550.291 (LADE) FREQUENTLY ASKED QUESTIONS FOR HOMEWORK 9

PROBLEM 6 (7.5.15): I am having trouble finding a generalized eigenvector
using the method presented in class.

ANSWER:  In class we discussed what happens when the eigenvalue has defect
1 and provided an example when the algebraic multiplicity of said eigenvalue
is 2.  In problem 7.5.15, the issue is that the eigenvalue has defect 3 so
the method presented in class won't always work (as exhibited by this
problem.)

There are a couple of ways to handle the issue.  The first is to use the
method presented in Example 7.5.4.  Alternatively, you can pick any
regular eigenvector w of A so that 

                    rank(A - lambda*I) = rank([A - lambda*I|w])

then use the method from class.  Notice that w = (-3, 1, 1)
is one such regular eigenvector (why?)

PROBLEM 7 (7.5.37): Do we have to find Q inverse by hand?

ANSWER: No.  Feel free to use MATLAB, Excel, or any other method.