GaussElimination.cpp

#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;
    cout << setprecision(3) << fixed;

    cout << "Enter number of unknowns: ";
    cin >> n;
    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];
        }
    }
    for(int i=1;i<=n;i++){
        for(int j=1;j<=n;j++){
            cout<<a[i][j]<<" ";
        }
        cout<<endl;
    }
    
    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];
            }
        }
    }
    for(int i=1;i<=n;i++){
        for(int j=1;j<=n;j++){
            cout<<a[i][j]<<" ";
        }
        cout<<endl;
    }
    /* 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);
}