Question

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 + ... *
* + ain * bnj. *
* *
* Write a test program that prompts the user to enter two 3 * 3 matrices and *
* displays their product.

Answer 1

I am writing JAVA program:

import java.util.Scanner; // to take input from user

public class MatrixMultiplication {

public static void main(String[] args) { // start of main function

double[][] matrixA = new double[3][3]; // matrix 1

double[][] matrixB = new double[3][3]; // matrix 2

Scanner input = new Scanner(System.in); // scans user input

System.out.print("Enter matrix A: "); // prompts to enter matrix A

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

//loop to enter values in matrix A till length of matrixA

for (int j = 0; j < matrixA.length; j++)

// reads the matrixA values entered by the user

matrixA[i][j] = input.nextDouble(); }

System.out.print("Enter matrix B: "); // prompts to enter matrix B

//loop to enter values in matrix B till length of matrixB

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

for (int j = 0; j < matrixB.length; j++)

// reads the matrixB values entered by the user

matrixB[i][j] = input.nextDouble();}

//matrixC stores the result of the product of matrixA and matrixB

double[][] matrixC = Multiplication(matrixA, matrixB);

// Display function is called to display the matrices A, B and product //result which is matrixC

Display(matrixA, matrixB, matrixC); }

//function Multiplication to calculate the product of matrixA and matrixB

public static double[][] Multiplication(double[][] inputMatrix1, double[][] inputMatrix2) {

//stores the product of two matrices

double[][] outputMatrix = new double[3][3];

//the loops below are used to move through the rows of outputMatrix

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

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

for (int k = 0; k < outputMatrix.length; k++) {

/* takes the product of inputMatrix1 and inputMatrix2 and adds result of product of each row and stores the result in matrix outputMatrix*/

outputMatrix[i][j] += inputMatrix1[i][k] * inputMatrix2[k][j];

} } }

return outputMatrix; } //returns the resultant matrix

public static void resultMatrix(double[][] matrix, int row) {

//displays all the values in row form

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

System.out.printf("%.1f", matrix[row][j]); } }

public static void Display(double[][] matrix1, double[][] matrix2, double[][] matrix3) { //displays the result of product of two matrices

System.out.println("The product of two 3*3 matrices is: ");

for (int i = 0; i < 3; i++) {

resultMatrix(matrix1, i); //displays elements of matrix A

System.out.print((i == 1 ? " * " : " "));

resultMatrix(matrix2, i); //displays elements of matrix B

System.out.print((i == 1 ? " = " : " "));

resultMatrix(matrix3, i); //displays elements of resultant matrixC

System.out.println(); } } }

Step-by-step explanation:

The program has three functions and main() function. In the main() function programs prompts the user to enter the elements of matrix A and matrix B and uses Scanner class to take this input from the user. Then Multiplication() function is called which computes the product of the two 3*3 matrices i.e. matrixA and matrixB and stores the result in matrixC. Next Display() function is called which displays the elements of matrix A, matrix B and the resultant matrix C in the matrix form with * between matrix A and B and the = sign between the input matrices and their product matrix.

The output of the program is attached as screen shot.