messages listlengths 1 1 | ground_truth stringclasses 4
values | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[33, 0, -37, 38, 3],\n [-43, 3, 13, -46, 11],\n [14, -42, 15, 10, -19],\n [15, -36, -15, 24, -12],\n [-25, 7, 18, -32, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[13, -19, -46, 35, -46],\n [7, 12, -27, -4, -23],\n [38, 0, 10, 20, 38],\n [15, -15, 0, 55, 0],\n [22, -18, -2, -5, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-5, 2, -23, 42, -29],\n [-4, -38, 10, 15, -4],\n [11, -6, -54, 60, -12],\n [-7, -38, 12, 18, -10],\n [-8, 6, -6, 21, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-8, -14, -18, 8, -48],\n [-18, 4, -6, 4, 23],\n [-7, -36, 35, 31, -51],\n [45, 26, 23, -31, 27],\n [-39, -21, 32, 35, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-1, -2, 10, -1, -9],\n [-13, -36, -18, -30, -26],\n [0, 6, -10, 5, 13],\n [8, 12, -10, 8, 20],\n [-15, 10, 20, 15, -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[[-20, 21, -17, 2, -21],\n [30, -35, 15, 4, 21],\n [15, -16, 12, -1, 15],\n [-15, 13, -21, 7, -24],\n [-15, 19, -3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[17, 24, 18, -40, 2],\n [6, -20, -48, 26, 24],\n [34, 26, -6, -49, 22],\n [-9, -14, -12, 23, 0],\n [-14, -12, 0, 22, -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[[10, -2, -4, 4, 0],\n [-5, 1, 2, -2, 0],\n [-20, 4, 8, -8, 0],\n [15, -3, -6, 6, 0],\n [-15, 3, 6, -6, 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[[0, 0, 0, 0, 0],\n [-2, -1, 6, 0, -3],\n [-12, -6, 36, 0, -18],\n [0, 0, 0, 0, 0],\n [-2, -1, 6, 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[[-6, -30, 0, 6, -6],\n [0, 0, 0, 0, 0],\n [2, 10, 0, -2, 2],\n [3, 15, 0, -3, 3],\n [5, 25, 0, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[12, 0, 8, 2, 12],\n [18, 0, 12, 3, 18],\n [30, 0, 20, 5, 30],\n [-30, 0, -20, -5, -30],\n [-12, 0, -8, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-24, 58, 1, 32, 23],\n [4, 46, 36, 2, 16],\n [-48, 13, 15, -21, 15],\n [-17, -71, -45, -13, -17],\n [-40, -24, -6, -2, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-6, -5, 2, 14, 13],\n [-9, -26, 34, 1, 11],\n [12, 3, -2, 4, 5],\n [-27, 47, -8, -59, -52],\n [24, -31, -2, 22, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[16, 24, -8, 4, 8],\n [-20, -30, 10, -5, -10],\n [12, 18, -6, 3, 6],\n [-16, -24, 8, -4, -8],\n [12, 18, -6, 3, 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[[-8, -8, 8, -20, 18],\n [8, 56, 24, 14, 42],\n [1, -2, 8, 25, -8],\n [15, 0, 30, 26, 46],\n [18, 0, 4, 16, 18]]\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, 16, -16, 0, -8],\n [8, -16, 16, 0, 8],\n [-12, 24, -24, 0, -12],\n [8, -16, 16, 0, 8],\n [6, -12, 12, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[4, -25, 13, -1, 34],\n [10, -35, 27, -21, 10],\n [-8, -29, 17, 23, 30],\n [4, 3, 5, -17, -32],\n [-3, -2, 6, 1, -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[[3, -22, -43, -30, -7],\n [14, -7, -3, 27, 8],\n [-17, 9, 26, 6, 25],\n [43, -9, -4, 24, -59],\n [-71, 35, -12, -81, 47]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[10, -24, 0, 16, -12],\n [24, -4, -8, -14, 4],\n [4, -14, -8, 16, -16],\n [-46, 38, 16, -6, 16],\n [9, -42, -16, 46, -42]]\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, -41, -8, -36, 20],\n [-14, -10, 0, -18, -1],\n [36, 39, 13, -1, -32],\n [9, 0, -1, 60, -18],\n [-81, -45, -3, -36, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[8, 