# Gauss Elimination Method Using C++ with Output

## Program

``````
/*
Program: Gauss Elimination Method
All array indexes are assumed to start from 1
*/

#include<iostream>
#include<iomanip>
#include<math.h>
#include<stdlib.h>

#define   SIZE   10

using namespace std;

int main()
{
float a[SIZE][SIZE], x[SIZE], ratio;
int i,j,k,n;

/* Setting precision and writing floating point values in fixed-point notation. */
cout<< setprecision(3)<< fixed;

/* Inputs */
/* 1. Reading number of unknowns */
cout<<"Enter number of unknowns: ";
cin>>n;

/* 2. Reading Augmented Matrix */
cout<<"Enter Coefficients of Augmented Matrix: "<< endl;
for(i=1;i<=n;i++)
{
for(j=1;j<=n+1;j++)
{
cout<<"a["<< i<<"]"<< j<<"]= ";
cin>>a[i][j];
}
}
/* Applying Gauss Elimination */
for(i=1;i<=n-1;i++)
{
if(a[i][i] == 0.0)
{
cout<<"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 Substitution Method */
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 */
cout<< endl<<"Solution: "<< endl;
for(i=1;i<=n;i++)
{
cout<<"x["<< i<<"] = "<< x[i]<< endl;
}

return(0);
}

``````

## Output

```Enter number of unknowns: 3
Enter Coefficients of Augmented Matrix:
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
```