Question

The inverse of a square matrix A is denoted A-1 , such that A × A-1 = I, where I is the identity matrix with all 1s on the diagonal and 0 on all other cells. The inverse of a 2×2 matrix A can be obtained using the following formula:       = c d a b A      − − − = − c a d b ad bc A 1 1 Implement the following method to obtain an inverse of 2×2 matrix: public static double[][] inverse(double[][] A) The method returns null if ad – bc is 0. Write a test program that prompts the user to enter a, b, c, d for a matrix, and displays its inverse matrix. Here are three sample runs: Enter a, b, c, d: 1 2 3 4 -2.0 1.0 1.5 -0.5 Enter a, b, c, d: 0.5 2 1.5 4.5 -6.0 2.6666666666666665 2.0 -0.6666666666666666 2 Enter a, b, c, d: 1 2 3 6 No inverse matrix

Answer 1

package Lab_5;

 

import java.util.Scanner;

 

public class InverseMatrix {

 

     public static void main(String[] args) {

         

          //initializing Scanner and variables

          Scanner input = new Scanner(System.in);

          System.out.print("Enter a, b, c, d: ");

         

          double [][] squareMatrix = new double [2][2];

         

          //taking input from the user

          for (int i = 0; i < 2; i++) {

               for (int j = 0; j < 2; j++) {

                     squareMatrix [i][j] = input.nextDouble();

               }

          }

         

          //calling the inverse method

          double [][] returnInverseMatrix = inverse(squareMatrix);

         

         

          //checking to see if the inverse matrix is null or not

          if (returnInverseMatrix == null) {

               System.out.print("No inverse matrix");

          } else {

              

               //printing the inverse matrix according to the format

               for (int i = 0; i < 2; i++) {

                     for (int j = 0; j < 2; j++) {

                          System.out.print(squareMatrix [i][j] + " ");

                     }

                     System.out.print("\n");

               }

          }

         

          input.close();

     }

    

     public static double[][] inverse(double[][] A) {

         

          //calculating the denominator

          double denominator = (A[0][0]*A[1][1]) - (A[0][1]*A[1][0]);

         

          //checking if the denominator is 0. if it is zero then returning null

          if (denominator == 0) {

               return null;

          }

         

          //interchanging the values of a and d

          double temp;

          temp = A[0][0];

          A[0][0] = A[1][1];

          A[1][1] = temp;

         

          //making the value of b and c negative

          A[0][1] = -A[0][1];

          A[1][0] = -A[1][0];

         

         

          // dividing all the values of matrix of A by the denominator to get the inverse matrix

          for (int i = 0; i < 2; i++) {

               for (int j = 0; j < 2; j++) {

                     A[i][j] = (A[i][j]/denominator);

               }

          }

         

          //returning the matrix

          return A;

         

     }

}