 ## Matrix Class

A matrix is rectangular array of items laid out in rows and columns. The dimensions, or size, of a matrix can be expressed as m x n or m-by-n, where m is the number of rows in the matrix and n is the number of columns in the matrix.

The individual elements in A can be expressed as ai,j, where i (the row) is a number from 1 to m and j (the column) is a number from 1 to n. For example, the value at element a1,3 is 2.

Write a program (called matrix.cpp) that does that following:

1. Implement a class called Matrix that:
• Contains private member fields for the number rows and columns of the matrix
• Contains a public member field to contain the matrix elements
• This should be a 2D array of integers that is implemented dynamically
• Contains five public functions
• add function, that adds two same sized matrices together and returns a new matrix with the result
• subtract function, that subtracts two same sized matrices together and returns a new matrix with the result
• multiply function, that performs proper matrix multiplication and returns a new matrix with the result
• scalar function, that performs scalar multiplication with an integer value and a matrix, and returns a new matrix with the result
• print function, that outputs the contents of the matrix in tabular form that matches the dimensions of the matrix
• Contains a non-default constructor
• Constructor that accepts size information, and dynamically creates the matrix
• Contains a destructor
• That properly handles discarding the dynamically created 2D array (using delete and setting the member field to null
2. Prompts the user for:

• The dimensions of a first matrix
• The contents of the first matrix, which is then filled into the newly created matrix object instance.
• The dimensions of a second matrix
• The contents of the second matrix, which is used to fill the newly created matrix instance
Sample prompts with appropriate user responses:

Number of Rows in Matrix 1: 5
Number of Columns in Matrix 1: 2
Values of Matrix 1 (expecting 10): 6 7 10 3 5 31 0 9 2
Note: You must use the above format for entering the values of the matrix.
When entering values to fill a matrix, all values should be provided on one line.

3. Performs the following calculations and prints each result using the print function
• Each of the four matrix mathematical methods should be called, each result stored in a new object
• If the dimensions of the two matrices involved do not allow for the operation to be performed, skip performing this calculation, and display a message stating that step has been skipped.
• For example, if I have a 3x4 matrix and a 4x2 matrix, I cannot add or subtract these together, but I can perform multiplication
• Each calculation should be printed with a full explanation
• For scalar multiplication, you can either use an integer literal or generate a random integer. Just be sure to print the value of the integer value as part of the output when performing this function.
• The calculation being performed should be explained; and the contents of each matrix or value involved should be printed and identified.

## Matrix Class with Overloaded Operators

Using the class from the first portion of the assignment, write a program (called matrix_ops.cpp) that does the following:

1. Overloads the following operators using friend:
• `+` Replicate the functionality of the add function from matrix.cpp
• `-` Replicate the functionality of the subtraction function from matrix.cpp
• `*` Overload this to replicate the functionality of both the matrix multiplication and scalar multiplication functions from matrix.cpp. This operator should be overloaded a total of 3 times.
• `<<` Replicate the functionality of the print function from matrix.cpp
Used in the following way: `cout << matrix_instance1`;
• `>>` Used as the only way to fill in a matrix with values. Used in the following way: `cin >> matrix_instance1`;
2. Remove the five public functions of the Matrix class, and use only overloaded operators to perform the same functionality/output as in the matrix.cpp
3. Performs the following calculations and prints each result using the overloaded `>>` operator
• Each of the four matrix mathematical methods should be called, each result stored in a new object. Be sure you invoke scalar multiplication once for each overloaded operator
• int * Matrix
• Matrix * int
• If the dimensions of the two matrices involved do not allow for the operation to be performed, skip performing this calculation, and display a message stating that step has been skipped.
• For example, if I have a 3x4 matrix and a 4x2 matrix, I cannot add or subtract these together, but I can perform multiplication
• Each calculation should be printed with a full explanation
• For scalar multiplication, you can either use an integer literal or generate a random integer. Just be sure to print the value of the integer value as part of the output when performing this function.
• The calculation being performed should be explained; the contents of each matrix or value involved should be printed and identified.

## Compiling the Program

Use the following command to compile your classes:

``````g++ -Wall -o <output_name> <program_name.cpp>
``````

Example:

``````g++ -Wall -o matrix matrix.cpp
``````

Remember: Your code must successfully compile without any warnings or errors, or a zero will be given for the assignment.

## Submission

• Electronic Submission
• Your two source code files (matrix.cpp, matrix_ops.cpp)
• Zip file of source code (can include optional README file to demonstrate how to run your program) submitted via CANVAS drop box by close of assignment