Question

For this lab, you will write a C++ program that will calculate the matrix inverse of a matrix no bigger than 10x10. I will guarantee that the matrix will be invertible and that you will not have a divide by 0 problem.

For this program, you are required to use the modified Gaussian elimination algorithm. Your program should ask for the size (number of rows only) of a matrix. It will then read the matrix, calculate the inverse, and print the inverse, and quit. I do not care if you use two separate matrices one for the original and one for the inverse or if you combine the two. Note: the matrix should be a float, and you will need to use the cmath round function to get the output below.

Sample Run:

./a.out
input row size 3
input the matrix to invert
-1 2 -3
2 1 0
4 -2 5
the inverse is:
-5  4  -3  
10  -7  6  
8  -6  5  

Please, i have had two people answer this question but the output gives me Garbage. Please help solve this problem using C++.

Answer 1

#include <iostream>
#include <cmath>

using namespace std;

void inverse(float mat[][10], int order) 
{ 
    float temp; 
    // Creating the augmented matrix for gauss elemination method 
    for (int i = 0; i < order; i++) { 
  
        for (int j = 0; j < 2 * order; j++) { 
            if (j == (i + order)) 
                mat[i][j] = 1; 
        } 
    } 
   
    // Interchanging of rows of the matrix 
    for (int i = order - 1; i > 0; i--) { 
 
        if (mat[i - 1][0] < mat[i][0])
        {
            for (int j = 0; j < 2 * order; j++) 
            { 
                temp = mat[i][j]; 
                mat[i][j] = mat[i - 1][j]; 
                mat[i - 1][j] = temp; 
            } 
        }
    } 
 
    for (int i = 0; i < order; i++) { 
  
        for (int j = 0; j < order; j++) { 
  
            if (j != i) { 
  
                temp = mat[j][i] / mat[i][i]; 
                for (int k = 0; k < 2 * order; k++) { 
  
                    mat[j][k] -= mat[i][k] * temp; 
                } 
            } 
        } 
    } 
  
    // Multipling each row by a nonzero integer and then dividing a row element by the diagonal element 
    for (int i = 0; i < order; i++) { 
  
        temp = mat[i][i]; 
        for (int j = 0; j < 2 * order; j++) { 
  
            mat[i][j] = round(mat[i][j] / temp);    
        } 
    } 
  
    // print the resultant Inverse matrix. 
    cout<<"\nthe inverse is\n"; 
    for (int i = 0; i < order; i++)
    { 
        for (int j = order; j < 2*order; j++) 
        { 
            cout<<mat[i][j]<<" "; 
        } 
        cout<<"\n"; 
    }  
  
    return; 
} 

int main()
{
    int r;
    float mat[10][10];
    cout<<"input row size ";
    cin>>r;
    cout<<"\ninput the matrix to invert\n";
    for(int i=0;i<r;i++)
    {
        for(int j=0;j<r;j++)
        {
            cin>>mat[i][j];
        }
    }
    inverse(mat,r);

    return 0;
}

output: