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Homework Help: Show if its a lin. independent subset

  1. Apr 8, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex] V = { (x_{1},x_{2},x_{3},x_{4},x_{5}) \in R^{5} : x_{1} -2x_{2} + 3x_{3} - x_{4} + 2x_{5} = 0 } [/tex]

    show that S = { (0,1,1,1,0) } is a linearly independent subset of V.



    3. The attempt at a solution

    I don't get it.. it's a set with 1 non zero vector, it's going to be linearly independent? then do I just have to show that it's actualy in V?

    thanks
     
  2. jcsd
  3. Apr 8, 2010 #2
    Yes, a set with 1 element is going to be linearly independent. You must verify that (0,1,1,1,0) is actually in V to show that S is a subset of V. Just plug the vector into the equation and see if you get 0.
     
  4. Apr 8, 2010 #3
    thanks, I thought I was misunderstanding something.. since it looked to trivial to me haha
     
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