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Linear Algebra linear combinations help

  1. Sep 12, 2010 #1
    The linear combinations of v=(a,b) and w=(c,d) fill the plane unless _____.
    Find four vectors u, v, w, z with four components each so that their combinations cu+dv+ew+fz produce all vectors (b1, b2, b3, b4) in four dimensional space.

    I think that the first part of the answer, that fills the blank, is unless v is a scalar multiple of w, or vice versa.

    But as far as the second part of the question, I have no idea what it is even asking. Are b1, etc. referencing the first part of the question? Or is it just asking to write vectors that have all zero components except b1 etc. Any help is much appreciated?
     
  2. jcsd
  3. Sep 12, 2010 #2

    Dick

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    The first answer looks fine. I THINK the second one is just asking you to write down four vectors that span R^4. Like u=(1,0,0,0) might be a good choice for the first one. Can you give me a v, w and z that span together with u?
     
  4. Sep 12, 2010 #3
    That's what I thought it might mean v=(0,1,0,0), w=(0,0,1,0), z=(0,0,01), but that seems too simple. It's listed in the book as a challenge problems
     
  5. Sep 12, 2010 #4

    Dick

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    Sure. But I can't think what else it might mean. It certainly can't be referencing any symbols in the first part, since the first part is about R^2.
     
  6. Sep 12, 2010 #5
    Alright, thanks for the help,
     
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