from sympy import Matrix, I
def stats(m):
rref_matrix, pivot_columns = m.rref()
print("Reduced Row Echelon Form (RREF):")
print(rref_matrix)
print("Pivot columns:", pivot_columns)
print("Rank of the matrix:", m.rank())
print("Inverse of the matrix", m.inv())
u1 = Matrix([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]])
u2 = Matrix([[1.0, 2.0, 0.0, 0.0], [2.0, 4.0, 0.0, 0.0], [-1.0, 2.0, 1.0, 1.0]])
u3 = Matrix([[8.0, 5.0, -2.0], [4.0, 7.0, 20.0], [7.0, 6.0, 1.0], [21.0, 18.0, 7.0]])
stats(u3)
u4 = Matrix(
[
[1 + 12 * I, 2 + 13 * I, 3 + 14 * I],
[4 + 15 * I, 5 + 16 * I, 6 + 17 * I],
[7 + 18 * I, 8 + 19 * I, 9 + 20 * I],
]
)
u5 = Matrix(
[
[1 + 12 * I, 2 + 13 * I, 3 + 14 * I, 4 + 15 * I],
[5 + 16 * I, 6 + 17 * I, 7 + 18 * I, 8 + 19 * I],
[9 + 20 * I, 10 + 21 * I, 11 + 22 * I, 12 + 23 * I],
]
)
u6 = Matrix(
[
[41 + 12 * I, 22 + 13 * I, 13 + 14 * I, 4 + 15 * I, 5 + 16 * I],
[6 + 17 * I, 7 + 18 * I, 8 + 19 * I, 9 + 20 * I, 10 + 21 * I],
[11 + 22 * I, 12 + 23 * I, 14 + 24 * I, 15 + 25 * I, 16 + 26 * I],
[17 + 27 * I, 18 + 28 * I, 19 + 29 * I, 20 + 30 * I, 21 + 31 * I],
[22 + 32 * I, 23 + 33 * I, 24 + 34 * I, 25 + 35 * I, 26 + 36 * I],
]
)
u7 = Matrix(
[
[1 + 12 * I, 2 + 13 * I, 3 + 14 * I, 4 + 15 * I],
[5 + 16 * I, 6 + 17 * I, 7 + 18 * I, 8 + 19 * I],
[9 + 20 * I, 10 + 21 * I, 11 + 22 * I, 12 + 23 * I],
[13 + 24 * I, 14 + 25 * I, 15 + 26 * I, 16 + 27 * I],
[17 + 28 * I, 18 + 29 * I, 19 + 30 * I, 20 + 31 * I],
]
)