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([[-5,-2,1],[3,1,-2]]);
It gives the matrix in terms of its rows.

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.

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

We can do the three different row operations as follows:
> A1:=RowOperation(A,[1,2]);
will swap row 1 and row 2 of A and make it into a new matrix A1.
> A2:=RowOperation(A1,2,-1);
would take this new A1 and multiply row 2 by -1 and make A2 
> A3:=RowOperation(A2,[2,1],-3);
will replace row 2 of A2 by itself minus 3 times row 1 to make A3

Note that this last operation will not give you the desired 0 in row 2
of column 2, so change this operation to make an A4 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 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 numbers of rows and columns of the matrix, the -4 
is the lowest possible integer allowed and 5 is the highest possible.

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 the "|" operator:
> K0:=< K | Matrix(3,1,[-1,-4,1]) >;

Use row operations to get 
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