## Yet More Solutions

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.

## More Solutions

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.

## Suggested Problems

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
*A*^{k}x_{0} in terms of *S* and *D*.
In each case, what happens to *A*^{k}x_{0} as *k* goes to infinity?

## Solutions

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.

## Group Homework #6

May 24, 2013

Here's the last group assignment! It's due on
June 5th, and it's a little bit longer than usual.