# 1. Introduction

Adding two matrices involves adding corresponding elements of these matrices. It is a fundamental operation in linear algebra used in various computations and algorithms. In this tutorial, we will write a Java program to add two matrices.

# 2. Program Steps

1. Define a class named AddMatrices.

2. Inside the main method, define two 2D arrays matrix1 and matrix2 representing the matrices to be added.

3. Verify that the matrices have the same dimensions, as matrices of different dimensions cannot be added together.

4. Define a 2D array sumMatrix to store the sum of the matrices.

5. Use nested for loops to perform the addition of matrix1 and matrix2 and store the result in sumMatrix.

6. Print the original matrices and the resultant sumMatrix.

# 3. Code Program

``````public class AddMatrices { // Step 1: Define a class named AddMatrices

public static void main(String[] args) { // Main method

// Step 2: Define two 2D arrays matrix1 and matrix2 representing the matrices to be added
int[][] matrix1 = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9}
};

int[][] matrix2 = {
{9, 8, 7},
{6, 5, 4},
{3, 2, 1}
};

// Step 3: Verify that the matrices have the same dimensions
int rows = matrix1.length;
int columns = matrix1[0].length;

if (rows != matrix2.length || columns != matrix2[0].length) {
System.out.println("Matrices of different dimensions cannot be added!");
return;
}

// Step 4: Define a 2D array sumMatrix to store the sum of the matrices
int[][] sumMatrix = new int[rows][columns];

// Step 5: Use nested for loops to perform the addition of matrix1 and matrix2
for (int i = 0; i < rows; i++) {
for (int j = 0; j < columns; j++) {
sumMatrix[i][j] = matrix1[i][j] + matrix2[i][j];
}
}

// Step 6: Print the original matrices and the resultant sumMatrix
System.out.println("Matrix 1:");
for (int i = 0; i < rows; i++) {
for (int j = 0; j < columns; j++) {
System.out.print(matrix1[i][j] + " ");
}
System.out.println();
}

System.out.println("Matrix 2:");
for (int i = 0; i < rows; i++) {
for (int j = 0; j < columns; j++) {
System.out.print(matrix2[i][j] + " ");
}
System.out.println();
}

System.out.println("Sum of Matrices:");
for (int i = 0; i < rows; i++) {
for (int j = 0; j < columns; j++) {
System.out.print(sumMatrix[i][j] + " ");
}
System.out.println();
}
}
}
``````

### Output:

```Matrix 1:
1 2 3
4 5 6
7 8 9
Matrix 2:
9 8 7
6 5 4
3 2 1
Sum of Matrices:
10 10 10
10 10 10
10 10 10
```

# 4. Step By Step Explanation

Step 1: A class named AddMatrices is defined.

Step 2: Two 2D arrays matrix1 and matrix2 representing the matrices to be added are defined inside the main method.

Step 3: The program verifies that matrix1 and matrix2 have the same dimensions.

Step 4: A 2D array sumMatrix is defined to store the sum of matrix1 and matrix2.

Step 5: Nested for loops are used to perform the addition of matrix1 and matrix2 and store the result in sumMatrix.

Step 6: The program prints the original matrices matrix1 and matrix2 and the resultant sumMatrix.