Brief Introduction to Matlab

Matlab is software package that is extremely useful in solving linear algebra problems.
It is quite easy to use and there is ample documentation.  A basic introduction is given
in the Appendix of Leon's book (6th edition, pg. 505).  There is also extensive online help
in the program in the Learning Matlab section of Matlab help.

To begin using Matlab on a PC, double-click on the Matlab icon.  Matlab will start 3 windows.
The window on the right is the command window where Matlab commands are entered and
executed.

Leon, pg 98, problem 2b:

First, the FLOPS command is no longer availabe so ignore any reference to it.  Below is
the result of rref command on a random 4x4 matrix A and corresponding vector b.  The 
commands are entered to right of >>   and the results appear below.

Matlab session:


>> A = rand(4,4)

A =

    0.0579    0.1389    0.2722    0.4451
    0.3529    0.2028    0.1988    0.9318
    0.8132    0.1987    0.0153    0.4660
    0.0099    0.6038    0.7468    0.4186

>> b = rand(4,1)

b =

    0.8462
    0.5252
    0.2026
    0.6721

>> Augm = [A,b]

Augm =

    0.0579    0.1389    0.2722    0.4451    0.8462
    0.3529    0.2028    0.1988    0.9318    0.5252
    0.8132    0.1987    0.0153    0.4660    0.2026
    0.0099    0.6038    0.7468    0.4186    0.6721

>> rref(Augm)

ans =

    1.0000         0         0         0    1.6172
         0    1.0000         0         0   -6.1557
         0         0    1.0000         0    5.8295
         0         0         0    1.0000    0.0469

>> sol = A\b

sol =

    1.6172
   -6.1557
    5.8295
    0.0469