Step 1: Divide the Matrices

Divide each \(16 \times 16\) matrix into four \(8 \times 8\) submatrices:

\[ A = \begin{bmatrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{bmatrix}, \quad B = \begin{bmatrix} B_{11} & B_{12} \\ B_{21} & B_{22} \end{bmatrix} \]

Where:

• \(A_{11}, A_{12}, A_{21}, A_{22}\) are \(8 \times 8\) submatrices of \(A\).
• \(B_{11}, B_{12}, B_{21}, B_{22}\) are \(8 \times 8\) submatrices of \(B\).

Step 2: Multiply the Submatrices

The product \(C = A \times B\) can also be expressed in terms of the submatrices:

\[ C = \begin{bmatrix} C_{11} & C_{12} \\ C_{21} & C_{22} \end{bmatrix} \]

Where:

• \(C_{11} = A_{11} \times B_{11} + A_{12} \times B_{21}\)
• \(C_{12} = A_{11} \times B_{12} + A_{12} \times B_{22}\)
• \(C_{21} = A_{21} \times B_{11} + A_{22} \times B_{21}\)
• \(C_{22} = A_{21} \times B_{12} + A_{22} \times B_{22}\)

Each of these multiplications (\(A_{11} \times B_{11}\), \(A_{12} \times B_{21}\), etc.) is an \(8 \times 8\) matrix multiplication, which your processor can handle.

Step 3: Combine the Results

After computing all the submatrix products, combine them to form the final \(16 \times 16\) result matrix \(C\):

\[ C = \begin{bmatrix} C_{11} & C_{12} \\ C_{21} & C_{22} \end{bmatrix} \] Algorithm

Explanation of Functions

• matrix_multiply(X, Y): Performs \(8 \times 8\) matrix multiplication using the processor’s capabilities.
• combine_submatrices(C11, C12, C21, C22): Combines the four \(8 \times 8\) submatrices into a single \(16 \times 16\) matrix.

🎥 Video Solution: 16*16 Matrix multiplication by 8*8 matrix

#include <stdio.h>

int main() {
    int number, rev = 0, remainder;
    
    // Taking input
    printf("Enter a number: ");
    scanf("%d", &number);

    // Reversing the number
    while (number != 0) {
        remainder = number % 10;   // Get the last digit
        rev = rev * 10 + remainder; // Append to reversed number
        number /= 10;              // Remove last digit
    }

    // Printing the reversed number
    printf("Reversed Number: %d\n", rev);
    
    return 0;
}

    
        Sample I/O:
Enter a number: 9876
Reversed Number: 6789
=== Code Execution Successful ===
        

🔗 Run Online: Reverse Number

(i)

SELECT e.name
FROM employees e
JOIN employees r 
ON e.salary = r.salary 
AND e.name <> 'Rahim' 
AND e.job <> r.job
WHERE r.name = 'Rahim';

Explanation:

• We join the employees table with itself.
• We match employees (e) who have the same salary as Rahim (r).
• We exclude Rahim himself.
• We ensure that the job of the selected employee is different from Rahim’s.

(ii)

SELECT name
FROM employees
GROUP BY name
HAVING AVG(salary) > (SELECT AVG(salary) FROM employees);

• We calculate the average salary for each employee.
• We compare it with the company’s overall average salary.
• We select only those employees whose average salary is higher than the company’s average.

Loopback Address: This refers to IP addresses within the 127.0.0.0/8 range, commonly starting with 127. It is used for testing and internal communication within the same device.

Host Address: These are IP addresses assigned to specific devices within a network, allowing communication between them.

This Host: Identifies the IP address of the local machine currently in use.

Network Broadcast Address: This is determined based on the network ID and subnet mask, and it is used to send data to all devices within a network.

Broadcast Outbound Address: This address is used to send data packets outside the current network, typically reaching all nodes in a broader network scope.