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

Example run:

Enter matrix1: 1 2 3 4 5 6 7 8 9 (enter)

Enter martix2: 0 2 4 1 4.5 2.2 1.1 4.3 5.2 (enter)

The matrices are added as follows:

1.0 2.0 3.0              0.0 2.0 4.0            1.0 4.0 7.0

4.0 5.0 6.0        +    1.0 4.5 2.2     =      5.0 9.5 8.2

7.0 8.0 9.0              1.1 4.3 5.2           8.1 12.3 14.2

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:

Example run:

Enter matrix1: 1 2 3 4 5 6 7 8 9 (enter)

Enter matrix2: 0 2 4 1 4.5 2.2 1.1 4.3 5.2 (enter)

The multiplication of the matrices is

1 2 3           0 2.0 4.0               5.3 23.9 24

4 5 6     *     1 4.5 2.2     =       11.6 56.3 58.2

7 8 9           1.1 4.3 5.2            17.9 88.7 92.4

Answer 1

import java.util.Scanner;

public class AddMatrix {

    public static double[][] addMatrix(double[][] a, double[][] b) {
        double[][] result = new double[a.length][a[0].length];
        for(int i = 0; i < a.length; ++i) {
            for(int j = 0; j < a[i].length; ++j) {
                result[i][j] = a[i][j] + b[i][j];
            }
        }
        return result;
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        double[][] matrix1 = new double[3][3];
        double[][] matrix2 = new double[3][3];
        System.out.print("Enter matrix1: ");
        for(int i = 0; i < matrix1.length; ++i) {
            for(int j = 0; j < matrix1[i].length; ++j) {
                matrix1[i][j] = in.nextDouble();
            }
        }
        System.out.print("Enter matrix2: ");
        for(int i = 0; i < matrix2.length; ++i) {
            for(int j = 0; j < matrix2[i].length; ++j) {
                matrix2[i][j] = in.nextDouble();
            }
        }
        double[][] matrix3 = addMatrix(matrix1, matrix2);
        System.out.println("\nThe addition of the matrices is");
        double minSum = 0;
        int minRow = 0;
        for(int i = 0; i < 3; ++i) {
            for(int j = 0; j < 3; ++j) {
                System.out.printf("%5.1f\t", matrix1[i][j]);
            }
            if(i == 1) {
                System.out.printf(" + ");
            } else {
                System.out.printf("   ");
            }
            for(int j = 0; j < 3; ++j) {
                System.out.printf("%5.1f\t", matrix2[i][j]);
            }
            if(i == 1) {
                System.out.printf(" = ");
            } else {
                System.out.printf("   ");
            }
            for(int j = 0; j < 3; ++j) {
                System.out.printf("%5.1f\t", matrix3[i][j]);
            }
            double sum = 0;
            for(int j = 0; j < 3; ++j) {
                sum += matrix3[i][j];
            }
            if (i == 0 || sum < minSum) {
                minSum = sum;
            }
            System.out.printf("\n");
        }
    }
}

import java.util.Scanner;

public class MultiplyMatrix {

    public static double[][] multiplyMatrix(double[][] a, double[][] b) {
        double[][] result = new double[a.length][b[0].length];
        for(int i = 0; i < a.length; ++i) {
            for(int j = 0; j < b[i].length; ++j) {
                double total = 0;
                for(int k = 0; k < a[i].length; ++k) {
                    total += (a[i][k] * b[k][j]);
                }
                result[i][j] = total;
            }
        }
        return result;
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        double[][] matrix1 = new double[3][3];
        double[][] matrix2 = new double[3][3];
        System.out.print("Enter matrix1: ");
        for(int i = 0; i < matrix1.length; ++i) {
            for(int j = 0; j < matrix1[i].length; ++j) {
                matrix1[i][j] = in.nextDouble();
            }
        }
        System.out.print("Enter matrix2: ");
        for(int i = 0; i < matrix2.length; ++i) {
            for(int j = 0; j < matrix2[i].length; ++j) {
                matrix2[i][j] = in.nextDouble();
            }
        }
        double[][] matrix3 = multiplyMatrix(matrix1, matrix2);
        for(int i = 0; i < 3; ++i) {
            for(int j = 0; j < 3; ++j) {
                System.out.printf("%5.1f\t", matrix1[i][j]);
            }
            if(i == 1) {
                System.out.printf(" * ");
            } else {
                System.out.printf("   ");
            }
            for(int j = 0; j < 3; ++j) {
                System.out.printf("%5.1f\t", matrix2[i][j]);
            }
            if(i == 1) {
                System.out.printf(" = ");
            } else {
                System.out.printf("   ");
            }
            for(int j = 0; j < 3; ++j) {
                System.out.printf("%5.1f\t", matrix3[i][j]);
            }
            System.out.printf("\n");
        }
    }

}