Start Maple from Start Menu/Program Files/ or using the icon
in f:\math115

You can keep this text file open and use copy and paste to get the commands
to the Maple worksheet (don't include the >, that is already there)

Every Maple command must end with a semi-colon ";" for instance
>   8+5;

We can use ":=" to assign a value to a name, usually a letter
>   a:=3;

Set b to have any value between 1 and 9 and determine the values of 
a+b, 2*b 4*a-b, a*b and a^b.

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
>    A:=Matrix([[1,-1,2],[3,0,1]]);

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

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

Next we create a random matrix B, with integer entries between -4 and +5
>    B:=RandomMatrix(2,3,generator=rand(-4..5));
Note that it is "pseudo random" so you may get the same as your neighbour.
the 2 and 3 are the sizes of the matrix, the -4 is the lowest possible integer
allowed and 5 is the highest possible.

If you want to know more about a Maple command, type ? and the command e.g.:
>    ?RandomMatrix
to exit from the help page, close the subwindow, or use the 
Window menu to move between them.

As A and B are the same size we can add these matrices together using + 
>    C:=A+B;

D is a letter which is reserved for differentiation so we can't use it or
I which is the square root of minus one. We can use AA or D1 if we want 
although it is usually just simpler to keep single letters.

Define 
>    E:=RandomMatrix(2,2,generator=rand(0..3));
and note the error given when you try to add E to B, it isn't very informative.

Evaluate the scalar multiple
    F:=-1*A;
Check that you get the all zero matrix when you add F to A.

We can, of course, multiply matrices, the command is "Multiply".
Try multiplying E and A, and A and E, and note the error given is better. 
Define
>    G:=RandomMatrix(2,2,generator=rand(-2..2));
and check that when you multiply G and E you will probably get a different 
answer depending on which order you multiply them in.

Define
> K:=Matrix([[-1, 5, 2], [-4, 2, -4], [1, 1, 2]]);

We can augment a column to our matrix K (but not make a dotted 
line unfortunately) using this command:
> K0:=< K | Matrix(3,1,[-1,-4,1]) >;

We can do the three different row operations as follows:
> K1:=RowOperation(K0,[1,3]);
will swap row 1 and row 3 of K and make it into a new matrix K1.
> K2:=RowOperation(K1,2,1/2);
will take this new K1 and multiply row 2 by 1/2 and make K2
> K3:=RowOperation(K2,[2,1],3);
will replace row 2 of K2 by itself plus 3 times row 1 to make K3

Note that this last operation will not give you the desired 0 in row 2
of column 1, so change this line to do so, then continue to reduce your 
matrix to have as many zeros as you can force. We will explore the 
most efficient ways to do this in class.

Check your answer with
> ReducedRowEchelonForm(K0);

Create, using Maple, a random 3x3 matrix J with integers between 1 and 9
and use RowOperation to get J0:=<J | Matrix(3,1,[3,-2,4])>; to RREF 

Check your answer by multiplying your final solution by J using the command
Multiply.