In this article, we will understand how to multiply to matrix using multi-dimensional arrays. The matrix has a row and column arrangement of its elements. A matrix with m rows and n columns can be called as m × n matrix.
Individual entries in the matrix are called element and can be represented by a[i][j] which suggests that the element a is present in the ith row and jth column.
Below is a demonstration of the same −
Suppose our input is −
First matrix: 2 3 4 5 2 3 4 6 9 Second matrix: 1 5 3 5 6 3 8 1 5
The desired output would be −
The product of two matrices is: 49 32 35 39 40 36 106 65 75
Algorithm
Step 1 - START Step 2 - Declare three integer matrices namely input_matrix_1, input_matrix_1 and resultant_matrix Step 3 - Define the values. Step 4 - Iterate over each element of the both the matrices using for-loop, multiply the element at [i][j] position of the first matrix with each element of the row of the second matrix and add the values, store the value at [i][j] position of the resultant matrix. Repeat this for each element of the first matrix. Step 5 - Display the result Step 5 - Stop
Example 1
Here, we bind all the operations together under the ‘main’ function.
public class MultiplyMatrices {
public static void main(String[] args) {
int matrix_size = 3;
int[][] input_matrix_1 = {
{2, 3, 4},
{5, 2, 3},
{4, 6, 9}
};
System.out.println("The first matrix is defined as: ");
for (int i = 0; i < matrix_size; i++) {
for (int j = 0; j < matrix_size; j++) {
System.out.print(input_matrix_1[i][j] + " ");
}
System.out.println();
}
int[][] input_matrix_2 = {
{1, 5, 3},
{5, 6, 3},
{8, 1, 5}
};
System.out.println("The second matrix is defined as: ");
for (int i = 0; i < matrix_size; i++) {
for (int j = 0; j < matrix_size; j++) {
System.out.print(input_matrix_2[i][j] + " ");
}
System.out.println();
}
int[][] resultant_matrix = new int[matrix_size][matrix_size];
for(int i = 0; i < matrix_size; i++) {
for (int j = 0; j < matrix_size; j++) {
for (int k = 0; k < matrix_size; k++) {
resultant_matrix[i][j] += input_matrix_1[i][k] * input_matrix_2[k][j];
}
}
}
System.out.println("\n The product of two matrices is: ");
for(int[] row : resultant_matrix) {
for (int column : row) {
System.out.print(column + " ");
}
System.out.println();
}
}
}Output
The first matrix is defined as: 2 3 4 5 2 3 4 6 9 The second matrix is defined as: 1 5 3 5 6 3 8 1 5 The product of two matrices is: 49 32 35 39 40 36 106 65 75
Example 2
Here, we encapsulate the operations into functions exhibiting object-oriented programming.
public class MultiplyMatrices {
static int matrix_size = 3;
static void multiply(int input_matrix_1[][], int input_matrix_2[][]){
int[][] resultant_matrix = new int[matrix_size][matrix_size];
for(int i = 0; i < matrix_size; i++) {
for (int j = 0; j < matrix_size; j++) {
for (int k = 0; k < matrix_size; k++) {
resultant_matrix[i][j] += input_matrix_1[i][k] * input_matrix_2[k][j];
}
}
}
System.out.println("\n The product of two matrices is: ");
for(int[] row : resultant_matrix) {
for (int column : row) {
System.out.print(column + " ");
}
System.out.println();
}
}
public static void main(String[] args) {
int matrix_size = 3;
int[][] input_matrix_1 = {
{2, 3, 4},
{5, 2, 3},
{4, 6, 9}
};
System.out.println("The first matrix is defined as: ");
for (int i = 0; i < matrix_size; i++) {
for (int j = 0; j < matrix_size; j++) {
System.out.print(input_matrix_1[i][j] + " ");
}
System.out.println();
}
int[][] input_matrix_2 = { {1, 5, 3},
{5, 6, 3},
{8, 1, 5}
};
System.out.println("The second matrix is defined as: ");
for (int i = 0; i < matrix_size; i++) {
for (int j = 0; j < matrix_size; j++) {
System.out.print(input_matrix_2[i][j] + " ");
}
System.out.println();
}
multiply(input_matrix_1, input_matrix_2);
}
}Output
The first matrix is defined as: 2 3 4 5 2 3 4 6 9 The second matrix is defined as: 1 5 3 5 6 3 8 1 5 The product of two matrices is: 49 32 35 39 40 36 106 65 75