First, log on to your account. If you are unable to do that, please get hold of me. On your first UNIX prompt type

% mkdir matlab (or whatever you wish to name this directory)

% cd matlab

Then type

% matlab

You should get a brief graphic display and then the prompt

>>

Type the command

>> A = randn(5,5)

This generates a random 5 by 5 matrix according to the normal distribution.

Open a second X-window and also type

% cd matlab

You will use this second X-window to download and use m-files.

In the matlab window type

>> Ainv=inv(A)

Type

>> I= eye(5,5)

What do inv and eye do? Use help command if this is not obvious.

Compute

>> R= I-Ainv*A

Is the answer what you expected? Now type

>> B=ones(5,5)

and type

>> inv(B)

Type

>> help sum

Use the sum function to sum all of the elements in A.

Type

>> ii=[1 4 5]
>> jj=[2 3 5]
>> C=A(ii,jj)

What did you just do? Do you now see how MATLAB indexes arrays? What is A(:,1: 3 ), A(2:4 ,:) and A(2 : 4, 1 :3 )?

Notice MATLAB automatically prints the results of any computation on the screen. Under some circumstances, that is not a good idea. If we type

>> ii=[1 4 5];
>> jj=[2 3 5];
>> C=A(ii,jj);

then MATLAB does its work ``silently.'' But everything is still there. Type

>> C

to display the answer.

Now a brief introduction to plotting.

Type

>> inc=pi/25
>> x=0:inc:2*pi
>> y=sin(x)
>> plot(x,y)

To label the graph type

>> title('Plot of sin x for one period')
>> xlabel('Domain - From zero to 2*pi')
>> ylabel('Range - From -1 to 1')

You can print the plot clicking on ``File'' and then on ``Print'' and then click on ``Print.'' DO NOT DO THIS NOW. For now, click ``Cancel.'' Print it at your convenience some other time. If you click on ``Save As..'' in the file menu, you can save the graph as .ps (PostScript) file which can be viewed with ghostview.

Type

>> diary
>> a=1
>> b=1e10
>> c=1
>> [x1,x2,ier]=quadroots0(a,b,c)
>> [y1,y2,ier]=quadroots(a,b,c)
>> z=roots([a b c])
>> diary off

In your other window, look in your diary file.

If you want to know what ``roots'' does, type ``help roots.''

Here are a couple of other functions that you will become familiar with.

Type

>> eps

This is the maximum relative spacing between two floating point numbers.

>> realmax

This the largest floating point number.

>> 2*realmax

Does this get what you expected?

>> x= realmin

This is the smallest ``useful'' floating point number. Now try

>> x/2, x*x

Explain this result.

Next we have two functions that you will learn more about this semester, lu and qr.

>> A=ones(5,5)+sqrt(eps)*rand(5,5)

This will yield a mildly ill-conditioned matrix, close to singular, but we can work with it.

>> b=[1:5]'

Don't forget the transpose. We are going to solve A x = b three different ways.

>> format short e

The e format tells us more of what we need to know. (You might try  >> help format at this point.)

>> x1=A\b

This asks MATLAB to solve it for you.(A\b stands for  A^(-1) *b), allowing you to bypass Chapter  Four.

Here are the main steps   MATLAB uses to solve the problem.

>> [L,U]=lu(A)

This is the LU decomposition from Chapter Six. L is a row permutation of a lower triangular matrix, U is an upper triangular matrix. The solve requires two more steps. The matrix A satisfies A = L*U. Then, A^(-1) =U^(-1) * L^(-1).

>> y2=L\b
>> x2= U\y2
After this, type

>> demo

and choose whichever demo you wish.