Using this diagram, identify which Matrix you will be using: (1 mark)

 E F D C              A B E F
 =======              =======      
 C A B E              F D C A
                                         
 F D E B              C A F D     
 =======              =======
 B C A F              D E B C
                     
 D E F A              B C D E
 =======              =======      
 A B C D              E F A B      
B182 entrance     B184

All students in every row and column will have a different 
matrix to answer the questions on.

Students in the A position:
M := Matrix([[3, 1, -2], [-3, 4, 3], [4, 5, -2]]);
Students in the B position:
M := Matrix([[-3, -5, 1], [1, 5, 2], [1, -2, -3]]);
Students in the C position:
M := Matrix([[-1, -4, 2], [2, -4, 3], [5, 1, 1]]);
Students in the D position:
M := Matrix([[-3, 2, 4], [-5, 2, 3], [-5, -1, -5]]);
Students in the E position:
M := Matrix([[-3, -2, -2], [-4, -5, 3], [0, -2, 5]]);
Students in the F position:
M := Matrix([[-4, 3, 3], [0, 3, -4], [-5, 5, 2]]);


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.

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.

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  20132613

Use
> #  the answer is ... because
if any of your lines need further explanation. 

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
I recommend that you save regularly in case your computer crashes
Once I have confirmed receipt of the file you are free to leave.

Start your session by loading the LinearAlgebra package as usual.

Q1: (11 marks)
Augment the identity matrix and use RowOperations on that matrix 
without introducing fractions to find the inverse of M.

What do you believe the largest number could be in the adjoint of a 
3 by 3 matrix which has all of its entries with absolute value less 
than 6? Give an example of such a matrix that you believe nobody 
else will choose (marks will be shared for duplicated matrices).

Q2: (8 marks)
Create a matrix A using diagonalisation; M's columns should be A's 
eigenvectors and let the eigenvalues be 7, -2 and 7.

Solve the eigenvector equation for eigenvalue 7 of A using LinearSolve
and check that both your eigenvectors Multiply with A as they should.

Verify that your set of solutions are equivalent to the columns of M,
explaining their relation.