[tmoertel]

In that case, pick up a good book on linear algebra. Gilbert Strang's Introduction to Linear Algebra is inexpensive and solid on the fundamentals, and there are related lectures from Strang's MIT course on the subject [1]. Jim Hefferon's Linear Algebra is also good and you can download it for free (GFDL) [2]. It takes a different approach to Strang's book. The two work well together for self-study since for most subjects you can see two different approaches.

Also, for this particular problem, see the "Topic: Linear Recurrences" chapter of Hefferon's book. It actually uses the Fibonacci series as its example (this example seems popular with authors of textbooks and lecture notes).

[1] http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...

[2] http://joshua.smcvt.edu/linearalgebra/