matrixinvertible.cpp

// Program to find if a particular matrix is invertible or not.
// A given matrix is invertible only if its determinant is non-zero.

#include<iostream>
#include<conio.h>
#include<math.h>

using namespace std;
double d=0;
double det(int n, double mat[10][10]);
double det(int n, double mat[10][10])
{
    double submat[10][10];
    if(n == 2)
        return((mat[0][0] * mat[1][1]) - (mat[1][0] * mat[0][1]));
    else
    {
        for(int c = 0; c < n; c++)
        {
            int subi = 0; //submatrix's i value
            for(int i = 1; i < n; i++)
            {
                int subj = 0;
                for(int j = 0; j < n; j++)
                {
                    if(j == c)
                        continue;
                    submat[subi][subj] = mat[i][j];
                    subj++;
                }
                subi++;

            }
            d = d + (pow(-1, c) * mat[0][c] * det(n - 1, submat));
        }
    }
    return d;
}
int main(int argc, char **argv)
{

    cout<<"Enter the dimension of the matrix:\n";
    int n;
    cin>>n;
    double mat[10][10];
    cout<<"Enter the elements of the matrix:\n";
    for(int i = 0; i < n; i++)
    {
        for(int j = 0; j < n; j++)
        {
            cin>>mat[j][i];
        }
    }
    if(det(n, mat) != 0)
    {
        cout<<"The given matrix is invertible";
    }
    else
    {
        cout<<"The given matrix is not invertible";
    }
}