C++ Program to Implement Gauss-Jordan Elimination

This is a C++ Program to Implement Gauss Jordan Elimination. It is used to analyze linear system of simultaneous equations. It is mainly focused on reducing the system of equations to a diagonal matrix form by row operations such that the solution is obtained directly.

Algorithm

Begin
   n = size of the input matrix
   To find the elements of the diagonal matrix:
   Make nested for loops j = 0 to n and i = 0 to n
      The element in the first row and the first column is made 1
      and then the remaining elements in the first column are made 0.
      Similarly, the elements in the second row and the second
      column is made 1, and then the other elements in the second
      column are reduced to 0 and so on.
   Print all calculated solution values.
End

Example

#include<iostream>
using namespace std;
int main() {
   int i,j,k,n; // declare variables and matrixes as
   input
   float a[10][10],b,x[10];
   printf("\nEnter the size of matrix: ");
   scanf("%d",&n);
   printf("\nEnter the elements of augmented matrix (rowwise):\ n");
   for(i=1; i<=n; i++) {
      for(j=1; j<=(n+1); j++) {
         cout << "A[" << i << ", " << j << " ]=";
         cin >> a[i][j];
      }
   }
   //to find the elements of diagonal matrix
   for(j=1; j<=n; j++) {
      for(i=1; i<=n; i++) {
         if(i!=j) {
            b=a[i][j]/a[j][j];
            for(k=1; k<=n+1; k++) { 
               a[i][k]=a[i][k]-b*a[j][k];
            }
         }
      }
   }
   cout<<"\nThe solution is:\n";
   for(i=1; i<=n; i++) {
      x[i]=a[i][n+1]/a[i][i];
      cout<<"x"<<i << "="<<x[i]<<" ";
   }
   return(0);
}

Output

Enter the size of matrix: 3
Enter the elements of augmented matrix row-wise:
A[1, 1 ]=1
A[1, 2 ]=2
A[1, 3 ]=-4
A[1, 4 ]=2
A[2, 1 ]=7
A[2, 2 ]=6
A[2, 3 ]=-2
A[2, 4 ]=-5
A[3, 1 ]=0
A[3, 2 ]=-3
A[3, 3 ]=-5
A[3, 4 ]=-8
The solution is:
x1=-2.89831 x2=2.5678 x3=0.059322