messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine the rank of the following matrix:\n[[-2, -3, -50, -9, -36],\n [12, -13, -5, 21, -17],\n [-46, 14, 25, 2, -9],\n [6, 5, 52, 3, 46],\n [-10, 12, 58, -2, 46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[12, -18, 12, 6, 12],\n [-8, 12, -8, -4, -8],\n [-8, 12, -8, -4, -8],\n [12, -18, 12, 6, 12],\n [10, -15, 10, 5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-8, -16, 4, 16, 12],\n [4, 8, -2, -8, -6],\n [-6, -12, 3, 12, 9],\n [10, 20, -5, -20, -15],\n [2, 4, -1, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[15, 25, -25, 10, 25],\n [9, 15, -15, 6, 15],\n [12, 20, -20, 8, 20],\n [15, 25, -25, 10, 25],\n [-3, -5, 5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-85, 50, -5, 0, -50],\n [66, -36, 0, 0, 42],\n [5, 5, 48, -35, -17],\n [-63, 40, 9, -10, -42],\n [-1, 1, -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[[-24, -22, -20, -11, -15],\n [-44, 18, -38, 43, 55],\n [-31, 20, -42, -17, 24],\n [25, -8, 24, -13, -24],\n [-31, -22, -24, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-12, 12, -39, 36, -9],\n [8, -8, 26, -24, 6],\n [19, -19, 13, -5, -15],\n [22, -22, 34, -26, -6],\n [-6, 6, 3, -6, 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[[16, 24, 8, 12, 12],\n [12, 18, 6, 9, 9],\n [16, 24, 8, 12, 12],\n [-8, -12, -4, -6, -6],\n [-20, -30, -10, -15, -15]]\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, -66, -33, -11, 57],\n [2, -12, 9, 13, -11],\n [-18, 60, 30, 6, -60],\n [-26, 32, 13, -19, -67],\n [-2, -24, 3, 3, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[6, -24, 12, 12, -18],\n [-6, 24, -12, -12, 18],\n [-1, 4, -2, -2, 3],\n [2, -8, 4, 4, -6],\n [-4, 16, -8, -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[[21, 40, 26, 20, 7],\n [5, -19, -25, 1, -15],\n [-16, -38, -26, -18, -12],\n [-18, 20, 44, -16, 18],\n [19, -17, -38, 14, -21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-40, 30, 35, 33, 27],\n [-14, 26, -11, 10, 11],\n [-34, 26, 29, 28, 23],\n [22, -8, -32, -19, -14],\n [34, -26, -29, -28, -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[[22, -4, 38, -24, -28],\n [16, 16, 17, -34, 8],\n [8, 16, 4, -24, 16],\n [-14, 4, -25, 14, 20],\n [18, 4, 27, -26, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-8, -13, 2, 44, -3],\n [14, 16, 10, 4, -6],\n [-14, -16, -10, -4, 6],\n [-26, -31, -16, 8, 9],\n [-7, -8, -5, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-8, 8, -4, 8, 6],\n [6, -15, 0, -12, -13],\n [36, 18, 36, 0, 24],\n [16, 2, 14, -4, 5],\n [60, -6, 48, -24, 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[[-13, -14, 2, -18, -23],\n [-17, 8, 4, 0, -19],\n [-4, 7, -7, 6, 4],\n [13, 36, 32, 32, 7],\n [-20, 1, 7, -8, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[2, -18, 0, -10, 4],\n [2, -21, -3, -14, 8],\n [2, -6, 12, 6, -12],\n [3, 3, 30, 25, -34],\n [4, -24, 12, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[0, 18, 30, -12, 26],\n [12, 42, 60, 0, 42],\n [-24, -12, 0, -48, 20],\n [-18, -9, 0, -36, 15],\n [10, -10, -25, 30, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-6, -6, 18, -18, 66],\n [-2, 5, 0, 4, -16],\n [-2, 5, 0, 4, -16],\n [1, -6, 3, -7, 27],\n [-22, 20, 30, -6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-5, 19, -6, 22, -21],\n [7, 2, 15, 0, 3],\n [0, -13, -3, -14, 12],\n [28, -31, 51, -42, 48],\n [-6, 