py39. Matrix inversion in Python

The function numpy.linalg.inv can be used to find the inverse of matrix.

We find x in the linear equation (Ax=b) using inversion x=inv(A)*b and also with numpy.linalg.solve.

# ex39.py
from __future__ import print_function, division
import numpy as np
A = np.array([[1, 1, 1],[1, -1, 1], [3, 5, -1] ])
print('A =\n',A)
print('shape of A =',A.shape)
inverse = np.linalg.inv(A)
print('inverse of A\n', inverse)
b = np.array([1,0,2])
print('b =\n',b)
print('For Ax=b')
x = np.linalg.solve(A,b)
print('x = ',x)
print('inv(A)*b =',inverse.dot(b))

#A =
# [[ 1  1  1]
# [ 1 -1  1]
# [ 3  5 -1]]
#shape of A = (3, 3)
#inverse of A
# [[-0.5   0.75  0.25]
# [ 0.5  -0.5  -0.  ]
# [ 1.   -0.25 -0.25]]
#b =
# [1 0 2]
#For Ax=b
#x =  [ 0.   0.5  0.5]
#inv(A)*b = [ 0.   0.5  0.5]