**Title: Calculate the sum of diagonals in a matrix**

In this blog post, we’ll delve into the world of matrices and explore how to calculate the sum of diagonals in a 3×3 matrix using Java. We’ll provide a Java program with detailed comments and explanations, along with examples to illustrate the concept. By the end, you’ll have a clear understanding of how to perform this operation efficiently in Java.

**Understanding the 3×3 Matrix**

A 3×3 matrix is a fundamental structure in linear algebra, represented as:

In this matrix, we have two main diagonals: the principal diagonal (from the top-left to the bottom-right) and the secondary diagonal (from the top-right to the bottom-left). Our goal is to calculate the sum of elements along these diagonals.

**Java Program for Diagonal Sum Calculation**

Let’s dive into the Java program that calculates the sum of diagonals in a 3×3 matrix:

```
public class DiagonalSum3x3Matrix {
public static void main(String[] args) {
// Initialize the 3x3 matrix
int[][] matrix = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9}
};
// Initialize variables to hold sum of principal and secondary diagonals
int principalSum = 0;
int secondarySum = 0;
// Loop through the rows of the matrix
for (int i = 0; i < matrix.length; i++) {
// Add elements of principal diagonal (from top-left to bottom-right)
principalSum += matrix[i][i];
// Add elements of secondary diagonal (from top-right to bottom-left)
secondarySum += matrix[i][matrix.length - 1 - i];
}
// Display the sums of principal and secondary diagonals
System.out.println("Sum of Principal Diagonal: " + principalSum);
System.out.println("Sum of Secondary Diagonal: " + secondarySum);
}
}
```

**Explanation of the Java Program**

- We start by initializing our 3×3 matrix
`matrix`

with values from 1 to 9. - Two variables
`principalSum`

and`secondarySum`

are used to store the sums of the principal and secondary diagonals, respectively. - We then enter a
`for`

loop that iterates through each row of the matrix. - For the principal diagonal, we add the element at the position
`[i][i]`

to`principalSum`

. - For the secondary diagonal, we add the element at the position
`[i][matrix.length - 1 - i]`

to`secondarySum`

.

**Example Calculation**

Let’s consider the following 3×3 matrix:

- Principal Diagonal Sum: ( 1 + 5 + 9 = 15 )
- Secondary Diagonal Sum: ( 3 + 5 + 7 = 15 )

Learn and practice more on Array Programs: Array

**Conclusion**

In this blog post, we’ve explored how to calculate the sum of diagonals in a 3×3 matrix using Java. The program efficiently computes the sums of the principal and secondary diagonals, demonstrating a fundamental matrix operation.

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