15, -9, 18, -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, -24, -8, -20, 8],\n [0, 0, 0, 0, 0],\n [3, 18, 6, 15, -6],\n [0, 0, 0, 0, 0],\n [5, 30, 10, 25, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-8, -20, 16, 16, 20],\n [4, 10, -8, -8, -10],\n [12, 30, -24, -24, -30],\n [-10, -25, 20, 20, 25],\n [-2, -5, 4, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-5, -10, -23, -8, 18],\n [3, -38, -27, 14, 14],\n [2, -7, -29, -20, 2],\n [-10, -27, 3, 36, 34],\n [-24, 43, 59, 20, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[1, -1, -4, 0, -1],\n [-5, 5, 20, 0, 5],\n [-4, 4, 16, 0, 4],\n [1, -1, -4, 0, -1],\n [5, -5, -20, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-17, 44, -28, 32, -56],\n [-55, 17, 6, 11, -28],\n [-9, -20, 26, -19, -2],\n [7, 7, 8, 18, -2],\n [32, -3, 2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-35, 33, 40, 22, 39],\n [8, -58, -30, 12, -12],\n [15, 69, 32, 12, 0],\n [-43, -14, 9, -8, 42],\n [-13, -69, -38, -34, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-8, 31, 72, 37, -21],\n [28, -14, -34, -16, 0],\n [-10, 1, -1, 7, -33],\n [-24, -10, 4, 6, -24],\n [16, 10, -24, -6, -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[[3, 3, 3, -9, 0],\n [2, 2, 2, -6, 0],\n [4, 4, 4, -12, 0],\n [2, 2, 2, -6, 0],\n [-2, -2, -2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-12, -32, -24, 40, -34],\n [-2, -32, -14, 18, -17],\n [-6, -31, -12, 19, -16],\n [24, -8, -6, -14, 2],\n [-34, -21, -7, 38, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[34, -14, -33, -30, -24],\n [-23, -3, 58, -36, -46],\n [16, -5, -54, 51, 63],\n [-9, 1, 21, -12, -16],\n [-34, 29, 35, 21, 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, -6, -2, 4, 6],\n [0, -6, -2, 4, 6],\n [0, 0, 0, 0, 0],\n [0, -36, -12, 24, 36],\n [0, -30, -10, 20, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[10, 0, -45, 30, 5],\n [10, 20, 15, -14, 13],\n [-18, -35, -24, 23, -23],\n [8, 25, 39, -31, 14],\n [16, 10, -42, 26, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[5, 7, 17, 35, 28],\n [-15, -5, -19, -9, -4],\n [20, 3, 18, -10, -13],\n [-20, 0, -12, 28, 28],\n [15, 6, 21, 15, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[24, -1, 40, -23, 1],\n [-29, -10, -31, 34, 17],\n [-33, 20, 1, -20, -35],\n [8, -29, -35, 46, 36],\n [26, 6, 47, -41, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[18, 25, 0, -14, 19],\n [-36, -29, 9, 13, -35],\n [12, -23, -17, 19, 7],\n [30, 16, -11, -5, 28],\n [60, 18, -28, 0, 54]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[8, 8, -8, -2, 0],\n [12, 12, -12, -3, 0],\n [16, 16, -16, -4, 0],\n [0, 0, 0, 0, 0],\n [-12, -12, 12, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[21, 0, -6, 24, 3],\n [-11, 8, -14, -20, 19],\n [-21, 0, 6, -24, -3],\n [-7, 0, 2, -8, -1],\n [-6, -16, 36, 8, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-27, -42, 60, 39, -39],\n [-29, -39, 55, 36, -37],\n [1, -49, -35, -50, 17],\n [-12, -20, 25, 18, -17],\n [12, -25, -70, -65, 37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-6, 4, 4, -1, -4],\n [12, -8, -8, 2, 8],\n [12, -8, -8, 2, 8],\n [0, 0, 0, 0, 0],\n [-6, 4, 4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[5, 1, -3, -23, -3],\n [-4, 6, -27, 43, 27],\n [10, 9, 7, 57, 17],\n [47, 13, -18, -44, 12],\n [-89, -20, 46, 2, -47]]\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, -23, -1, 