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.
Please help.
You know that addition and multiplication of numbers (and the function values are numbers) are commutative, associative, etc. so all you need to determine is if addition and scalar multiplication are closed. That was the point of Jose27's post. For (1) f(0) must be real for all f in the set. But what happens if you multiply by i?