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 An', 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]

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