27, -18],\n [14, 21, 9, -3, 26],\n [16, -6, -7, -13, 36],\n [-21, -4, 9, 32, -59],\n [-3, -6, -16, -37, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[20, 30, 5, -20, -10],\n [-12, -18, -3, 12, 6],\n [16, 24, 4, -16, -8],\n [-12, -18, -3, 12, 6],\n [-16, -24, -4, 16, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[33, -3, 29, -23, 24],\n [-26, -54, 8, -23, -26],\n [19, 15, -7, 0, 18],\n [-17, -33, -1, -13, -16],\n [5, 3, -11, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[38, -36, -45, 33, 20],\n [6, 19, 11, 5, 10],\n [-21, 8, 17, -27, -30],\n [15, 6, -13, -2, -13],\n [13, 21, 13, 16, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[20, -4, 1, -25, -17],\n [35, 16, 5, -16, 28],\n [16, 6, 9, -5, 23],\n [-20, 7, 26, -58, 68],\n [-48, -24, 15, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[24, 36, -12, 6, -36],\n [-20, -30, 10, -5, 30],\n [24, 36, -12, 6, -36],\n [-24, -36, 12, -6, 36],\n [4, 6, -2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[46, -16, 64, 14, -40],\n [-37, 31, -17, 24, 6],\n [12, -27, 5, 11, -19],\n [38, -41, 23, -5, -23],\n [29, -48, 16, 13, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[30, -25, 10, 5, -5],\n [-6, 5, -2, -1, 1],\n [-36, 30, -12, -6, 6],\n [-36, 30, -12, -6, 6],\n [24, -20, 8, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-28, -2, -10, 10, -12],\n [-8, 36, -8, 0, -8],\n [-42, -40, 2, 0, -4],\n [-1, -36, -13, 30, -10],\n [-32, -42, -20, 36, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-50, 75, 78, -3, 18],\n [32, 23, 5, 10, -14],\n [30, -1, -16, 15, -2],\n [-14, 5, 20, 17, -38],\n [-58, 33, 48, -3, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-16, 20, 24, -2, 8],\n [9, 8, 3, 8, 12],\n [-3, 2, 3, -1, 0],\n [-4, 26, 24, 7, 20],\n [11, 16, 9, 12, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-26, 37, 16, 6, -12],\n [-34, 64, 8, 24, -6],\n [-17, 36, 18, 6, -13],\n [-14, -30, -2, -18, 0],\n [-4, -40, -3, -21, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-12, 54, -30, -3, -36],\n [-4, -12, 24, -8, 4],\n [-32, 54, 8, -27, -34],\n [-1, -3, -8, 0, 15],\n [-10, 24, 10, -9, -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[[78, 42, 18, 12, 62],\n [4, 13, -3, -2, 3],\n [-40, 14, -14, -60, -34],\n [0, -45, 10, 46, 2],\n [25, 16, 4, 8, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-12, -10, 15, 6, 11],\n [-46, -36, 49, 22, 27],\n [-27, -15, 45, 36, 12],\n [-32, -30, 35, 6, 35],\n [-3, -7, -12, -18, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-60, 0, -14, 16, -14],\n [-48, -7, -13, 9, -19],\n [30, 26, 29, 31, 13],\n [12, 17, 25, 35, -5],\n [18, 41, 36, 52, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-5, 8, -1, 12, 0],\n [-25, 8, 19, 20, 24],\n [-30, -8, 36, 2, 42],\n [-10, -16, 22, -16, 24],\n [15, 16, -27, 14, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-38, -22, -8, 14, 6],\n [-35, -27, -32, -33, 37],\n [-37, -25, -22, -19, 28],\n [13, 8, 4, -5, -2],\n [47, 32, 26, 5, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-33, -3, 49, 36, 14],\n [-36, -5, 51, 6, -65],\n [-17, -10, 26, 38, 67],\n [-25, 3, 7, -7, 5],\n [-22, 4, 20, -4, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [12, -12, -30, -12, -12],\n [12, -12, -30, -12, -12],\n [6, -6, -15, -6, -6],\n [6, -6, -15, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[0, -20, 24, -16, -16],\n [0, 0, 0, 