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# CMPSC 122.2 Homework 1 Solution

1.   (60 points)   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.

For example, consider A, which is the following 2 x 4 matrix:

𝟓 𝟏 𝟐 𝟑
[                          ]

𝟑 𝟒 𝟒 𝟏

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 o This should be a 2D array that is implemented dynamically

•       Contains five public functions o add function, that adds two same sized matrices together and returns a new matrix with the result

o   subtract function, that subtracts two same sized matrices together and returns a new matrix with the result

o   multiply function, that performs proper matrix multiplication and returns a new matrix with the result

o   scalar function, that performs scalar multiplication with an integer value and a

matrix, and returns a new matrix with the result

o   print function, that outputs the contents of the matrix in tabular form that matches the dimensions of the matrix

•       Contains a non-default constructor o Constructor that accepts size information, and dynamically creates the matrix

•       Contains a destructor o 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

•       Each calculation should be printed with a full explanation o The calculation being performed should be explained, the contents of each matrix or value involved should be printed and identified.

2.   (40 points)   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 o int * Matrix

Matrix * int

•       Each calculation should be printed with a full explanation

o 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.