# Math Help - Subspaces

1. ## Subspaces

Consider the vector space $\mathcal{F} = \lbrace f : \mathbb{R} \to \mathbb{R} \rbrace$.

(a) Let

$\mathcal{U} = \lbrace f : \mathbb{R} \to \mathbb{R} : f(3) = 0 \rbrace$

Prove true or show to be false: $\mathcal{U}$ is a subspace of $\mathcal{F}$.

(b) Let

$\mathcal{V} = \lbrace f : \mathbb{R} \to \mathbb{R} : f(3) = 3 \rbrace$

Prove true or show to be false: $\mathcal{V}$ is a subspace of $\mathcal{F}$.

2. I don't really know how to begin this problem. If someone could tell me how to start it I'm sure I'd be able to figure it out...

3. Remember that a vector space must contain the zero vector. In F, the zero vector is f(x)=0. Thus, V can't be a subspace since it doesn't contain the zero vector.