [7, -8, -22, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[-6, -2, -2, -2],\n [-9, -3, -3, -3],\n [-12, -4, -4, -4],\n [-12, -4, -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 [-4, -2, -2, 2],\n [0, 0, 0, 0],\n [8, 4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[-12, -8, 4, 16],\n [-3, -5, 16, 10],\n [20, 12, 0, -24],\n [11, 9, -12, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "What is the rank of the matrix:\n[[1, 5, -4, 5],\n [-12, 12, 16, -12],\n [-6, -3, 12, -12],\n [2, 1, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "What is the rank of the matrix:\n[[-9, -12, 0, -3],\n [12, 16, 0, 4],\n [6, 8, 0, 2],\n [0, 0, 0, 0]]?\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, 3, 4, 2],\n [0, 0, 0, 0],\n [16, -12, -16, -8],\n [-16, 12, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[-10, 0, 6, 10],\n [6, 12, -6, 6],\n [12, 14, -10, 2],\n [-2, -4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[-11, -5, -7, -5],\n [0, -2, -1, -4],\n [0, 10, -1, -10],\n [10, 8, 7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[-9, 3, -6, -12],\n [-9, 3, -6, -12],\n [3, -1, 2, 4],\n [-9, 3, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "Compute the rank of the given 4x4 matrix:\n[[3, -7, -2, 1],\n [11, 1, 6, 7],\n [1, 3, 2, 1],\n [2, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Calculate the rank of matrix A where A =\n[[6, -4, 14, 20],\n [-11, 12, 0, 16],\n [10, -4, 13, -8],\n [0, 0, -14, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "What is the rank of the matrix:\n[[8, 13, -2, 32],\n [18, -4, -8, 16],\n [24, -8, -22, 8],\n [0, -13, 6, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[-7, 2, -6, 9],\n [-9, -3, -9, 18],\n [5, -7, 3, 0],\n [18, -20, 12, -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[[-28, -44, 40, 12],\n [28, 20, -16, 6],\n [-1, 11, -14, -14],\n [18, 10, -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[[-9, 9, 9, -3],\n [6, -6, -6, 2],\n [12, -12, -12, 4],\n [12, -12, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "What is the rank of the matrix:\n[[5, -13, 9, 10],\n [4, -14, 12, 8],\n [4, 16, 4, -12],\n [10, 34, -6, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[6, -4, -8, 1],\n [15, -1, 15, -18],\n [-3, -11, -11, 22],\n [1, 9, 7, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Find the rank of the matrix:\n[[-16, 6, 22, -25],\n [10, -27, -4, -2],\n [-12, -13, -2, 1],\n [14, -17, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[-4, 6, 11, -6],\n [-5, 3, 1, 3],\n [11, -3, 8, -15],\n [-3, 3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
[
{
"content": "Determine the rank of the following matrix:\n[[-12, 5, -9, -3],\n [7, 2, 2, 4],\n [28, 3, 11, 7],\n [-41, -10, -12, -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[[6, -8, 4, -2],\n [-6, 8, -4, 2],\n [12, -16, 8, -4],\n [9, -12, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1
|
MATH
|
[
{
"content": "What is the rank of the matrix:\n[[20, -12, -9, -2],\n [-4, 4, -3, -2],\n [-20, 16, -3, -4],\n [-8, 8, -6, -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[[-6, -9, 3, -12],\n [8, 12, -4, 16],\n [2, 3, -1, 4],\n [-8, -12, 4, -16]]\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, 14, -14, -10],\n [0, 10, -8, -8],\n [12, 3, 6, -6],\n [4, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2
|
MATH
|
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