Check if a Matrix is Invertible in C++

Here we will see how to check whether a matrix is invertible or not. If one matrix is M, then the inverted matrix M-1 will be −

$$M^-1=\frac{adj(M)}{|M\lvert}$$

So if the determinant of M is non-zero, then only we can get the inverse, otherwise, we will not get the inverse of it. So here we have to check the determinant is non-zero or not. Finding a determinant is one recursive process. We have to find submatrix, then find the determinant of it, then use that result for the final calculation. Let us see the code to get a better idea.

Example

 Live Demo

#include <iostream>
#define N 4
using namespace std;
void findCoFactor(int mat[N][N], int mat2[N][N], int p, int q, int n) {
   int i = 0, j = 0;
   for (int row = 0; row < n; row++) {
      for (int col = 0; col < n; col++) {
         if (row != p && col != q) {
            mat2[i][j++] = mat[row][col];
            if (j == n - 1) {
               j = 0;
               i++;
            }
         }
      }
   }
}
int getDeterminant(int mat[N][N], int n) {
   int determinant = 0;
   if (n == 1)
      return mat[0][0];
   int temp[N][N];
   int sign = 1;
   for (int f = 0; f < n; f++) {
      findCoFactor(mat, temp, 0, f, n);
      determinant += sign * mat[0][f] * getDeterminant(temp, n - 1);
      sign = -sign;
   }
   return determinant;
}
bool isMatrixInvertible(int mat[N][N], int n) {
   if (getDeterminant(mat, N) != 0)
      return true;
   else
      return false;
}
int main() {
   int matrix[N][N] = {
      { 1, 0, 2, -1 },
      { 3, 0, 0, 5 },
      { 2, 1, 4, -3 },
      { 1, 0, 5, 0 }
   };
   if (isMatrixInvertible(matrix, N))
      cout << "The matrix is invetible";
   else
      cout << "The matrix is not invetible";
}

Output

The matrix is invetible

Arnab Chakraborty

Published on 22-Oct-2019 08:36:20

• Related Questions & Answers
• C++ Program to Check if a Matrix is Invertible
• How to check if a matrix is invertible or not in R?
• Program to check if a matrix is symmetric in C++
• Program to check if a matrix is Binary matrix or not in C++
• C++ Program to Check if it is a Sparse Matrix
• Check if a given matrix is Hankel or not in C++
• Check if a given matrix is sparse or not in C++
• Program to check if matrix is lower triangular in C++
• Program to check if matrix is upper triangular in C++
• C Program to check if matrix is singular or not
• How to check if a matrix in R is in binary form?
• Check if a pair with given product exists in a Matrix in C++
• Check if a File is hidden in C#
• Check if a number is Palindrome in C++
• Check if a number is Bleak in C++