### Eigenvector hw

- Review the Healthy Sick worker problem from Problem Set 3 (solutions are
on ASULearn, for example).

- Summarize in your own words how we calculated the steady state
vector on that problem set.

- Read through the following definition:

**Definitions**
If a square matrix N, a column vector x, and a real number lambda
satisfy the equation
N x=lambda x [which is equivalent to (N- lambda I) x = 0], then
x is an *eigenvector* and lambda is an *eigenvalue*.

- Rewrite the definition when lambda = 1, ie substitute 1 for every place
you see lambda, and write this out.

- Apply the language of eigenvectors to the
computational work we have already completed in problem set 3.
In this problem, lambda = 1, and we have already
solved for (N-I)x=0 [ie Nx=1x]. So write down
the eigenvector here, which is the steady state vector you found on the
problem set.

- In general, using material from 4.1,
how does scalar multiplication

lambda x

relate to

x

geometrically and algebraically
[again x is a column vector, say in the plane, and lambda is a real number].

- Read through the Final Research Sessions
for Dec 12th, and write down any questions you have.