Write a single makefile to compile all your programs. Write a document to describe or explain how you designed and solved each problem briefly. Put all your codes, makefile and document into a zip file.

1. Input from the command line two positive integers p and q between 1 and 10 inclusive. Generate two random matrices A and B with elements of type double. A should be a p by q matrix and B should be a q by p matrix. Output the two matrix products AB and BA. Print all four matrices A, B, AB and BA to standard output with two digits after the decimal point. Write both a C version and a C++ version program for this problem. In the C version design a struct for the matrix. In the C++ version design a class for the matrix. You need to include the two dimension sizes (number of rows and columns) as member variables and make the storage for matrix elements dynamically allocated.

2. Convert the gcd.c into a C++ program. You need to design a suitable class.

3. Convert testShape.cpp into a C program. You need to design suitable structs.

4. Write a C or C++ program to input a hexadecimal number from the command line and output the equivalent binary number to the standard output. Note that both upper case A~F and lower case a~f are allowed in the hexadecimal number. (Example: input 123 should output 100100011 because 12316=29110=1001000112 ; input a4B should output 101001001011 because a4B16=263510=1010010010112)

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#include <cstdlib>
#include <iostream>
using namespace std;

class calculation{
    int gcd(int x, int y){
       int t;
       int a = x;
       int b = y;

       while (b != 0) {
          t = b;
          b = a % b;
          a = t;
       return a;
    int lcm(int x, int y){
       int gcd = this->gcd(x, y);
       return x * y / gcd;
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