June 8, 2013
Here are solutions to the two proof questions I gave you in class yesterday. The first one is much harder than I thought it was when I wrote the question. I strongly recommend ignoring it completely, since it won't really help you prepare for the midterm, but I've included a solution just in case you're interested.
June 7, 2013
Here are solutions to the problems we did in class today. The person who wrote these solutions emphasized some things in his class that I didn't (in particular, the method of finding an algebraic specification for the range of a matrix, given in Example 4 on p. 182 of the textbook). Some of the solutions might seem weird to you as a result. Don't be discouraged by that.
I'll post solutions for the proofs tomorrow. Good luck studying and email me if you have questions.
June 7, 2013
To study for the final, I recommend you do the following problems:
| Section | Problems |
|---|---|
| 4.7: | #2, 3, 7 |
| 4.8: | #7, 8, 9 |
For 4.8 #7, 8, 9, use the matrices and vectors they give, but let me rephrase the question: Write A as A = SDS-1. Then use this to find a formula for Akx0 in terms of S and D. In each case, what happens to Akx0 as k goes to infinity?
June 6, 2013
Solutions to the last group assignment are now available. The solutions include a totally awesome example of a 4 by 4 matrix whose square is the zero matrix.
May 24, 2013
Here's the last group assignment! It's due on June 5th, and it's a little bit longer than usual.