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Spanning of vectors

  1. Jan 27, 2013 #1
    1. The problem statement, all variables and given/known data
    Suppose u,v,w are linearly independent, is it true that <u,v,w> does not equal <u,v>


    2. Relevant equations



    3. The attempt at a solution
    I started by defining what it meant to be linearly independent but am unsure where to go from there. I think the statement is true since the span <u,v> won't include any multiple of w but i can't give a solid proof
     
  2. jcsd
  3. Jan 27, 2013 #2

    micromass

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    Assume by contradiction that <u,v,w>=<u,v>. Then [itex]w\in <u,v>[/itex]. Thus...
     
  4. Jan 27, 2013 #3
    oh i think i get it, by assuming that we can say by definition

    w=λ1u + λ2v
    then there is now a non trivial solution to
    λ1u + λ2v + λ3w=0 which contradicts the statement that u,v,w are linearly independent, is that right?
     
  5. Jan 27, 2013 #4

    micromass

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    That's right!
     
  6. Jan 27, 2013 #5
    Sweet, cheers
     
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