For matrix multiplication to take place, the number of columns of first matrix must be equal to the number of rows of second matrix. In our example, i.e.
c1 = r2
Also, the final product matrix is of size r1 x c2
, i.e.
product[r1][c2]
You can also multiply two matrices using functions.
Example: Program to Multiply Two Matrices
public class MultiplyMatrices {
public static void main(String[] args) {
int r1 = 2, c1 = 3;
int r2 = 3, c2 = 2;
int[][] firstMatrix = { {3, -2, 5}, {3, 0, 4} };
int[][] secondMatrix = { {2, 3}, {-9, 0}, {0, 4} };
// Mutliplying Two matrices
int[][] product = new int[r1][c2];
for(int i = 0; i < r1; i++) {
for (int j = 0; j < c2; j++) {
for (int k = 0; k < c1; k++) {
product[i][j] += firstMatrix[i][k] * secondMatrix[k][j];
}
}
}
// Displaying the result
System.out.println("Multiplication of two matrices is: ");
for(int[] row : product) {
for (int column : row) {
System.out.print(column + " ");
}
System.out.println();
}
}
}
Output
Multiplication of two matrices is: 24 29 6 25
In the above program, the multiplication takes place as:
|- (a11 x b11) + (a12 x b21) + (a13 x b31) (a11 x b12) + (a12 x b22) + (a13 x b32) -| |_ (a21 x b11) + (a22 x b21) + (a23 x b31) (a21 x b12) + (a22 x b22) + (a23 x b32) _|
In our example, it takes place as:
|- (3 x 2) + (-2 x -9) + (5 x 0) = 24 (3 x 3) + (-2 x 0) + (5 x 4) = 29 -| |_ (3 x 2) + ( 0 x -9) + (4 x 0) = 6 (3 x 3) + ( 0 x 0) + (4 x 4) = 25 _|
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