To write a program to find the solution of a matrix using Gaussian Elimination.
- Hardware โ PCs
- Anaconda โ Python 3.7 Installation / Moodle-Code Runner
- Import numpy as np.
- Get the values from the user as input.
- Use Gaussian elimination method without partial pivoting to solve a matrix.
- Find the solution.
- Display the result.
'''Program to solve a matrix using Gaussian elimination with partial pivoting.
Developed by: Syed Abdul Wasih H
RegisterNumber: 21002291
'''
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]
# Back Substitution
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]
# Displaying Solution
for i in range(n):
print('X%d = %0.2f' %(i,x[i]), end = ' ')
Thus the program to find the solution of a matrix using Gaussian Elimination is written and verified using python programming.