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

Answer 1

#include <iostream> 
#include <vector> 
using namespace std; 
  
// Function to Print matrix. 
void PrintMatrix(float ar[][10], int n, int m) 
{ 
    for (int i = 0; i < n; i++) { 
        for (int j = 0; j < m; j++) { 
            cout << ar[i][j] << "  "; 
        } 
        printf("\n"); 
    } 
    return; 
} 
  
// Function to Print inverse matrix 
void PrintInverse(float ar[][10], int n, int m) 
{ 
    for (int i = 0; i < n; i++) { 
        for (int j = n; j < m; j++) { 
            printf("%.3f  ", ar[i][j]); 
        } 
        printf("\n"); 
    } 
    return; 
} 
  
// Function to perform the inverse operation on the matrix. 
void InverseOfMatrix(float matrix[][10], int order) 
{ 
    // Matrix Declaration. 
  
    float temp; 
  
    // PrintMatrix function to print the element 
    // of the matrix. 
    printf("=== Matrix ===\n"); 
    PrintMatrix(matrix, order, order); 
  
    // Create the augmented matrix 
    // Add the identity matrix 
    // of order at the end of original matrix. 
    for (int i = 0; i < order; i++) { 
  
        for (int j = 0; j < 2 * order; j++) { 
  
            // Add '1' at the diagonal places of 
            // the matrix to create a identity matirx 
            if (j == (i + order)) 
                matrix[i][j] = 1; 
        } 
    } 
  
    // Interchange the row of matrix, 
    // interchanging of row will start from the last row 
    for (int i = order - 1; i > 0; i--) { 
  
        // Swapping each and every element of the two rows 
        // if (matrix[i - 1][0] < matrix[i][0]) 
        // for (int j = 0; j < 2 * order; j++) { 
        // 
        //        // Swapping of the row, if above 
        //        // condition satisfied. 
        // temp = matrix[i][j]; 
        // matrix[i][j] = matrix[i - 1][j]; 
        // matrix[i - 1][j] = temp; 
        //    } 
  
        // Directly swapping the rows using pointers saves time 
  
        if (matrix[i - 1][0] < matrix[i][0]) { 
            // float* temp = matrix[i]; 
            // matrix[i] = matrix[i - 1]; 
            // matrix[i - 1] = temp; 
            swap(matrix[i], matrix[i-1]);
        } 
    } 
  
    // Print matrix after interchange operations. 
    printf("\n=== Augmented Matrix ===\n"); 
    PrintMatrix(matrix, order, order * 2); 
  
    // Replace a row by sum of itself and a 
    // constant multiple of another row of the matrix 
    for (int i = 0; i < order; i++) { 
  
        for (int j = 0; j < order; j++) { 
  
            if (j != i) { 
  
                temp = matrix[j][i] / matrix[i][i]; 
                for (int k = 0; k < 2 * order; k++) { 
  
                    matrix[j][k] -= matrix[i][k] * temp; 
                } 
            } 
        } 
    } 
  
    // Multiply each row by a nonzero integer. 
    // Divide row element by the diagonal element 
    for (int i = 0; i < order; i++) { 
  
        temp = matrix[i][i]; 
        for (int j = 0; j < 2 * order; j++) { 
  
            matrix[i][j] = matrix[i][j] / temp; 
        } 
    } 
  
    // print the resultant Inverse matrix. 
    printf("\n=== Inverse Matrix ===\n"); 
    PrintInverse(matrix, order, 2 * order); 
  
    return; 
} 
  
// Driver code 
int main() 
{ 
    int order; 
  
    // Order of the matrix 
    // The matrix must be a square a matrix 
    cout << "Enter the size of the matrix\n";
        cin >> order;    
    float matrix[10][10];
    for(int i = 0;i<order;i++){
        for(int j = 0;j<order;j++){
                cin >> matrix[i][j];
        }
    }
    matrix[order][0] = 0;
    // Get the inverse of matrix 
    InverseOfMatrix(matrix, order); 
  
    return 0; 
}