Due Wednesday, September 25, in class

Section 1.7 problems 1, 3*, 5, 6
Section 2.1 problems 1, 5, 6, 10, 14, 35

and

A. Use Theorem 2.6 to prove this problem. If \(V\) is a finite dimensional vector space over \(F\) of dimension \(n\), then there is a one-to-one and onto linear transformation \(T:\ V \to F^n\).

* Hint to the book’s hint (or simply a hint on its own): The idea is to find an infinite set that is linearly independent. Then carefully argue why an infinite linearly independent set implies \(V\) is infinite dimensional. There are such linearly independent sets that do not use the transcendence of \(\pi\), if you don’t want to follow the book’s hint.