Gaussian Elimination

AIM:

To write a program to find the solution of a matrix using Gaussian Elimination.

Equipments Required:

1. Hardware – PCs
2. Anaconda – Python 3.7 Installation / Moodle-Code Runner

Algorithm

Program:

/*
Program to find the solution of a matrix using Gaussian Elimination.
Developed by: SUMITH M
RegisterNumber: 24900643
*/
import numpy as np
import sys
n=int(input())
a=np.zeros((n,n+1))
x=np.zeros(n)
for i in range(n):
    for j in range(n+1):
        a[i][j]=float(input())
for i in range(n):
    if a[i][i]==0.0:
        sys.exit('Divide by zero detected!')
    for j in range(i+1,n):
        ratio=a[j][i]/a[i][i]
        for k in range(n+1):
            a[j][k]=a[j][k]-ratio*a[i][k]
x[n-1]=a[n-1][n]/a[n-1][n-1]
for i in range(n-2,-1,-1):
    x[i]=a[i][n]
    for j in range(i+1,n):
        x[i]=x[i]-a[i][j]*x[j]
    x[i]=x[i]/a[i][i]
for i in  range(n):
    print('X%d = %0.2f'%(i,x[i]),end = ' ')

Output:

Result:

Thus the program to find the solution of a matrix using Gaussian Elimination is written and verified using python programming.