Explain Gauss Elimination Method with algorithm

GAUSS ELIMINATION METHOD

Algorithm:

1.       Read n

2.       for i=1 to n

3.       for j=1 to n+1

4.       Read aij

5.       next j

6.       next i

Reduce to upper triangular matrix:

7.       for k=1 to n-1

8.       for i=k+1 to n

9.       ratio=aik/akk

10.   for j=1 to n+1

11.   aij=aij-ratio*akj

12.   next j

13.   next i

14.   next k

Using Back Substitution:

15.   x0= an, n+1/ann

16.   for k= n-1 to 1

17.   xk= ak, n+1

18.   for j= k+1 to n

19.   ak= xk-akj*xj

20.   next j

21.   xk=xk/akk

22.   next k

Printing the Result:’

23.   for i=1 to n

24.   print xi

25.   next i

26.   END

Source code:

#include<stdio.h>

void main()

{

/*Reading Matrix*/

int i, j, k, n;

float a[10][10], x[10];

float ratio;

printf(“enter the order of matrix\n”);

scanf(“%d”, &n);

printf(“enter the elements of the matrix\n”);

for(i=1; i<=n; i++)

{

for(j=1; j<=n+1; j++)

{

scanf(“%f”, &a[i][j]);

}

}

/*Reducing to upper triangular matrix*/

for(k=1; k<=n-1; k++)

{

for(i=k+1; i<=n; i++)

{

ratio=a[i][k]/a[k][k];

for(j=1; j<=n+1; j++)

{

a[i][j]=a[i][j]-(ratio*a[k][j]);

}

}

}

/*Using backsubstitution method*/

x[n]=a[n][n+1]/a[n][n];

for(k=n-1; k>=1; k--)

{

a[k]=a[k][n+1];

for(j=k+1; j<=n; j++)

{

x[k]=x[k]-(a[k][j]*x[j]);

}

x[k]=x[k]/a[k][k];

}

/*Printing the Answer*/

for(i=1; i<=n; i++)

printf(“The answer is %f\n”, x[i]);

getch();

}