20, 41, -7, 19],\n [-12, 20, -26, -50, -32],\n [-16, -38, 12, -22, 1],\n [-31, 33, 24, -10, 13],\n [-1, -39, -12, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-3, -29, 5, -44, 8],\n [-2, -12, 4, -18, 4],\n [6, -32, -3, -45, 8],\n [5, -3, -13, -6, -4],\n [30, -23, 43, 5, 38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[3, 7, 2, -3, -16],\n [-2, -18, 0, 6, 44],\n [-16, -22, -4, 8, 30],\n [-4, -33, 12, 6, 55],\n [-1, -5, 16, -5, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[10, 5, 6, -1, 6],\n [7, 15, -1, 4, -7],\n [-2, -2, 18, -8, -18],\n [-8, -7, 22, -11, -26],\n [-4, 20, -9, 8, -27]]\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, 31, 21, 13, 26],\n [-8, -53, 50, 11, -21],\n [17, 16, 17, -12, -13],\n [20, 15, 6, 23, 43],\n [-23, -29, -3, -18, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[51, -12, -9, 12, 9],\n [15, -21, 20, 32, -20],\n [-38, 1, 17, 4, -17],\n [12, 21, -33, -36, 33],\n [7, 19, -28, -32, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[20, -11, -6, -20, -6],\n [6, -15, -18, 12, 18],\n [9, -3, 0, -12, -6],\n [-14, 22, 24, -8, -20],\n [27, -35, -36, 4, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-46, -40, 32, 42, 10],\n [16, 12, 17, -21, 30],\n [25, 24, -3, -51, 86],\n [-4, -4, -19, 24, -71],\n [18, 16, -10, -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[[22, -10, 0, -22, 15],\n [39, 27, 0, 18, -9],\n [-14, -38, 0, -32, 6],\n [-4, -20, 0, -16, 0],\n [2, 34, 0, 30, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[28, 28, -10, 23, -24],\n [-24, 12, 42, -21, 36],\n [30, 48, 6, 24, -18],\n [28, 28, -10, 23, -24],\n [-16, -20, 2, -13, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-18, -30, -18, 0, -18],\n [-9, -15, -9, 0, -9],\n [0, 0, 0, 0, 0],\n [12, 20, 12, 0, 12],\n [-15, -25, -15, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-25, 6, 33, -27, -31],\n [-2, 31, -22, 21, 35],\n [-2, -17, -52, 27, -3],\n [6, -21, -41, 23, -10],\n [5, 23, -17, 27, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[23, -27, -25, 25, 6],\n [26, 6, -10, 18, 0],\n [19, -31, -25, 21, 9],\n [36, -24, -30, 34, 6],\n [29, 29, 0, 18, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[4, -24, 0, -4, 24],\n [0, 0, 0, 0, 0],\n [-6, 36, 0, 6, -36],\n [-1, 6, 0, 1, -6],\n [-4, 24, 0, 4, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-20, 10, 11, 53, -63],\n [7, -10, 27, -10, 3],\n [-7, -18, 2, 13, -34],\n [6, 6, 30, 0, 20],\n [-18, -18, 9, 45, -57]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-9, 7, 29, -10, 40],\n [-5, 8, -19, 6, -3],\n [33, 36, -23, -8, 27],\n [39, 4, -4, -36, -75],\n [22, -5, 5, -26, -59]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[10, 8, 2, 10, 8],\n [-20, -16, -4, -20, -16],\n [20, 16, 4, 20, 16],\n [5, 4, 1, 5, 4],\n [20, 16, 4, 20, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-43, -73, -20, 35, 16],\n [-1, 11, 16, 7, 8],\n [-16, -10, -20, 62, -20],\n [-9, -30, 6, -34, 25],\n [-17, -26, -34, 50, -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[[-15, 15, -18, 0, 12],\n [30, -30, 36, 0, -24],\n [-20, 20, -24, 0, 16],\n [-10, 10, -12, 0, 8],\n [-30, 30, -36, 0, 24]]\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, 57, -3, 21, -37],\n [18, -47, 31, -10, 48],\n [-2, -22, 7, 18, 9],\n [-16, -33, -8, 19, 12],\n [6, 17, 17, 46, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-2, 32, 9, -27, -2],\n [13, 