# Linear Algebra- Subspaces

## Homework Statement

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.

## 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.

## Homework Statement

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.

## 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.

f i suppose is a function right?

Dick
Homework Helper
f i suppose is a function right?

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.

HallsofIvy