0, 0],\n [0, -25, 30, -20, -20],\n [0, -30, 36, -24, -24],\n [0, 15, -18, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[48, 44, -26, -20, -56],\n [50, 34, 20, -12, -4],\n [-9, -13, 16, 6, 20],\n [31, 21, 9, -8, -8],\n [51, 29, 19, -12, -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, 0],\n [-6, -6, -4, -8, 10],\n [-3, -3, -2, -4, 5],\n [12, 12, 8, 16, -20],\n [-18, -18, -12, -24, 30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-12, -22, 12, -30, -22],\n [18, -25, -9, -11, 2],\n [-6, 24, -24, 5, 9],\n [40, -11, -3, 32, 27],\n [6, 11, -6, 15, 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[[17, -12, 34, 34, -42],\n [-4, 5, -10, -14, 14],\n [33, 25, -2, -23, -20],\n [20, 33, -30, -40, 6],\n [3, -1, 6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-16, -20, 20, -4, 4],\n [-12, -15, 15, -3, 3],\n [8, 10, -10, 2, -2],\n [24, 30, -30, 6, -6],\n [12, 15, -15, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[10, 5, 20, 10, 30],\n [4, 2, 8, 4, 12],\n [-10, -5, -20, -10, -30],\n [2, 1, 4, 2, 6],\n [2, 1, 4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-44, -58, -78, -16, 46],\n [23, 30, 75, 10, 9],\n [-5, 0, 41, 16, 53],\n [-10, -16, -16, 2, 18],\n [-28, -41, -56, -6, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[0, 34, -38, -38, 26],\n [-13, -15, -2, -8, 6],\n [41, 10, -22, -28, -13],\n [21, -17, -6, -16, -14],\n [-18, 1, -15, -19, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-5, -3, 2, 43, 0],\n [-30, -46, 75, -14, 16],\n [30, 24, -42, 8, -24],\n [-18, 4, -2, 38, 22],\n [32, 36, -62, 12, -24]]\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, 6, 12, 36, 18],\n [0, 0, 0, 0, 0],\n [-6, -6, -12, -36, -18],\n [5, 5, 10, 30, 15],\n [-2, -2, -4, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[25, 1, 38, -20, -6],\n [-31, 17, -4, -7, 10],\n [-18, 7, 10, 5, 11],\n [38, 6, -20, 4, -26],\n [-49, 11, 20, -1, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-23, -21, 17, 15, -10],\n [21, 6, -4, -25, 19],\n [-42, 36, 12, 12, 18],\n [-26, 3, 19, 0, 15],\n [-20, 54, -6, 2, 22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-4, -19, 21, 0, 16],\n [-24, 19, 25, -15, -35],\n [54, 21, -69, 36, 24],\n [48, 37, -41, 39, 11],\n [16, 6, -4, 15, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[32, -24, 0, -16, 12],\n [-14, 2, -9, -6, -9],\n [-5, 57, -3, 25, 27],\n [-9, -29, -39, -45, -27],\n [0, 23, -9, 3, 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[[7, 20, -6, -17, 12],\n [-6, -24, 12, -36, 24],\n [-47, 23, 49, 38, 57],\n [-32, -23, 27, 32, 11],\n [23, -1, -22, -67, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-17, -8, 6, 6, -24],\n [22, -30, 0, 48, -10],\n [44, -17, 0, 36, 20],\n [-29, 40, 30, -66, 0],\n [15, -1, -6, 6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[37, 2, 53, -19, 38],\n [-16, 14, -21, 20, -4],\n [-25, 34, -26, 22, 2],\n [8, 48, -36, -33, -32],\n [23, 42, 8, -3, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[6, -24, -24, -24, -6],\n [6, 18, 3, 30, -15],\n [-15, 18, 33, 6, 24],\n [-13, -32, -2, -56, 31],\n [13, 4, -16, 20, -25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[5, -1, 2, -5, -6],\n [40, 58, 6, -35, -26],\n [-39, -92, -10, 37, 9],\n [10, 13, 26, 24, -10],\n [22, 77, 8, -38, 11]]\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, 0, -25, -10, 10],\n [-28, -18, 25, 28, -16],\n [12, 