Matrix Inversion in C++

In this tutorial, we are going to learn about the matrix inversion.

Definition

Assuming that there is non-singular ( i.e. determinant(A) is not equal to zero) square matrix A, then an n × n matrix A-1  will exist, called the inverse of such that:
                                    AA-1 = A-1A = I, where I is the identity matrix.

Finding Matrix Inversion in C++

Firstly, we will see how to calculate the inversion of a matrix mathematically

The inverse can be obtained using the formula:

Matrix Inversion in C++

We will solve one example:

Matrix Inversion in C++

Now, let’s implement it on C++

#include<iostream>
 
using namespace std;
 
int main(){
  int m[3][3]; //3x3 matrix
  float d = 0;
  
  cout<<"Enter elements of the matrix:\n";
  for(int i = 0; i < 3; i++)
    for(int j = 0; j < 3; j++)
           std::cin>>m[i][j];
  
  
  //finding determinant of the matrix
  for(int i = 0; i < 3; i++)
    d = d + (m[0][i] * (m[1][(i+1)%3] * m[2][(i+2)%3] - m[1][(i+2)%3] * m[2][(i+1)%3]));
    
  if(d>0)         //Condition to check if the derterminat is zero or not if zero than inverse dont exists
  {
      cout<<"\nInverse of the matrix is: \n";
      for(int i = 0; i < 3; i++){
        for(int j = 0; j < 3; j++)
          std::cout<<((m[(j+1)%3][(i+1)%3] * m[(j+2)%3][(i+2)%3]) - (m[(j+1)%3][(i+2)%3] * m[(j+2)%3][(i+1)%3]))/ d<<"\t"; //finding adjoint and dividing it by determinant
        std::cout<<"\n";
     }
  }
  else std::cout<<"Inverse does'nt exist for this matrix";
     return 0;
}

 

OUTPUT:

Enter elements of the matrix:
5 
7 
9 
4
3 
8
7
5
6
Inverse of the matrix is: 
-0.209524          0.0285714         0.27619 
 0.304762         -0.314286          -0.0380952
-0.00952381        0.228571          -0.12381

 

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