messages listlengths 1 1 | ground_truth stringclasses 4 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the rank of the matrix:\n[[-9, 4, 16, -2, -7],\n [21, -22, -12, 11, -9],\n [9, -14, 4, 7, -13],\n [-21, 24, 8, -12, 13],\n [0, 4, -8, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[16, -8, -32, -28, -10],\n [8, 22, 44, 29, -2],\n [3, -10, -24, -18, -9],\n [-43, -14, 30, 33, 9],\n [-39, -18, 4, 14, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[16, -11, -67, 7, -19],\n [10, 1, -7, 2, -7],\n [-18, -23, -3, 1, 9],\n [-29, -36, -5, -7, 22],\n [24, 34, 12, 6, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-9, -4, -4, 9, -4],\n [29, 24, 8, -31, 14],\n [-8, 6, 12, 12, 0],\n [-7, -40, -34, 0, -13],\n [-1, -27, -26, -5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-11, 9, 8, 10, 1],\n [9, 19, 15, -15, -24],\n [-2, 46, 30, 20, -24],\n [-21, 7, 10, 10, 5],\n [46, 12, -11, 15, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[18, 24, 0, 6, -3],\n [32, 17, 5, 6, 20],\n [-33, -34, -3, -10, 20],\n [-11, -13, -20, 11, 11],\n [1, -6, 55, -41, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[30, -6, -25, -6, -10],\n [0, 12, 19, 21, -17],\n [-8, 26, 13, -22, -12],\n [-9, -3, -2, -4, 6],\n [6, 18, -5, -28, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[28, -25, -10, -33, 15],\n [-24, 20, 28, 18, -27],\n [-4, -10, -4, 2, 6],\n [0, 0, 0, 0, 0],\n [-32, 15, 10, 33, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-3, -1, -33, -33, -5],\n [-15, -25, -5, -25, 20],\n [6, -23, 22, 11, -21],\n [10, 2, -13, -9, -20],\n [-7, 22, 0, 17, 2]]\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, -20, -25, 25],\n [-17, 21, -27, 20, -16],\n [15, -15, 5, 1, -1],\n [-35, 30, 38, 0, -5],\n [20, -15, -11, 39, -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[[-20, 10, 5, -15, 0],\n [-22, 0, 10, -16, -2],\n [-28, -8, 16, -20, -4],\n [23, -6, -8, 17, 1],\n [4, -2, -1, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[2, 1, 2, 2, -4],\n [6, 11, 8, 2, -12],\n [-8, 16, -3, -18, 16],\n [6, 3, 6, 6, -12],\n [-10, 11, -6, -18, 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[[5, -6, -5, 12, 13],\n [32, 15, 0, -4, 7],\n [12, 14, 30, -37, -30],\n [10, 14, 26, -34, -28],\n [25, 20, 13, -23, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-12, 28, -17, 4, 18],\n [22, 35, -21, -21, -22],\n [-26, 10, -12, 32, 38],\n [22, 6, 3, -16, -16],\n [-32, -21, -3, 13, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[8, 29, -42, -42, 15],\n [-7, 19, 20, 24, -25],\n [26, -24, 13, 2, 35],\n [8, -24, 2, -6, 25],\n [28, -5, 9, 2, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[12, -13, -15, 0, 1],\n [0, -10, -15, 0, -5],\n [-32, 16, 12, 0, -12],\n [20, -13, -12, 0, 6],\n [-16, 8, 6, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[2, 0, -5, 3, 1],\n [-2, 0, 5, -3, -1],\n [-14, -10, 7, -11, -11],\n [-24, -25, -10, -11, -22],\n [10, 0, -25, 15, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[6, 29, -12, 22, -25],\n [-27, -28, 24, -9, 30],\n [12, -2, -6, 2, -8],\n [-7, -12, 8, 3, 6],\n [4, 18, -8, 4, -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[[20, -13, -17, 36, 24],\n [16, -5, -19, 36, 21],\n [12, -18, 0, 8, 11],\n [-4, 14, -8, 8, -1],\n [-4, 11, -5, 4, -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[[28, 1, -5, 1, -8],\n [-25, 20, 25, 6, -5],\n [44, -1, -35, 35, -11],\n [2, -18, 0, -42, 21],\n [7, 15, 0, 25, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[14, 8, 8, 22, -10],\n [28, 20, 6, 20, -11],\n [3, 0, 6, 15, -6],\n [26, 20, 2, 10, -7],\n [-5, -4, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-10, -6, 16, -10, 6],\n [11, 0, -20, 20, -12],\n [0, 0, 0, 0, 0],\n [13, 21, -16, -5, 3],\n [9, 23, -8, -15, 9]]\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, -19, -11, -7, 3],\n [-16, 28, 20, 8, -8],\n [-4, -3, -15, 7, 13],\n [4, -3, 3, -4, -4],\n [-16, 26, 16, 9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[9, -5, 16, 19, 17],\n [4, 4, 38, 15, -30],\n [-13, -14, 0, -14, -9],\n [-10, 2, 16, -16, 2],\n [-13, -37, -8, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[8, 6, 2, -18, -14],\n [4, 19, -3, -13, -35],\n [4, 7, -7, -17, -7],\n [12, -21, 13, -17, 29],\n [-6, -4, 6, 21, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[18, -9, 3, 27, -12],\n [-18, 3, 3, -25, 0],\n [3, 0, -1, 4, 1],\n [3, -12, 11, 8, -23],\n [-9, 6, -3, -14, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[0, -15, -2, -6, -13],\n [2, 10, -1, 3, 8],\n [-2, 5, 3, 3, 5],\n [2, 40, 3, 15, 34],\n [-22, -5, 25, 9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[11, 17, 6, 9, -12],\n [-4, 2, -6, 0, 0],\n [23, 26, 17, 15, -20],\n [-23, -26, -17, -15, 20],\n [-35, -20, -35, -15, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-12, 2, 26, 0, 6],\n [-12, 15, 0, 47, -9],\n [-25, 7, 25, 0, 2],\n [-15, 7, 16, 13, 0],\n [3, -8, 34, -16, 15]]?\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, -6, -2, -17, -10],\n [5, 5, 42, -13, -31],\n [-10, 27, 63, 23, -40],\n [-2, 5, 9, 21, 8],\n [-7, -24, -10, -39, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-36, -9, 19, -15, 3],\n [-23, 13, 11, 21, -43],\n [-9, -3, -32, -14, 25],\n [-31, -7, -1, -9, 2],\n [-9, -12, -8, -22, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-25, -6, 19, -4, 4],\n [40, -4, -10, 20, -20],\n [30, 0, -12, 12, -12],\n [30, 4, -18, 8, -8],\n [15, 2, -9, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-25, -16, -26, -23, -8],\n [-4, -39, 29, 31, -16],\n [5, 7, -18, -15, 5],\n [42, 34, 7, 12, 34],\n [33, 8, -1, 9, 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, 30, -3, -27, -9],\n [11, -20, 1, 19, 11],\n [17, -30, 1, 29, 19],\n [-9, 15, 0, -15, -12],\n [-9, 20, -3, -17, -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[[0, 14, 3, 9, 7],\n [5, -13, 4, -3, -9],\n [-17, 5, -22, -15, 11],\n [-18, 2, -24, -18, 10],\n [12, -20, 12, 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[[-8, -17, -6, 18, -10],\n [11, -17, 21, 5, 1],\n [-9, -12, -9, 15, -9],\n [9, 31, 3, -29, 15],\n [17, 10, 21, -19, 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[[-36, -3, 17, 23, 1],\n [35, 7, -1, -15, 30],\n [-14, 15, 33, 3, 20],\n [-1, 12, 19, -5, -8],\n [3, 10, 21, 1, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-6, -46, -25, -7, -1],\n [-16, -42, -3, 17, -30],\n [-4, 0, -7, 20, -21],\n [9, 16, 28, -19, 15],\n [1, 24, -4, 5, 8]]\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, 8, 6, -6, -4],\n [6, 9, -7, -8, -7],\n [1, 15, -39, -10, -29],\n [-5, -3, -12, 5, -8],\n [-5, -5, -18, 9, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-20, 5, 15, 8, -4],\n [15, -3, -12, -6, 3],\n [25, -19, -6, -10, 5],\n [10, 11, -21, -4, 2],\n [15, 0, -15, -6, 