GAUSS ELIMINATION METHOD

         Gauss Elimination method is one of the procedures to solve the simultaneous algebraic equation.

          In this method, the unknowns are eliminated successively and the system is reduced to an upper triangular system from which the unknown are found by back substitution. The method is quite general and is well adapted for computer operations.

Program Code

#include<stdio.h>

#include<conio.h>

#include<math.h>

void main()

{

    int i,n,j,k;

    float pivot,f,x[10],sum=0;

    float a[10][10];

    printf("\n\n\t\tEnter the no of eqns\n\t\t");

    scanf("%d",&n);

    printf("\n\t\tEnter the matrix:\n");

    for(i=1;i<=n;i++)

    {

        for(j=1;j<=n+1;j++)

        {

            printf("\t\ta[%d][%d]=",i,j);

            scanf("%f",&a[i][j]);

        }

    }

    for(k=1;k<=n-1;k++)

    {

        pivot=a[k][k];

        for(i=k+1;i<=n;i++)

        {

            f=a[i][k]/pivot;

            for(j=k;j<=(n+1);j++)

            {

                a[i][j]=a[i][j]-f*a[k][j];

            }

        }

    }

    printf("\tMatrix in echelon form:\n\n");

    for(i=1;i<=n;i++)

    {

        for(j=1;j<=(n+1);j++)

        {

            printf("\t%f",a[i][j]);

        }

        printf("\n");

    }

    x[n]=(a[n][n+1])/a[n][n];

    for(i=n-1;i>=1;i--)

    {

        sum=0;

        for(j=i+1;j<=n;j++)

        {

            sum=sum+a[i][j]*x[j];

        }

        x[i]=(a[i][n+1]-sum)/a[i][i];

    }

    printf("\n\tThe solution is:\n");

    for(i=1;i<=n;i++)

    {

       printf("\n\tx%d  =  %f\t",i,x[i]);

    }

    getch();

}

Sample output:

In this output only two equations is taken for references. Any number of equations can be taken.

The output of Gauss Elimination method is shown as:

Note: This code is implemented in C programming using TurboC++ libraries.