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Basic linear algebra proof

  1. Mar 3, 2013 #1
    1. The problem statement, all variables and given/known data
    This should be an easy one, I'm just making sure that I'm not screwing up horribly.

    Prove that if v is in span(v1,v2, ..., vN), then v, v1, v2, ..., vN are linearly dependent.


    2. Relevant equations
    span(v1,v2, ..., vN) = {Ʃaivi}.


    3. The attempt at a solution
    If v is in span(v1,v2, ..., vN), then for some scalars a1, ..., aN, v = Ʃaivi. This means that 0 = Ʃaivi - v, which means that there exists a set of scalars, not all 0, that satisfy the homogeneous equation. This is because the scalar coefficient of v is -1.
     
    Last edited: Mar 3, 2013
  2. jcsd
  3. Mar 3, 2013 #2

    LCKurtz

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    You mean dependent of course. But your argument is OK.
     
  4. Mar 3, 2013 #3
    Okay, thanks. I was just making sure!
     
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