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Saturday 7 March 2015

Solution of System of Linear Equations by Gauss Elimination Method

#include<iostream>
#include<iomanip>

using namespace std;
int main()
{
    int i,j,k,n;
    float a[10][10],x[10];
    cout<<"Enter Order of Equation: ";
    cin>>n;
    cout<<"Enter Coefficients of Equation Row-wise\n";

    for(i=1;i<=n;i++)
    {
        for(j=1;j<=n+1;j++)
            cin>>a[i][j];
    }
    for(i=1;i<=n;i++)
    {
        for(j=1;j<=n;j++)
        {
            if(j>i)
            {
                float s=a[j][i]/a[i][i];
                for(k=1;k<=n+1;k++)
                    a[j][k]=a[j][k]-s*a[i][k];
            }
        }
    }
    setprecision(10);
     x[n]=a[n][n+1]/a[n][n];
    for(i=n-1;i>=1;i--)
    {
        float sum=0.0;
        for(j=i+1;j<=n;j++)
        {
            sum=sum+a[i][j]*x[j];
        }
        x[i]=(a[i][n+1]-sum)/a[i][i];
    }
    cout<<"\nThe Solutions are:\n\n";
    for(i=1;i<=n;i++)
    {
        cout<<"X"<<i<<"="<<x[i]<<"\n";
    }
    return(0);
}

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