Math 2406: Abstract Vector Spaces

Lecture 3 Plan  (Tuesday, August 28, 2007).

Apostol 1.13-1.16, 2.1-2.2.

Today we are going through some fairly complicated proofs. The goal is to be able to follow the logic from
one step to the next, and then to organize these steps in your mind and on paper. This will help us to understand the overall structure of the proof. Then we can use these strategies again in our own proofs.


Review questions:

1. Regarding the second equation on page 45 of Apostol, why is it written for i = 2 to k+1 only?
2. Why can we assume a_{11} is non-zero in the proof of Theorem 1.8?
3. How many times is proof by contradiction used in the proofs of Theorems 1.8, 1.9, 1.10?