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[[-9, 43, 10, 37, 10],\n [9, -16, -4, -2, -8],\n [-15, 17, 2, -5, 8],\n [6, -2, 4, 2, 4],\n [-3, -6, -6, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-20, 8, 16, 20, 20],\n [-9, 6, 15, 12, 3],\n [2, 0, 1, -1, -4],\n [15, -10, -25, -20, -5],\n [1, -2, -6, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, -3, -17, -8, -23],\n [-2, -6, -2, -21, -11],\n [-31, 22, -7, -23, -18],\n [-30, 30, 2, -7, -1],\n [-1, -3, 4, -16, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-46, -29, 45, 27, 18],\n [2, 0, -8, -23, 16],\n [-30, -10, 19, 31, 25],\n [-3, 12, 3, -5, -15],\n [-23, 11, 0, 35, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[7, 11, -30, 4, -7],\n [13, 14, 38, 5, 5],\n [24, 30, 16, 14, 0],\n [25, 27, 14, 38, -41],\n [-2, 3, -36, -17, 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[[-17, 4, 12, -24, -8],\n [10, -3, 2, 7, -5],\n [5, 0, -20, 20, 20],\n [-19, 5, 6, -21, -1],\n [-20, 5, 10, -25, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-14, -27, -14, 16, -3],\n [16, 13, 21, -9, 17],\n [6, 13, 21, -9, 10],\n [-26, 7, -9, -3, -28],\n [-8, -19, 4, 10, 8]]\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, 12, -53, -23, -3],\n [21, 12, 22, 1, -5],\n [9, 6, -29, -11, -6],\n [6, 9, -46, -19, -6],\n [4, 25, 44, -4, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[11, -8, -36, -27, 23],\n [-33, 4, 4, 11, 7],\n [3, -5, 1, -17, 14],\n [-11, -11, 14, -13, 23],\n [-35, 42, -26, 9, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-17, 25, -1, 12, -18],\n [-21, 33, -1, 17, -23],\n [-17, 21, 3, -1, 19],\n [18, -2, 2, 16, -4],\n [4, -8, -4, 3, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-5, 0, -10, -25, -20],\n [-6, -9, -9, -15, -15],\n [-2, -9, -1, 5, 1],\n [-8, 0, -9, -23, -15],\n [25, 3, 7, 18, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[12, 20, -22, -10, -17],\n [-14, -35, 26, 3, 18],\n [-12, -16, 21, -5, 10],\n [9, -23, -7, 15, 20],\n [-12, -30, 25, 5, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[6, 14, 14, -4, 5],\n [-3, 38, 12, 12, -2],\n [3, -1, -9, 12, -11],\n [9, 2, -8, 16, -15],\n [9, 9, 9, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-18, 5, -15, -3, -15],\n [4, 20, 16, -12, 16],\n [-22, 15, -13, -9, -13],\n [-2, 25, 13, -15, 13],\n [-6, -15, -15, 9, -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[[5, 18, -7, 6, 2],\n [25, -12, 31, -3, -13],\n [4, 2, 63, 12, 25],\n [-23, 57, 16, 39, 48],\n [-22, 21, -7, 27, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[5, 40, 20, -30, -5],\n [5, 35, 21, -28, -1],\n [-2, 14, -14, 0, -22],\n [-3, -24, -12, 18, 3],\n [-5, -10, -26, 18, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[17, 4, -11, 23, -10],\n [45, -1, 18, 22, -1],\n [-3, -4, -27, -1, 21],\n [26, -6, 16, 0, 16],\n [-5, 0, 35, -15, -10]]\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, 7, -20, -17, 13],\n [-12, -12, 0, -12, -4],\n [-3, -12, 15, 6, -12],\n [11, 8, 5, 14, 0],\n [9, 9, 0, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[30, 10, 49, -28, 28],\n [-5, -9, 9, 5, 23],\n [20, 21, 42, -21, 10],\n [0, -15, 27, 1, 48],\n [55, -5, 10, -45, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[3, -5, 6, 6, 8],\n [1, -5, 1, 4, 4],\n [6, 0, 15, 6, 12],\n [2, 10, 8, -4, 0],\n [3, -15, 3, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[34, -34, 