# Linear Algebra- Subspaces

1. Oct 3, 2008

### iwonde

1. The problem statement, all variables and given/known data
Let S be a nonempty set and F a field. Prove that for any s_0 $$\in$$ S, {f $$\in$$
K(S,F): f(s_0) = 0}, is a subspace of K(S,F).

K here is supposed to be a scripted F.

2. Relevant equations

3. The attempt at a solution
I don't know how to approach this problem. I know the three requirements that must be satisfied for a subset of a vector space to be defined as a subspace.

2. Oct 3, 2008

### sutupidmath

f i suppose is a function right?

3. Oct 3, 2008

### Dick

Good guess. iwond, can you define your terms? 'Scripted F' doesn't necessarily mean much to people that don't have the same text as you.

4. Oct 5, 2008

### HallsofIvy

I'm going to assume that K is the set of all functions, f, such that f(s0)= 0 for a fixed point s0.

Iwonde, you say, " I know the three requirements that must be satisfied for a subset of a vector space to be defined as a subspace." Okay, what are those requirements? Are they satisified by this set?