Question

Lab # 4 Multidimensional Arrays

Please write in JAVA.

Programming Exercise 8.5 (Algebra: add two matrices)

Write a method to add two matrices. The header of the method is as follows:

public static double[][] addMatrix(double[][] a, double[][] b

In order to be added, the two matrices must have the same dimensions and the same or compatible types of elements. Let c be the resulting matrix. Each element cij is aij + bij. For example, for two 3 * 3 matrices a and b, c is

Write a test program that prompts the user to enter two 3 * 3 matrices and displays their sum. Here is a sample run

Programming Exercise 8.6 (Algebra: multiply two matrices)

Write a method to multiply two matrices. The header of the method is:

public static double[][] multiplyMatrix(double[][] a, double[][] b)

To multiply matrix a by matrix b, the number of columns in a must be the same as the number of rows in b, and the two matrices must have elements of the same or compatible types. Let c be the result of the multiplication. Assume the column size of matrix a is n. Each element cij is ai1 * b1j + ai2 * b2j + c + ain * bnj. For example, for two 3 * 3 matrices a and b, c is

where cij = ai1 * b1j + ai2 * b2j + ai3 * b3j. Write a test program that prompts the user to enter two 3 * 3 matrices and displays their product. Here is a sample run:

Answer 1

Here is the completed code for this problem. Comments are included, go through it, learn how things work and let me know if you have any doubts or if you need anything to change. If you are satisfied with the solution, please rate the answer. Thanks

// Program1.java (code for Exercise 8.5)

import java.util.Scanner;

public class Program1 {

      // required method to add two matrices

      public static double[][] addMatrix(double[][] a, double[][] b) {

            if (a.length != b.length || a[0].length != b[0].length) {

                  return null; // cannot be added

            }

            // creating a matrix to store results

            double[][] result = new double[a.length][a[0].length];

            // looping and adding corresponding elements and saving to result

            for (int i = 0; i < a.length; i++) {

                  for (int j = 0; j < a[0].length; j++) {

                        result[i][j] = a[i][j] + b[i][j];

                  }

            }

            return result;

      }

      // a helper method defined to read elements to a matrix

      static void readMatrix(double matrix[][]) {

            Scanner scanner = new Scanner(System.in);

            for (int i = 0; i < matrix.length; i++) {

                  for (int j = 0; j < matrix[0].length; j++) {

                        matrix[i][j] = scanner.nextDouble();

                  }

            }

      }

      // a helper method defined to print elements of a matrix

      static void printMatrix(double matrix[][]) {

            for (int i = 0; i < matrix.length; i++) {

                  for (int j = 0; j < matrix[0].length; j++) {

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

                  }

                  System.out.println();

            }

      }

      public static void main(String[] args) {

            // creating two matrices

            double a[][] = new double[3][3];

            double b[][] = new double[3][3];

            // asking and reading two matrices

            System.out.println("Enter first matrix (3x3)");

            readMatrix(a);

            System.out.println("Enter second matrix (3x3)");

            readMatrix(b);

            // finding sum

            double c[][] = addMatrix(a, b);

            // displaying resultant matrix

            System.out.println("\nSum of two matrices:");

            printMatrix(c);

      }

}

// Program2.java (code for Exercise 8.6)

import java.util.Scanner;

public class Program2 {

      // required method to multiply two matrices

      public static double[][] multiplyMatrix(double[][] a, double[][] b) {

            // finding rows and columns count for both matrices

            int row1 = a.length;

            int col1 = a[0].length;

            int row2 = b.length;

            int col2 = b[0].length;

            if (col1 != row2) {

                  // multiplication not possible

                  return null;

            }

            // creating a row1 x col2 matrix for storing the result

            double result[][] = new double[row1][col2];

            //looping and multiplying the matrix

            for (int i = 0; i < row1; i++) {

                  for (int j = 0; j < col2; j++) {

                        for (int k = 0; k < col1; k++) {

                              result[i][j] += a[i][k] * b[k][j];

                        }

                  }

            }

            return result;

      }

      // a helper method defined to read elements to a matrix

      static void readMatrix(double matrix[][]) {

            Scanner scanner = new Scanner(System.in);

            for (int i = 0; i < matrix.length; i++) {

                  for (int j = 0; j < matrix[0].length; j++) {

                        matrix[i][j] = scanner.nextDouble();

                  }

            }

      }

      // a helper method defined to print elements of a matrix

      static void printMatrix(double matrix[][]) {

            for (int i = 0; i < matrix.length; i++) {

                  for (int j = 0; j < matrix[0].length; j++) {

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

                  }

                  System.out.println();

            }

      }

      public static void main(String[] args) {

            // creating two matrices

            double a[][] = new double[3][3];

            double b[][] = new double[3][3];

            // asking and reading two matrices

            System.out.println("Enter first matrix (3x3)");

            readMatrix(a);

            System.out.println("Enter second matrix (3x3)");

            readMatrix(b);

            // finding product

            double c[][] = multiplyMatrix(a, b);

            // displaying resultant matrix

            System.out.println("\nProduct of two matrices:");

            printMatrix(c);

      }

}

//OUTPUT OF BOTH PROGRAMS

Enter first matrix (3x3)

1 2 3

4 5 6

7 8 9

Enter second matrix (3x3)

1 2 3

4 5 6

7 8 9

Sum of two matrices:

2.0 4.0 6.0

8.0 10.0 12.0

14.0 16.0 18.0

Enter first matrix (3x3)

1 2 3

4 5 6

7 8 9

Enter second matrix (3x3)

1 1 2

3 3 4

0 0 1

Product of two matrices:

7.0 7.0 13.0

19.0 19.0 34.0

31.0 31.0 55.0