Start Maple and load the LinearAlgebra package as usual.

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

Students in the 1 position:
> E:=Matrix([[4, -5, -4], [1, 2, 2], [-5, -2, -2]]);
Students in the 2 position:
> E:=Matrix([[-2, 1, -1], [-4, 0, -5], [-3, 4, 3]]);
Students in the 3 position:
> E:=Matrix([[-4, 1, -1], [-1, 5, 4], [5, -4, -1]]);
Students in the 4 position:
> E:=Matrix([[4, -2, 2], [3, -3, -5], [3, -2, 1]]);

Unless otherwise specified, you can use any known command to answer.
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

Q1:
Find the inverse of your matrix E using Row Operations and
check your answer by multiplying.

Q2:
Get the cubic polynomial which could be used to find the eigenvalues.
Do NOT attempt to factor it, instead identify the coefficients a, b and c
such that:    lambda^3 + a*lambda^2 + b*lambda = c
Evaluate E^3 + a*E^2 + b*E and E^2 + a*E^1 + b*IdentityMatrix(3)
and make a short note of how they are related to E.

Q3:
Find the value of x which makes your matrix singular if 
> E[3,1]:=x;

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.