8, -16, -7, -24],\n [-23, 6, 7, 1, 13],\n [-46, 6, 40, 1, 55],\n [27, -14, 7, 1, 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[[14, 15, -5, 6, -17],\n [14, 15, -5, 6, -17],\n [6, 3, 1, -2, -5],\n [-10, -9, 2, -2, 11],\n [-34, 3, -24, 38, 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[[12, -15, 15, 9, 6],\n [5, -22, 19, 21, 1],\n [9, -6, 7, 1, 5],\n [-35, 28, -31, -9, -19],\n [-12, 15, -15, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[36, 18, 0, -12, 36],\n [30, 15, 0, -10, 30],\n [24, 12, 0, -8, 24],\n [6, 3, 0, -2, 6],\n [24, 12, 0, -8, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[25, 30, 54, 20, 65],\n [-6, 40, 50, 35, 23],\n [8, -10, 8, 52, 32],\n [-53, 28, 11, 55, -56],\n [-11, 53, 44, 41, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[45, -8, -20, -24, -36],\n [41, -6, -16, 0, -22],\n [-4, 13, 19, 29, 11],\n [25, 4, 0, -28, -32],\n [23, -7, -13, 41, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[31, 6, 3, 31, 29],\n [-67, 19, -11, -4, -11],\n [-10, 8, 6, -27, -10],\n [-14, -9, -13, 49, 1],\n [31, 14, 17, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-19, 21, 2, 14, -18],\n [36, -54, 42, -36, 72],\n [24, -36, 28, -24, 48],\n [17, -15, -14, -10, 6],\n [16, -21, 9, -14, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-2, 5, -20, 34, -24],\n [24, 0, 0, 12, -12],\n [-22, -2, 8, -25, 21],\n [50, -5, 20, -10, 0],\n [-14, -1, 4, -14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[15, -3, -6, -15, 6],\n [-25, 5, 10, 25, -10],\n [0, 0, 0, 0, 0],\n [30, -6, -12, -30, 12],\n [15, -3, -6, -15, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-25, -24, -4, -28, -24],\n [-1, -32, -20, -30, -26],\n [-11, -4, 28, 12, 4],\n [-8, -22, 4, -12, -14],\n [-33, 19, 10, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[33, 39, -10, -7, -3],\n [-31, -22, -26, -28, -6],\n [-56, -64, 2, 2, -2],\n [-4, 14, 23, -27, 27],\n [4, 11, -14, 31, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-23, 9, -23, -23, 8],\n [26, 14, 38, -22, 16],\n [36, 24, 12, 6, -6],\n [6, -27, 5, 43, -19],\n [-35, -36, -28, 30, -15]]?\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, -15, -52, 51],\n [20, -12, 10, 40, -54],\n [20, -4, 14, 40, -42],\n [16, 2, 6, -16, 12],\n [-8, -8, -13, -32, 15]]?\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 [-5, -5, 5, 0, 1],\n [20, 20, -20, 0, -4],\n [25, 25, -25, 0, -5],\n [-10, -10, 10, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[28, 34, -50, -27, 29],\n [31, 31, -46, -53, 36],\n [-27, 0, 22, 7, -20],\n [-23, 14, 18, -36, -11],\n [18, 19, -13, -14, 4]]?\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, 50, -21, -15, -18],\n [-30, 57, 13, -36, 12],\n [-20, 35, 2, -25, 18],\n [4, 64, 8, -24, -42],\n [-28, 96, 29, -59, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-50, -52, 38, -54, -39],\n [-18, 25, 2, 27, -12],\n [-24, 22, -52, -9, 51],\n [-50, 13, -42, -21, 38],\n [12, 40, -48, 24, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-25, -14, -25, 4, -6],\n [-25, -20, -33, 6, 7],\n [17, 8, 2, 5, -4],\n [-14, 14, -19, -29, 10],\n [39, 24, 10, -5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-9, -10, 40, -4, 14],\n [35, 15, 10, 50, 15],\n [22, 4, -32, 32, 4],\n [-10, -1, 6, -16, -5],\n [-9, -2, 32, -11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-8, 18, -18, 30, -21],\n [-20, 30, 16, -38, 12],\n [-60, 8, 28, -24, 19],\n [-4, -6, 54, 27, 