Python Program to Inverse Matrix Using Gauss Jordan


To inverse square matrix of order n using Gauss Jordan Elimination, we first augment input matrix of size n x n by Identity Matrix of size n x n.

After augmentation, row operation is carried out according to Gauss Jordan Elimination to transform first n x n part of n x 2n augmented matrix to identity matrix.

Matrix Inverse Using Gauss Jordan Python Program


# Importing NumPy Library
import numpy as np
import sys

# Reading order of matrix
n = int(input('Enter order of matrix: '))

# Making numpy array of n x 2n size and initializing 
# to zero for storing augmented matrix
a = np.zeros((n,2*n))

# Reading matrix coefficients
print('Enter Matrix Coefficients:')
for i in range(n):
    for j in range(n):
        a[i][j] = float(input( 'a['+str(i)+']['+ str(j)+']='))

# Augmenting Identity Matrix of Order n
for i in range(n):        
    for j in range(n):
        if i == j:
            a[i][j+n] = 1

# Applying Guass Jordan Elimination
for i in range(n):
    if a[i][i] == 0.0:
        sys.exit('Divide by zero detected!')
        
    for j in range(n):
        if i != j:
            ratio = a[j][i]/a[i][i]

            for k in range(2*n):
                a[j][k] = a[j][k] - ratio * a[i][k]

# Row operation to make principal diagonal element to 1
for i in range(n):
    divisor = a[i][i]
    for j in range(2*n):
        a[i][j] = a[i][j]/divisor

# Displaying Inverse Matrix
print('\nINVERSE MATRIX IS:')
for i in range(n):
    for j in range(n, 2*n):
        print(a[i][j], end='\t')
    print()

Output

Enter order of matrix: 3
Enter Matrix Coefficients:
a[0][0]=1
a[0][1]=1
a[0][2]=3
a[1][0]=1
a[1][1]=3
a[1][2]=-3
a[2][0]=-2
a[2][1]=-4
a[2][2]=-4

INVERSE MATRIX IS:
 3.0	 1.0	 1.5	
-1.25	-0.25	-0.75	
-0.25	-0.25	-0.25	

Recommended Readings

  1. Matrix Inverse Using Gauss Jordan Method Algorithm
  2. Matrix Inverse Using Gauss Jordan Method Pseudocode
  3. Matrix Inverse Using Gauss Jordan C Program
  4. Matrix Inverse Using Gauss Jordan C++ Program