### Supplemental Material

- Handout from 10/10/06
- Some random thoughts on nullspace, columnspace, subspaces, bases and dimension. More philosophical than mathematical. Mainly provides a context for these ideas.
- A few solutions
- There are some solutions to two of the problems I stated/handed out on the week of 10/09/06.
- Halloween Fake Test (solutions)
- This 'test' is really just a handful of problems to get your brain to make some connections between new concepts and old concepts. This is far more theoretical than you should expect to see on your next midterm.
- Why are vectors in different eigenspaces independent?
- Here's a proof for why vectors in different eigenspaces are linearly independent. This proof is kind of tricky, so don't freak out if it seems complicated. I've only written it out for those people who have a burning desire for the truth!