14, -20, -8],\n [-35, 30, -16, 17, 15],\n [-30, 30, -24, 9, 19],\n [20, -8, -8, -16, 0],\n [-9, -3, 15, 12, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-12, 21, 8, 13, 4],\n [-13, 19, 12, 17, 6],\n [-9, 9, 12, 15, 6],\n [2, -5, 0, -1, 0],\n [-5, 17, -4, -1, -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[[-6, -55, 23, 9, 5],\n [13, -2, 2, -12, 15],\n [-49, 16, 23, 37, -26],\n [-15, -36, 35, -2, 2],\n [-4, 24, -3, -16, -13]]\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, 23, -12, 4, -8],\n [0, 28, -2, 8, -22],\n [-37, -9, -8, -36, 12],\n [-28, -9, -10, -27, 15],\n [-4, -26, -4, -10, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-15, 1, -20, 8, 6],\n [-20, -31, -29, 29, 9],\n [-6, -27, 7, 49, 42],\n [15, 45, 20, -40, -15],\n [-29, -6, -51, -1, -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[[36, -25, -10, -5, 16],\n [16, 5, -27, -28, -9],\n [0, 0, 0, 0, 0],\n [20, -5, -18, -17, 0],\n [12, -5, -8, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[20, -6, 10, 2, -30],\n [-15, 22, 3, 2, 5],\n [10, -18, -4, -2, 0],\n [-15, -3, -12, -3, 30],\n [-20, 1, -13, -3, 35]]?\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, 11, -9, 11, -1],\n [0, 0, -43, 39, -9],\n [12, -9, -2, 6, 4],\n [-12, -9, -12, 0, -10],\n [-7, 34, 8, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[2, -10, -6, -8, 0],\n [5, 19, 11, 13, 3],\n [26, -7, -22, -34, -1],\n [0, -2, -18, -24, -14],\n [19, -14, -24, -35, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[10, 4, -18, -16, 18],\n [-10, 22, 6, -18, -16],\n [-10, 34, -7, -36, -7],\n [12, -26, 15, 28, -5],\n [-2, -19, 12, 27, -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[[-16, -18, 6, -24, -16],\n [2, -3, 1, -11, -19],\n [-24, -21, 7, -20, 0],\n [-6, -6, 2, -7, -3],\n [12, 6, -2, -2, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[3, 12, 17, 4, 20],\n [0, -15, -20, 0, -25],\n [16, -32, -24, 8, -40],\n [8, -1, -2, 14, -5],\n [23, -37, -25, 14, -45]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-19, 11, 2, 2, 12],\n [0, 12, 25, -7, -9],\n [-16, 8, -20, 8, 22],\n [-11, -11, -33, 7, 19],\n [0, -1, 53, -33, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[2, 6, 12, -35, -16],\n [4, 0, 12, -22, -8],\n [6, -6, 12, -9, 0],\n [4, 0, 12, -22, -8],\n [8, -10, 14, -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[[42, -25, 39, -10, 56],\n [-30, 6, -14, -10, -42],\n [47, -37, 45, -25, 63],\n [13, 2, -8, 5, 29],\n [18, -2, 18, 10, 22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-6, 9, 28, 14, -6],\n [24, 12, -8, 8, 0],\n [20, 14, 2, 12, -2],\n [-16, -4, 14, 0, -2],\n [0, -12, -26, -16, 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[[-10, -13, -17, -8, -7],\n [6, 9, -5, -12, -11],\n [16, 17, 13, -22, -25],\n [0, 6, -8, 12, 16],\n [18, 18, 14, -30, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[4, -6, 24, 2, -1],\n [0, 3, -12, -1, -2],\n [40, -38, 40, -34, 15],\n [30, -24, 24, -22, 4],\n [-11, 6, 12, 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[[-5, 4, -13, 8, 8],\n [11, -7, 8, 13, -17],\n [10, -9, 11, 18, -22],\n [-15, -2, 3, 14, -6],\n [1, -3, 20, -24, -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, 34, 26, -8, 8],\n [-10, -20, -35, -2, 20],\n [8, -14, -24, 10, 6],\n [-26, -4, -1, -22, 12],\n [-33, 39, 24, -15, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-5, 1, -23, 17, -19],\n [23, -13, 3, 6, 27],\n [-5, 0, -25, 26, -18],\n [-29, 15, -17, 6, -41],\n [37, -19, 23, -9, 53]]?