22],\n [10, 27, -20, 4, -17]]\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, 0, 0, 0, 0],\n [-4, 3, 6, -4, -1],\n [24, -18, -36, 24, 6],\n [-24, 18, 36, -24, -6],\n [12, -9, -18, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[21, 8, -19, -14, -4],\n [23, 4, -7, -12, -2],\n [-8, -4, 10, 6, 2],\n [28, -6, 23, -7, 3],\n [3, 4, -11, -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[[30, -34, -30, 0, 22],\n [5, -55, -45, 10, 30],\n [-18, 34, 26, -18, -11],\n [-17, 24, 25, 20, -28],\n [33, 11, 7, -6, -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[[20, -1, 3, 19, 8],\n [20, -13, -11, -3, 4],\n [31, -2, 33, 63, 48],\n [8, -28, -10, -18, 20],\n [28, -2, 14, 38, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-17, 20, -43, -2, 11],\n [66, -39, -3, -78, 24],\n [16, -31, 25, -12, 3],\n [-29, 26, 10, 36, -18],\n [8, -12, 3, -20, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the rank of matrix A where A =\n[[-28, -16, -41, -23, 25],\n [14, 17, 16, 10, 1],\n [24, 24, 30, 18, -6],\n [-22, -13, -32, -18, 19],\n [-8, -14, -7, -5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-11, 17, -12, 2, 9],\n [-6, 0, 4, 4, 28],\n [53, -51, 16, 14, -47],\n [20, -11, -7, 21, 2],\n [-5, 5, 0, -10, -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[[-16, 30, 16, -7, 11],\n [-15, 27, 15, -15, 12],\n [16, -28, -16, 22, -14],\n [0, 4, 0, 30, -6],\n [-7, 13, 7, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-2, 16, 15, -6, -15],\n [-18, 24, 0, -24, 0],\n [25, -44, -12, 36, 12],\n [-16, 32, 12, -24, -12],\n [12, -24, -9, 18, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-28, 46, -8, 67, -8],\n [-46, -14, 12, 23, -20],\n [-26, -40, 0, -18, -14],\n [-33, 27, 24, 47, -4],\n [42, -41, 16, -71, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[30, -12, -18, -30, 12],\n [-21, 7, 10, 25, -15],\n [-6, 8, 14, -10, 24],\n [25, -17, -28, -5, -23],\n [3, -4, -7, 5, -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[[-11, -49, -11, 30, -31],\n [5, 23, -3, -14, 9],\n [5, 39, 1, -22, 17],\n [9, 31, 19, -20, 29],\n [4, 8, -14, -6, -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[[54, 18, -6, -29, -35],\n [-18, -33, 23, -11, -1],\n [60, 5, 5, 4, -34],\n [-12, -10, 6, 2, 5],\n [-18, 21, -19, 1, 17]]\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, 8, 5, 3],\n [3, -33, -49, 59, 21],\n [0, -40, -28, 2, -54],\n [24, 12, -8, -40, 0],\n [0, 27, 18, 1, 39]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[26, -28, -11, 19, 10],\n [-32, -28, 17, 19, -28],\n [12, 16, -37, -13, 18],\n [-13, 24, 4, -16, -3],\n [14, 2, 57, -15, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[0, -2, 5, 1, 5],\n [0, -8, 20, 4, 20],\n [0, -8, 20, 4, 20],\n [0, 6, -15, -3, -15],\n [0, -8, 20, 4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-3, -21, 27, 15, -18],\n [-18, 26, -42, -34, 12],\n [-56, -12, -6, -30, -36],\n [32, -4, 18, 26, 12],\n [-51, -15, 0, -24, -36]]\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, 0],\n [10, 0, -20, 25, 5],\n [12, 0, -24, 30, 6],\n [12, 0, -24, 30, 6],\n [-8, 0, 16, -20, -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[[-20, 2, -2, -9, 9],\n [-4, 14, -6, -5, -23],\n [12, -32, 14, 13, 50],\n [4, 6, -6, -11, 11],\n [-8, 20, -12, -18, -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[[-28, 18, 26, 20, -30],\n [-18, -3, -3, -6, -15],\n [10, 13, 17, 18, 5],\n [15, -6, -9, -6, 15],\n [5, 15, 