Start Maple 16 from the icon on the desktop Start Menu/Program Files/ 
or using the icon in f:\math 1204. Some windows may open, authorise them.

Every Maple command must end with a semi-colon ";" for instance
>   1+3;
Every time I give you a command to use I will give the > symbol.
You are free to copy from this file and paste into Maple, this
will ensure you don't make a mistake when typing it in.

We can use ":=" to assign a value to a name, usually a letter
>   a := 7;
This is case sensitive, so we can set 
>   A := 4;
For an unknown variable, Maple will just report that name:
> a+b;

Now set b to be some randomly chosen value and use Maple to 
determine the values of these expressions.
> 3*a-b ;
> 3*A-b;
> 3*(a-A);
> 3*a - A;
> 3*A/13;
> (b-a)^2;

Notice that Maple 
does not use decimals by default, and neither will I, in class.

Maple does not change the a+b line unless you
ask it again to evaluate a+b. Maple just answers questions sequentially,
and so I encourage you to work down the worksheet without editing earlier
lines so that the confusion is lessened. 

You can go back up the worksheet 
and insert new lines if necessary using control-j or control-k.
You can reset a variable's value to unknown using 
> a:='a';

Do this and verify that a+b is now what you would expect it to be.

 In the other labs I will use capital letters for matrices 
and lower case letters for numbers, but it isn't mandatory.

When I introduce a function it is a good idea to read the help page
for that function. You can do that for the function sqrt by 
visiting 
  http://www.maplesoft.com/support/help/Maple/view.aspx?path=sqrt
and can search for any other function in that webpage too.

We can use the command evalf to find the decimal value of a number.
If you want to know more about a Maple command, type
>    ?evalf
to exit from the help page, close the subwindow, or use the 
Window menu to move between them.

Use the function sqrt to determine the square roots of A and 3.
Notice that, similarly to fractions, square roots are left as is too.

Use evalf to find the 12th decimal place in the square root 
of 3 and the 100th digit of Pi (note Pi, not PI or pi, both of which
are greek letters, not the circle constant), being careful to
avoid rounding errors and picking the correct digit.

Set lambda (a lower case greek letter) equal to Pi+Pi/2 and find 
sin(lambda) and the square root of the sine of lambda too.
I is a reserved letter in Maple, and so is D and some other ones.


We are now ready to do some matrix algebra...
Load all of the linear algebra progams with the command:
>    with(LinearAlgebra);

All the new commands listed are now known by Maple, we will use some.

We can create a 2x3 matrix by using the following command
>    B:=Matrix([[-5,2,1],[3,-1,-2]]);
It gives the matrix in terms of its rows. Even though we are using this
to represent a system of equations Maple doesn't give a dotted line,
but we should try to remember it is there.

Notice that we again use ":=" to assign a value to B. I recommend using
a capital letter for all matrices, but Maple will not insist on that. 
Recall that Maple is case sensitive, so B is different from b.

Note that all of the LinearAlgebra commands also begin with a capital 
letter, although "matrix" is also defined, it will not always work properly.

We can do the three different row operations as follows:
> B1:=RowOperation(B,[1,2]);
will swap row 1 and row 2 of B and make it into a new matrix B1.
> B2:=RowOperation(B1,2,-1);
would take this new B1 and multiply row 2 by -1 and make B2 
> B3:=RowOperation(B2,[2,1],-3);
will replace row 2 of B2 by itself minus 3 times row 1 to make B3

I recommend using this scheme of naming each matrix sequentially, and
try to not reuse any name, if you don't get the matrix you wanted, just
use the next Bnumber matrix with the previous one.

Note that this last operation will not give you the desired 0 in row 2
of column 2, so change this operation to make a B4 with a 0 there, then 
continue to reduce your matrix to have two zeros on the left hand side.

Next we create a random matrix C, with integer entries between -6 and +5

>    Seed:=randomize(): C:=RandomMatrix(2,3,generator=rand(-6..5));

The 2 and 3 are the numbers of rows and columns of the matrix, the -6 
is the lowest possible integer allowed and 5 is the highest possible.

Use RowOperation to produce as many zeros as possible from C and check
your final answer with
> ReducedRowEchelonForm(C);

Try a different set of row operations and see that you get the same 
solution however you try.

Try to choose a matrix which starts with numbers different from 0 or 1
but which cannot end up with a 1 and a 0 in each row no matter which
row operations you choose.

Once you are completed, call me over and I'll make sure you've 
got all of your answers correct. You can save your work in your H:
drive and it will be available for you to consult in future labs.