Numerical Program

Gauss Elimination Definition

In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations. It is usually understood as a sequence of operations performed on the associated matrix of coefficients.

Program of Gauss Elimination in C Language

  #include<stdio.h>
  #include<conio.h>
  void main()
  {
    int i,j,k,n;
    float a[20][20],x[20];
    double s,p;
    clrscr();
    printf("Enter the number of equations : ");
    scanf("%d",&n);
    printf("\nEnter the co-efficients of the equations :\n\n");
    for(i=0; i<n; i++)
    {
        for(j=0; j<n; j++)
        {
            printf("a[%d][%d] = ",i,j);
            scanf("%f",&a[i][j]);
        }
	printf("b[%d] = ",i + 1);
	scanf("%f",&a[i][n]) ;
    }
    for(k=0; k<=n-1; k++)
    {
	for(i=k+1; i<n; i++)
	{
	    p = a[i][k]/a[k][k];
	    for(j=k; j<=n; j++)
	    {
		a[i][j] = a[i][j] - (p * a[k][j]);
		printf("\n a[%d][%d] = %f",i,j,a[i][j]);
	    }
	}
    }
    x[n-1] = a[n-1][n] / a[n-1][n-1];
    for(i=n-2; i>=0; i--)
    {
        s=0;
        for(j=i+1; j<n; j++)
        {
            s += (a[i][j]*x[j]);
            x[i] = (a[i][n]-s)/a[i][i];
        }
    }
    printf("\nThe result is :\n");
    for(i=0; i<n ; i++)
    {
        printf("\nx[%d] = %.2f",i+1,x[i]);
    }
    
    getch();
}

    

Output

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