This lab test is to be completed without any outside assistance, talking
or looking at other people's work. Identify which room column number you 
are working from using the key on the board, or from here:
   computer centre desk ...  1 2 3 1 2 3 2 1 3 wall corridor

You can add comments to your worksheet answers if necessary using
> #  the answer is ... because
if any of your lines needs further explanation.
Try to work sequentially, making sure your commands give the shown
responses 

When you have finished the test, save a copy to your H: drive and then
email me your worksheet to james_preen@capebretonu.ca


Q1: Given

> A:=Matrix([[20, 15, -9], [-40, -17, -60], [-2, -8, 23]]);

Use Maple to find all of the eigenvalues of A by factoring a particular
determinant (but not using row/column operations) and choose the one, mu, 
based on your column number.
Find its eigenvector v by reducing the appropriate matrix to row echelon form 
and verify that the eigenvector equation A v = mu v holds.


Q2: Define
> F:=Matrix([[2, -2, -1, 1], [1, 1, -2, 1], [2, 0, 0, 2], [2, 1, -2, -y]]);
and then set F[2,2]:=x if your column number is 1, F[2,3]:=x if your 
column number is 2 and F[3,3]:=x if your column number is 3.

Using determinant row and column operations create a row or column with
only 1 non-zero element and then use the new commands DeleteRow and 
DeleteColumn to produce the 3 by 3 matrix that would be produced by a 
Laplace Expansion. Repeat this to get a 2 by 2 matrix, then take the 
determinant of this one and verify how it is related to Determinant(F)

Using this expression, find which value of x will give a non-singular 
matrix for any given y.

Q3: Given that a[n+1] = 2a[n] +3a[n-1] and that a[0]=5 and a[1]= your column 
number, use any Maple commands you like to diagonalise the underlying matrix 
and hence find the general formula for a[k]