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Prove that α+β is linearly independent.

  1. Oct 8, 2011 #1
    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.
     
  2. jcsd
  3. Oct 8, 2011 #2

    LCKurtz

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    What have you tried?
     
  4. Oct 8, 2011 #3
    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.
     
  5. Oct 8, 2011 #4

    LCKurtz

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    So what happens if you have xδ+yη+zρ = 0? (Although why introduce new letters?)
     
  6. Oct 8, 2011 #5
    Ok, I think I know how to solve it.
     
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