Ready-to-use methods for the calculation of the kernel and the image of a matrix are only provided by the Symbolic Python (sympy) package.

>>> import sympy as sy for pretty printingvoor iets mooiere uitvoer
>>> A = sy.Matrix([[1, 0, 1], [2, 1, 1], [-1, 1, -2]]); A
⎡1   0  1 ⎤
⎢         ⎥
⎢2   1  1 ⎥
⎢         ⎥
⎣-1  1  -2⎦
>>> A.nullspace()    # spanning vectors of the kernel of A 
⎡⎡-1⎤⎤
⎢⎢  ⎥⎥
⎢⎢1 ⎥⎥
⎢⎢  ⎥⎥
⎣⎣1 ⎦⎦
>>> A.rank()         # rank of A
2
>>> A.columnspace()  # spanning vectors of the image of A
⎡⎡1 ⎤  ⎡0⎤⎤
⎢⎢  ⎥  ⎢ ⎥⎥
⎢⎢2 ⎥, ⎢1⎥⎥
⎢⎢  ⎥  ⎢ ⎥⎥
⎣⎣-1⎦  ⎣1⎦⎦

The Symbolic Python (scipy) package has a linear algebra module containing similar features as MATLAB. For numerical calculations, this approach is preferred.

>>> import scipy.linalg as la
>>> A = sp.array(A); print(A)
[[1 0 1]
 [2 1 1]
 [-1 1 -2]]
>>> la.null_space(A)  # spanning vectors of the kernel of A
 [[-0.57735027]
  [ 0.57735027]
 [ 0.57735027]]
>>> from numpy.linalg import matrix_rank
>>> matrix_rank(A)    # rank of  A
2
>>> la.orth(A)        # spanning vectors of the image of A
 [[-4.26401433e-01 -5.60016277e-18]
  [-6.39602149e-01 -7.07106781e-01]
 [ 6.39602149e-01 -7.07106781e-01]]