20, 20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-30, -30, 12, -30, 0],\n [-20, -20, 8, -20, 0],\n [10, 10, -4, 10, 0],\n [10, 10, -4, 10, 0],\n [20, 20, -8, 20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[10, 10, -13, 42, -23],\n [8, -2, 8, 11, -6],\n [-1, -15, 23, -8, 4],\n [3, -1, 5, -7, 4],\n [-11, -11, 15, -51, 28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-18, -26, 53, 8, -21],\n [11, 6, 5, -12, 4],\n [-20, -16, -4, 40, -28],\n [17, 6, -9, 24, -30],\n [18, 22, -54, 14, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-14, 66, 12, 4, -38],\n [12, -16, 2, -17, -18],\n [-2, 34, 6, -43, -21],\n [-1, 26, -10, 27, -28],\n [-6, -9, 8, 29, 14]]?\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, -12, 22, -35, 14],\n [8, 28, -8, 40, -16],\n [10, 31, 6, 30, -12],\n [-10, -33, 2, -40, 16],\n [12, 30, 36, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the rank of the following matrix:\n[[-72, -52, 38, 6, 8],\n [3, 10, 5, -3, 2],\n [-6, -18, 3, 5, 10],\n [69, 42, -43, -3, -10],\n [51, 28, -40, -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[[-8, 30, -11, 10, -29],\n [-34, -4, 10, -60, 6],\n [46, -30, 13, 56, 15],\n [3, 0, -24, 0, 24],\n [-34, 20, 1, -41, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[12, -6, 0, 14, 11],\n [4, 11, 13, 9, 21],\n [-12, 18, 12, -10, 5],\n [-16, 16, 8, -16, -4],\n [4, 5, 7, 7, 13]]?\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, -11, 7, -11, 32],\n [10, -10, 0, -16, 24],\n [10, 45, 25, -15, -10],\n [20, 20, 28, -19, 29],\n [0, 30, 18, 6, -16]]\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, 3, 21, -12, -30],\n [17, 14, -10, 16, 16],\n [42, 21, 3, 24, 2],\n [39, 15, -3, 24, 10],\n [53, 20, -16, 38, 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[[36, 41, 46, 0, 7],\n [-10, -32, -10, 17, 9],\n [6, -41, 31, 4, 13],\n [20, 4, 40, 12, 8],\n [-14, 37, 16, -15, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[8, -50, -36, -14, 23],\n [-5, 23, 18, 8, -11],\n [9, 29, 6, -8, -9],\n [16, 10, -12, -18, 1],\n [-13, 7, 18, 16, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-14, -34, 9, -8, -1],\n [52, -29, -55, -17, 43],\n [-6, 30, -15, 3, 15],\n [-38, 40, 36, 8, -26],\n [30, -30, -51, 3, 39]]\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, 3, 0, 3, 2],\n [-8, -12, 0, -12, -8],\n [6, 9, 0, 9, 6],\n [-7, -4, -1, -10, 0],\n [8, 25, -2, 13, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[-2, -4, -8, 2, -2],\n [-3, -6, -12, 3, -3],\n [5, 10, 20, -5, 5],\n [2, 4, 8, -2, 2],\n [2, 4, 8, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Compute the rank of the given 5x5 matrix:\n[[-4, -5, 0, 5, -6],\n [-44, -9, -2, 37, -62],\n [-22, 27, 47, 11, 2],\n [66, 15, -28, -39, 54],\n [12, -15, -34, 7, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[23, 12, -2, 10, -2],\n [42, -8, 20, 28, 20],\n [-10, 6, -8, -8, -8],\n [-39, -11, -4, -20, -4],\n [-19, -23, 12, -4, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the rank of the matrix:\n[[-18, -10, 8, -22, 7],\n [10, 4, -2, 12, -1],\n [2, -9, 15, 1, 18],\n [8, -8, 16, 8, 20],\n [-10, -25, 35, -15, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the rank of the matrix:\n[[16, 0, 34, -22, 11],\n [39, -30, 72, 20, -15],\n [17, -30, 24, 32, -15],\n [29, -12, 33, -41, 49],\n [-1, 18, 10, -2, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
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