12, 0, -12, 4],\n [12, 12, 0, -12, 4],\n [8, 12, 10, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-46, 32, -66, 16, 12],\n [-17, 35, -21, 66, -55],\n [37, -22, 38, -6, -10],\n [-38, 7, -40, -28, 40],\n [0, -35, -8, -56, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-4, -3, 27, 24, 0],\n [16, -27, 3, 0, 12],\n [-8, 20, -20, -16, -8],\n [8, -20, 20, 16, 8],\n [-28, 44, 4, 8, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[0, 12, 28, -15, 6],\n [44, -20, -10, -19, -54],\n [10, 20, 55, -35, 0],\n [-48, 12, -12, 33, 54],\n [-50, 20, 5, 25, 60]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[15, -9, 5, -1, -8],\n [14, 1, 15, -3, -4],\n [-16, -23, -45, -9, 8],\n [8, 22, 38, 20, -12],\n [-26, 2, -24, 3, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-36, 8, -24, -24, 23],\n [-27, -9, -11, -11, 14],\n [-18, -4, -10, -10, 18],\n [-30, -8, -10, -10, 1],\n [-27, -5, -15, -15, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[27, -7, 7, -5, 12],\n [-34, 10, -9, 21, -6],\n [60, -36, 42, 8, 11],\n [-43, 31, -39, -8, -2],\n [35, -23, 23, 18, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[7, -12, 20, 6, -15],\n [-46, 10, -2, -22, -50],\n [44, -4, 1, 13, 45],\n [11, 0, 7, -3, 0],\n [47, 3, 22, -12, 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[[26, -22, 7, -22, -20],\n [18, 76, 2, 4, -16],\n [-5, 26, 2, 3, 10],\n [-9, 35, -32, 29, -62],\n [11, 36, -26, 24, -68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[2, 70, 61, -16, 24],\n [-3, -75, -66, 16, -26],\n [-46, -20, -38, 52, -22],\n [26, -35, -18, -18, -3],\n [-32, -40, -49, 40, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[3, -9, -16, 2, 2],\n [-1, 1, 12, 18, -12],\n [-1, -3, 13, 27, -18],\n [-11, -1, 17, 5, 0],\n [-7, -7, -12, -20, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-22, 10, 30, -18, 3],\n [24, -16, -6, -2, -9],\n [-17, 11, 6, 0, 6],\n [2, 10, -60, 48, 12],\n [8, -8, 12, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-18, -43, -42, 23, -20],\n [16, 39, 4, -15, 41],\n [2, -12, -34, 24, 13],\n [-8, 5, 8, 44, 81],\n [7, 20, 11, -29, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-32, 3, 2, 2, -27],\n [-14, 20, 36, -56, 3],\n [-20, -21, 1, 12, -12],\n [22, 26, 24, 24, -20],\n [30, 34, 28, -64, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[66, -39, -76, -27, -27],\n [51, -27, -78, 4, -39],\n [-12, -5, 29, -39, 59],\n [24, -11, -18, -20, -20],\n [0, 0, -40, 18, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-5, 4, -2, -5, 6],\n [20, -16, 8, 20, -24],\n [15, -12, 6, 15, -18],\n [10, -8, 4, 10, -12],\n [0, 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[[-10, -3, 15, -12, 1],\n [4, 4, -20, -12, 36],\n [18, 3, -15, 36, -33],\n [-4, 1, -5, -18, 29],\n [30, 9, -45, 36, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-32, -11, -12, 13, 17],\n [13, 32, 20, -2, -2],\n [2, 10, 21, -14, -1],\n [-20, -32, 18, -32, 2],\n [3, -11, -3, -5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[9, 15, 9, -6, 16],\n [30, 47, -6, -28, 41],\n [-1, 47, -20, 2, 17],\n [13, 38, -8, -18, 13],\n [-29, -12, -16, 18, -44]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-7, 0, -36, 27, 41],\n [6, 0, 32, -14, -34],\n [0, 0, -6, -48, -6],\n [-3, 0, -13, 31, 20],\n [0, 0, -2, -16, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
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