Prove that α+β is linearly independent.

krozer

1. The problem statement, all variables and given/known data

Let F be a subset of the complex numbers. Let V be a vector space over F, and suppose α, β and γ are linearly independent vectors in V. Prove that (α+β), (β+γ) and (γ+α) are linearly independent.

2. Relevant equations

None.

3. The attempt at a solution

None.

Thanks for your time.

LCKurtz

What have you tried?

krozer

Given that α,β,ɣ are linearly independent then, if we have that

xα+yβ+zɣ=0 then x=y=z=0

Sup α+β=δ, β+γ=η and γ+α=ρ
How do I prove δ ,η and ρ are linearly independent?. But answering your question I'm trying to prove it with the Ʃ(cδ)=0 for all c in R.

LCKurtz

So what happens if you have xδ+yη+zρ = 0? (Although why introduce new letters?)

krozer

Ok, I think I know how to solve it.