- Thread starter
- #1

- Feb 5, 2012

- 1,621

Here's a problem that I need some help to continue. I would greatly appreciate if anybody could give me some hints as to how to solve this problem.

**Problem:**

Let \(f:V\rightarrow F\) be a linear function, \(f\neq 0\), on a vector space \(V\) over a field \(F\). Set \(U=\mbox{Ker } f\). Prove the following.

a) \(U\) is a maximal subspace, that is, not contained properly in any subspace, different from \(V\).

b) \(V=U\oplus<a>\), for any \(a\not\in U\).