Gauss Elimination Method Using C


Earlier in Gauss Elimination Method Algorithm and Gauss Elimination Method Pseudocode , we discussed about an algorithm and pseudocode for solving systems of linear equation using Gauss Elimination Method. In this tutorial we are going to implement this method using C programming language.

Complete Program for Gauss Elimination method using C Programming Language


#include<stdio.h>
#include<conio.h>
#include<math.h>
#include<stdlib.h>

#define   SIZE   10

int main()
{
	 float a[SIZE][SIZE], x[SIZE], ratio;
	 int i,j,k,n;
	
	 clrscr();
	
	 /* Inputs */
	 /* 1. Reading number of unknowns */
	 printf("Enter number of unknowns: ");
	 scanf("%d", &n);
	 /* 2. Reading Augmented Matrix */
	 for(i=1;i<=n;i++)
	 {
		  for(j=1;j<=n+1;j++)
		  {
			   printf("a[%d][%d] = ",i,j);
			   scanf("%f", &a[i][j]);
		  }
	 }
	/* Applying Gauss Elimination */
	 for(i=1;i<=n-1;i++)
	 {
		  if(a[i][i] == 0.0)
		  {
			   printf("Mathematical Error!");
			   exit(0);
		  }
		  for(j=i+1;j<=n;j++)
		  {
			   ratio = a[j][i]/a[i][i];
			   
			   for(k=1;k<=n+1;k++)
			   {
			  		a[j][k] = a[j][k] - ratio*a[i][k];
			   }
		  }
	 }
	 /* Obtaining Solution by Back Subsitution */
	 x[n] = a[n][n+1]/a[n][n];
	
	 for(i=n-1;i>=1;i--)
	 {
		  x[i] = a[i][n+1];
		  for(j=i+1;j<=n;j++)
		  {
		  		x[i] = x[i] - a[i][j]*x[j];
		  }
		  x[i] = x[i]/a[i][i];
	 }
	 /* Displaying Solution */ 
	 printf("\nSolution:\n");
	 for(i=1;i<=n;i++)
	 {
	  	printf("x[%d] = %0.3f\n",i, x[i]);
	 }
	 getch();
	 return(0);
}

Output: Gauss Elimination Method for Solving Systems of Linear Equations

Enter number of unknowns: 3
a[1][1] = 1
a[1][2] = 1
a[1][3] = 1
a[1][4] = 9
a[2][1] = 2
a[2][2] = -3
a[2][3] = 4
a[2][4] = 13
a[3][1] = 3
a[3][2] = 4
a[3][3] = 5
a[3][4] = 40

Solution:
x[1] = 1.000
x[2] = 3.000
x[3] = 5.000

Recommended Readings

  1. Gauss Elimination Method Algorithm
  2. Gauss Elimination Method Pseudocode
  3. Gauss Elimination Method Using C
  4. Gauss Elimination Method Using C++