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Find a linearly independent subset F of E

  1. Dec 14, 2011 #1
    1. The problem statement, all variables and given/known data
    Let U be the subspace of R5 spanned by the vectors
    E={(1,1,0,0,1),(1,1,0,1,1),(0,1,1,1,1),(2,1,-1,0,1)}.
    Find a linearly independent subset F of E with Span(E)=U


    2. Relevant equations



    3. The attempt at a solution
    I figured out that E is linearly dependent and that the solution set to it is
    c1=-t, c2=-t, c3=t, c4=t
    I'm not sure how to figure out which vectors are linear combos of the each other??
    I'm assuming that once I find the linearly dependent one(s), then the remaining vectors will be linearly independent. Will this be F?
     
  2. jcsd
  3. Dec 14, 2011 #2
    please please PLEASE help me someone, I have a final on this at 8AM :(
     
  4. Dec 15, 2011 #3

    Mark44

    Staff: Mentor

    From your work, the vectors in E are linearly dependent. If you set t = 1, you have -1v1 + (-1)v2 + 1v3 + 1v4 = 0, where the vi vectors are the ones in your set.

    This equation can be solved for v4 as a linear combination of the other three, so you can discard v4. If the resulting set is now linearly independent, then that's your answer. If the resulting set is still linearly dependent, keep discarding vectors until you get a set of vectors that is linearly independent.
     
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