
#1
Oct811, 02:19 PM

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. 



#3
Oct811, 05:01 PM

P: 13

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. 



#4
Oct811, 05:09 PM

HW Helper
Thanks
PF Gold
P: 7,226

Prove that α+β is linearly independent. 



#5
Oct811, 06:11 PM

P: 13




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