prashanthrathi / gaussian

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

1. First,we want to import numpy,then import sys,assume a variable.
2. For gaussian elimination method, we want to make 2nd and 3rd column zero.
3. For that we want to make a range accorting to our program output.
4. Then print the program with correct form then the output will display.

Program:

Program to solve a matrix using Gaussian elimination without partial pivoting.
Developed by: Prashanth.K
RegisterNumber:212223230152 

import numpy as np
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]=int(input())
        
for i in range(n):
    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.