# Prove that α+β is linearly independent.

by krozer
Tags: linear algebra, vectors
 P: 13 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.
 HW Helper Thanks PF Gold P: 7,666 What have you tried?
P: 13
 Quote by LCKurtz What have you tried?
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.

HW Helper
Thanks
PF Gold
P: 7,666
Prove that α+β is linearly independent.

 Quote by 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?.
So what happens if you have xδ+yη+zρ = 0? (Although why introduce new letters?)
P: 13
 Quote by LCKurtz So what happens if you have xδ+yη+zρ = 0? (Although why introduce new letters?)
Ok, I think I know how to solve it.

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