Question

C++ must use header files and implementation files as separate files. I’ll need a header file,
implementation file and the main program file at a minimum. Compress these files into one
compressed file.

Make sure you have adequate documentation.

We like to manipulate some matrix operations. Design and implement a class named
matrixMagic that can store a matrix of any size.

1. Overload the addition, subtraction, and multiplication operations.

2. Overload the extraction (>>) and insertion (<<) operators to read in the matrix
and to display its output.

3. Your class must have private attributes such as: int **matrix; and variables for
the number of rows and number of columns of the matrix.

4. Addition and subtraction: You can only add 2 matrices of the same size. For
example, the first matrix can have 3 rows and 3 columns and the second matric
could have 3 rows and 2 columns. We cannot add or subtract matrixes of different
size. Check this constraint before performing addition and subtraction of
matrices.

5. Multiplication: If the size of the first matrix is m X n (m is the number of rows
and n is the number of columns) and the size of the second matrix is n X t (n is the
number of rows and t is the number of columns), matrix multiplication only works
if the number of columns in the first matrix (n) is the same as the number of rows
in the second matrix (n). For example, we can multiply a 2 x 3 and a 3 x 4 matrix,
but not a 2 x 3 and 4 x 2 matrix. Check this constraint before performing
multiplication of matrices.

6. Use a continuous menu to allow the user for selecting the desired operation. Ask
the user for the entries in the matrix and display the output.

NOTE: The purpose of this exercise is to practice with overloading of operators. The
actual computation of matrices should be trivial.
Start with one operation at a time. Do not try to build the entire program before
running and testing individual pieces. For example, overload the input operator to read a
matrix and test it. Then, overload the output operator and test it. And, then move on to
matrix operations starting with the simple addition and subtraction, before moving to the
matrix multiplication operation.
If matrix 1 contains:
1 3
2 5
And matrix 2 contains:
4 3
6 -1
Then, the result will be:
M1 + M2 =
5 6
8 4
M1 - M2 =
-3 0
-4 6
M1 * M2 =
22 0
38 1
You can use the above matrices to test your code.
Here is a possible sample run:
Enter data for this matrix:
1 3
2 5
Enter data for this matrix:
4 3
6 -1

Here is what you entered:
Matrix 1:
1 3
2 5
Matrix 2:
4 3
6 -1
Adding matrices
5 6
8 4
Subtracting matrices
-3 0
-4 6
multiplying matrices
22 0
38 1
Matrix multiplication: Here is how we get the 22 in row 0, columns 0
1*4 + 3*6 = 22 1*3+3*(-1) = 0
2*4+5*6 = 38 2*3+5*(-1) = 1
The first row of the first matrix is multiplied by the first column of the second matrix and
added together, to give you the first element of the new matrix, etc.
As you see, you need to create a running total for the inner loop. To get the 22, you’ll
have the total of m1[0][0]*m2[0][0]+m1[0][1]*m2[1][0]

Answer 1

Code :

MagicMatrix.cpp :

#include "header.h"

class magicMatrix

{

int **matrix,nrows=MAX,ncolmns=MAX;

public:

magicMatrix()

{

matrix = new int *[nrows]; // Create a dynamicmatrix with maximum elements

for (int count = 0; count < nrows; count++)

matrix[count] = new int [ncolmns];

}

  

friend istream& operator >>(istream& din,magicMatrix &m);

friend ostream& operator <<(ostream& dout,magicMatrix& m);// display matrix

  

magicMatrix operator+(magicMatrix b)// sum

{

magicMatrix temp;

if((nrows!=b.nrows)||(ncolmns!=b.ncolmns)) //a.nrows!=b.nrows

{

cout<<"\n\tMatrix Addition is not possible the result is incorrect\n\n";

temp.nrows=0;

temp.ncolmns=0;

}

else

{

temp.nrows=nrows;

temp.ncolmns=ncolmns;

}

for(int i=0;i<nrows;i++)

for(int j=0;j<ncolmns;j++)

temp.matrix[i][j]=matrix[i][j]+b.matrix[i][j];

return temp;

}

magicMatrix operator-(magicMatrix b)// subtraction

{

magicMatrix temp;

if((nrows!=b.nrows)||(ncolmns!=b.ncolmns)) //a.nrows!=b.nrows

{

cout<<"\n\tMatrix Subtraction is not possible the result is incorrect\n\n";

temp.nrows=0;

temp.ncolmns=0;

}

else

{

temp.nrows=nrows;

temp.ncolmns=ncolmns;

}

for(int i=0;i<nrows;i++)

for(int j=0;j<ncolmns;j++)

temp.matrix[i][j]=matrix[i][j]-b.matrix[i][j];

return temp;

  

}

magicMatrix operator*(magicMatrix b)

{

magicMatrix r;

if((nrows!=b.ncolmns)||(ncolmns!=b.nrows))

{

cout<<"\n\tMatrix Multiplication is not possible the result is incorrect\n\n";

r.nrows=0;

r.ncolmns=0;

}

else

{

r.nrows=nrows;

r.ncolmns=b.ncolmns;

}

for(int i=0;i<nrows;i++)

for(int j=0;j<ncolmns;j++)

r.matrix[i][j]=0;

for(int i=0;i<nrows;i++)

for(int j=0;j<b.ncolmns;j++)

for(int k=0;(k<ncolmns)||(k<b.nrows);k++)

r.matrix[i][j]+=matrix[i][k]*b.matrix[k][j];

return r;  

}

  

};

istream& operator >>(istream& din,magicMatrix& m)

{

cout<<"Enter the size\n";

din>>m.nrows>>m.ncolmns;

m.matrix = new int *[m.nrows];

for (int count = 0; count < m.nrows; count++)

m.matrix[count] = new int [m.ncolmns];

cout<<"Enter the elements\n";

for(int i=0;i<m.nrows;i++)

for(int j=0;j<m.ncolmns;j++)

din>>m.matrix[i][j];

  

return din;

}

  

  

ostream& operator <<(ostream& dout,magicMatrix& m)

{

for(int i=0;i<m.nrows;i++)

{

for(int j=0;j<m.ncolmns;j++)

{

dout<<m.matrix[i][j]<<"\t";

}

dout<<endl;

}

return dout;

}

int main()

{

magicMatrix M1,M2,M3;

int temp=1;

cout<<"Matrix M1\n" ;

cin>>M1;

  

cout<<"\nMatrix M2\n";

cin>>M2;

cout<<"\n Matrix M1 is : \n";

cout<<M1<<endl;

cout<<"\n Matrix M2 is : \n";

cout<<M2<<endl;

M3=M1+M2;

cout<<"The Addition is:\n";

cout<<M3<<endl;

M3=M1-M2;

cout<<"The Subtraction is:\n";

cout<<M3<<endl;

M3=M1*M2;

cout<<"The Multiplication is:\n";

cout<<M3<<endl;

return 0;

}

header.h

#include<iostream>

using namespace std;

#define MAX 10

Output :