Using the diagram on the board, identify which Matrix you will be using.
All students in every row and column will have a different 
(but equally hard) matrix to answer the questions on.

Students in the A position:
A := Matrix([[5, 0, -3], [6, 11, -12], [8, 12, -14]]);
Students in the B position:
B := Matrix([[5, 2, -5], [6, 3, -7], [6, 2, -6]]);
Students in the C position:
C := Matrix([[12, 2, 9], [2, 0, 3], [-14, -2, -11]]);
Students in the D position:
D := Matrix([[-3, 7, -2], [-6, 10, -2], [-10, 13, -1]]);

Do not look at the work other students are doing or talk with them.
 
Unless otherwise specified, you can use any known command to answer.
You can check your answers after completion with any commands.

To write comments in your worksheet use the # symbol, do this to put 
your name and registration number at the top of your worksheet:
> # James Preen  26262626
Use
> #  the answer is ... because
if any of your lines needs further explanation. Try to work sequentially, 
making sure your commands give the shown responses, do not erase or correct 
lines, just redo your calculation on the next line if you get an error.

Save your work in your H:\ directory with your name somewhere in the filename
and then please email the file to me at james_preen@cbu.ca
Once I have confirmed receipt of the file you are free to leave.

Q1:
Find two different eigenvectors of your matrix by solving homogeneous 
systems of equations and check that they multiply with your matrix correctly.


Q2:
Find the inverse of your matrix using augmentation and RowOperation.


Q3:
Use Maple to automatically create a random 4x4 matrix E with entries 
between 1 and 5, then change the values of two of the entries to letters:
> E[3,2]:=x; E[1,4]:=y;

Find and check the value of y which guarantees that E is non-singular.

Create a matrix which has an x and a y in different positions but 
which is never singular and is different from everyone else's in the room.