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Homework Help: Linear independence

  1. Jan 18, 2010 #1
    1. The problem statement, all variables and given/known data
    If the set {v1,v2,v3} of vectors in R^(m) is linearly dependent, then argue that the set {v1,v2,v3,v4} is also linearly dependent for every choice of v4 in R^(m).


    2. Relevant equations
    Definitions would be more relevant so...

    Linearly Independent: If the only solution is the trivial solution

    Linearly Dependent: If there are more solutions than he trivial solution.

    3. The attempt at a solution

    I started out by writing out three vectors that are a dependent set, and I noticed that no matter what I added for v4 there would still be that non trivial solution, therefore making it remain dependent.

    Is that sound reasoning?
     
  2. jcsd
  3. Jan 18, 2010 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi EV33! :smile:

    (try using the X2 and X2 tags just above the Reply box :wink:)
    If I'm guessing correctly what you mean, then yes that's sound.

    But you should write it properly, starting "if v1 v2 and v3 are dependent, then there exist …" :wink:
     
  4. Jan 18, 2010 #3
    Thank you very much
     
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