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:=10;

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
>    ?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.

Check that C1:=B+A is the same as C and find E which is 3 times B 
minus 2 times A. Check that E+2*C is the expected matrix.

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

We can take the transpose of any matrix with "Transpose" (capital T).

Try 
>  Transpose(B);
and see that the same numbers show up, just that rows 
become columns and vice versa

Check that Transpose(C) = Transpose(A) + Transpose(B)

We can, of course, multiply matrices, the command is "Multiply".
Try multiplying A and B and note the error given. 

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 | Vector([-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 K
to reduced row echelon form.

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 | Vector([3,-2,4])>; to RREF 

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