# Thread: Vector space basic proof

1. ## Vector space basic proof

Hi everyone,

how can I show that:

1. F=C,V ={f∈C[t]|f(0)∈R},
2. F=R,V ={f∈C[t]|f(0)∈R}.

are or aren't vectorial spaces? I know the 8 axioms that I'm supposed to use to show it but I don't see how I can use them here.

2. Originally Posted by sunmalus
Hi everyone,

how can I show that:

1. F=C,V ={f∈C[t]|f(0)∈R},
2. F=R,V ={f∈C[t]|f(0)∈R}.

are or aren't vectorial spaces? I know the 8 axioms that I'm supposed to use to show it but I don't see how I can use them here.

Assume $a=f(0)$ such that $f \in V$, does $ia \in \mathbb{R}$? where $i= \sqrt {-1} \in \mathbb{C}$