# 1. Introduction

Matrix operations are foundational in various computational problems, especially in graphics, physics simulations, and machine learning. In this tutorial, we'll discuss how to perform matrix addition in Swift.

# 2. Program Overview

We will:

1. Define two matrices.

2. Perform the addition of the two matrices.

3. Print the resultant matrix.

# 3. Code Program

``````// Function to add two matrices
func addMatrices(_ matrixA: [[Int]], _ matrixB: [[Int]]) -> [[Int]]? {
// Ensure both matrices have the same dimensions
guard matrixA.count == matrixB.count && matrixA[0].count == matrixB[0].count else {
return nil
}

var result = [[Int]](repeating: [Int](repeating: 0, count: matrixA[0].count), count: matrixA.count)

for i in 0..<matrixA.count {
for j in 0..<matrixA[i].count {
result[i][j] = matrixA[i][j] + matrixB[i][j]
}
}

return result
}

// Defining two matrices for testing
let matrix1 = [    [1, 2, 3],
[4, 5, 6],
[7, 8, 9]
]

let matrix2 = [    [9, 8, 7],
[6, 5, 4],
[3, 2, 1]
]

print("Resultant Matrix:")
print(row)
}
} else {
print("Matrix addition is not possible due to different dimensions.")
}
``````

### Output:

```Resultant Matrix:
[10, 10, 10]
[10, 10, 10]
[10, 10, 10]
```

# 4. Step By Step Explanation

1. We have the function addMatrices(_:_) that's designed to add two matrices. It returns an optional 2D integer array, accounting for the possibility of matrices having different dimensions.

2. Inside the function:

- We first validate that both matrices have the same dimensions.- The result matrix is initialized to the same dimensions as the input matrices, filled with zeros.- Nested for loops traverse through the matrices. The elements at corresponding positions in the two matrices are added and stored in the result matrix.

3. To test the function, we define two matrices matrix1 and matrix2.

4. We then call the addMatrices(_:_) function, and if successful, we print out the resultant matrix.

This is a straightforward approach for matrix addition in Swift, ensuring that both matrices are compatible for addition.