\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, 4, 4, 0, 10],\n [-2, -7, 2, -6, 20],\n [10, -16, -10, -4, -15],\n [0, -12, 0, -8, 20],\n [2, 4, -2, 4, -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, -1, 8, 19, -17],\n [6, -2, -2, -10, 6],\n [9, 10, -17, -22, 30],\n [-9, 16, -11, 8, 12],\n [17, -10, -1, -26, 10]]\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, 11, 11, -26],\n [20, 15, -14, 1, 25],\n [29, 30, -19, 11, 4],\n [17, 10, -3, 7, 12],\n [-6, 0, 3, 3, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-4, 13, 10, 14, 14],\n [-6, 23, 18, 24, 24],\n [-1, -9, -8, -7, -7],\n [7, -7, -4, -11, -11],\n [-2, -11, -10, -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[[18, 9, -3, -20, 0],\n [-21, -33, 6, -14, 15],\n [2, 11, -9, -2, -18],\n [-7, -16, 3, -12, 9],\n [26, 28, 6, 22, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-20, 10, -5, -15, 15],\n [-23, 7, -8, 0, 0],\n [0, 0, 0, 0, 0],\n [-3, 3, 0, -8, 8],\n [-17, 1, -8, 16, -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, -8, -25, -7, 8],\n [-23, 2, -21, 2, 2],\n [18, 8, -10, 14, 0],\n [-9, 4, -11, 5, 0],\n [-1, 16, 33, 13, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[2, 14, 10, 2, -10],\n [-5, 5, -3, 3, -1],\n [20, -20, 12, -12, 4],\n [6, 2, 8, -2, -4],\n [15, -15, 9, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-15, 3, 24, 0, 13],\n [10, -33, 16, -7, -5],\n [-2, -1, 16, -3, 3],\n [1, 17, -41, 9, -5],\n [-10, 31, -37, 12, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-6, -9, 1, 19, -17],\n [-5, 3, -5, 3, -6],\n [1, 3, -1, -5, 4],\n [3, -9, 7, 7, -2],\n [-3, 9, -7, -7, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-18, 7, -10, 20, 33],\n [-18, -23, 29, 23, 15],\n [10, -5, 7, -11, -19],\n [-2, -17, 22, 4, -7],\n [-2, -27, 35, 5, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[8, -14, 20, 16, 8],\n [41, -33, -6, -11, 10],\n [-28, 24, 0, 4, -8],\n [19, -17, 2, -1, 6],\n [-25, 25, -10, -5, -10]]\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, -13, -12, 8, 14],\n [17, -8, -12, 13, -11],\n [7, 11, 12, -10, -4],\n [10, -19, -24, 23, -7],\n [6, -6, -8, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[2, 29, 10, -1, -15],\n [5, 3, 20, -13, -11],\n [-25, 17, 13, 44, 39],\n [-21, 4, -17, -11, 6],\n [21, 15, 14, -25, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[16, 24, -9, -16, -33],\n [-2, 28, -34, -23, -11],\n [10, 26, -17, -20, -27],\n [-15, -11, -1, 2, 22],\n [14, -6, 9, 22, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[18, -2, -7, -7, -24],\n [-4, 29, 29, -25, -9],\n [-20, -5, 36, -4, 31],\n [-3, 22, -2, -6, -8],\n [22, 5, -1, -18, -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[[-2, -1, 1, -10, 5],\n [-14, 9, -25, 3, -3],\n [-10, -3, 1, -12, 1],\n [-14, 10, -27, -11, 7],\n [6, -1, 5, -13, 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, 8, -6, 0, -16],\n [13, 36, -1, -26, -7],\n [-15, -40, 0, 30, 5],\n [11, 28, 1, -22, -1],\n [-13, -36, 1, 26, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-4, 0, 12, 4, 12],\n [-5, -11, 6, 4, 10],\n [-14, -10, -20, 8, -12],\n [-10, -6, -22, 5, -16],\n [8, -3, -13, -7, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
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