CS99 Fall 2002
Lab #10 (11/12/02)
Due 11/15 at noon.

Objective:
In Lab10, you will practice writing Function M-files.

Background:
Suppose that A and B are two matrices, as follows:

  A = [ 1 2 3 ; 4 5 6 ]

  B = [ 2 3 4 ; 3 4 5 ]

You can perform arithmetic on matrices. For instance, MATLAB has the following
two operations:

 * matrix addition: A+B, if A and B have the same size
 * element-by-element multiplication: A.*B
   Note that A*B is different from A.*B


Explanation of Matrix addition/multiplication:
Let X,Y be two matrices of the same size. Let Z=X+Y. Then Z is the matrix of 
the same size as X and Y such that each of its entry is the summation of 
the corresponding entries of X and Y. e.g., the second row and third column
of Z is the summation of the second row and the third column of X and 
the second row and the third column of Y. Similarly, W=X.*Y is the matrix
of the same size as X and Y such that each of its entry is the product of
the corresponding entries of X and Y.


Example:
For the given matrices A and B above, determine A+B and A.*B by hand. You can
easily check your work with MATLAB, of course:

Answer:

        +---------------+   +-----------+
        | 1+2  2+3  3+4 |   |  3  5   7 |
A + B = |               | = |           |
        | 4+3  5+4  6+5 |   |  7  9  11 |
        +---------------+   +-----------+

        +---------------+   +------------+
        | 1*2  2*3  3*4 |   |  2   6  12 |
A.*B  = |               | = |            |
        | 4*3  5*4  6*5 |   | 12  20  30 |
        +---------------+   +------------+

Functions:                         
Suppose that you didn't know or couldn't use MATLAB syntax, as in many other
languages. Write a script file lab9_sol.m to solve A+B and A.*B. In this
script file, two function files add.m and mul.m are called to perform matrix
addition and matrix element-by-element multiplication, respectively.

  lab9_sol.m:
 +-------------------+
 | A=[1 2 3; 4 5 6]  |
 | B=[2 3 4; 3 4 5]  |
 | C=add(A,B)        |
 | D=mul(A,B)        |
 +-------------------+

You need to write add.m and mul.m that will be called by lab9_sol.m.