// The program output's the solution if it exists.
//
#include<stdio.h>
#include<stdlib.h>

#define N 100

int solve_few_linear_eq( float a[][N], float x[N], int n, int m)
{
	int i=0,j=0,k=0,u=0,maxi=0;
	float tmp=0.0,temp=0.0;
	
	printf("\n\nOutput:\n\n");
			 	
	while(i<n && j<m)
	{
		maxi=i;
		for(k=i+1;k<n;k++)
		{
			if(abs(a[k][j])>abs(a[maxi,j]))
				maxi=k;
		}
		if(a[maxi,j]!=0)
		{
											//converting it to upper triangular matrix
			tmp=x[maxi];							//and doing similar operations on x
			x[maxi]=x[i];
			x[i]=tmp;
			
			for(k=0;k<m;k++)
			{
				tmp=a[i][k];
				a[i][k]=a[maxi][k];
				a[maxi][k]=tmp;
			}
			
			x[i]=(float)((float)x[i]/(float)a[i][j]);
			
			for(k=0;k<m;k++)					
				a[i][k]=(float)((float)a[i][k]/(float)a[i][j]);
			

			for(u=i+1;u<n;u++)
			{				
				x[u]=x[u]-x[i]*a[u][j];
				temp = a[u][j];
				for(k=0;k<m;k++)
					a[u][k]=a[u][k]-a[i][k]*temp;
			}
			i++;
		}
		j++;
	}
	


	i=n-1;
	j=m-1;
	
	while(i>=0 && j>=0)								//converting the Upper tri. matrix to identity matrix	
	{										//similar operations on x done...			
		
		x[i]=(float)((float)x[i]/(float)a[i][j]);
		for(k=0;k<m;k++)
			a[i][k]=(float)((float)a[i][k]/(float)a[i][j]);

		for(u=i-1;u>=0;u--)
		{	
			x[u]=x[u]-x[i]*a[u][j];	
			temp=a[u][j];	
			for(k=0;k<m;k++)
				a[u][k]=a[u][k]-a[i][k]*a[u][j];
		}
		i--;
		j--;
	}

	printf("\n\n");									//printing the row-echelon matrix
	for(i=0;i<n;i++)
	{
		for(j=0;j<m;j++)
			printf("\t%d",a[i][j]);
		printf("\n");
	}
		
	printf("\nSOLUTION\n");
		
	for(i=0;i<n;i++)								//printing solution
		printf("\t%d",x[i]);

	printf("\n");

}