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Linear combination help?

  1. Sep 10, 2012 #1
    1. The problem statement, all variables and given/known data

    Let S={r,u,d,x} be a set of vectors.
    If x=4r+4u+4d, determine whether or not the four vectors listed above are linearly independent or linearly dependent. If is dependent, find a non-trivial linear relation.
    2. Relevant equations



    3. The attempt at a solution

    I dont really know how to start the problem. But I tried to set it up this way.
    Let 0=4r-4d-4u+x. In order to make it zero would the scalar of x have to be
    1? but im really lost with lost with problem. Any help would great
     
  2. jcsd
  3. Sep 10, 2012 #2

    Dick

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    You've already written 0 as a linear combination of the vectors {r,u,d,x}. Doesn't that mean you are done??
     
  4. Sep 10, 2012 #3
    well I first have to figure out if its linear dependent or linear independent. I am not given any vectors, just scalars. Im supposed to figure out what scalar number goes in front of the x vector. What I do know when its linear dependent is when there is atleast one nontrivial scalar and when its linear independent is when all scalars are zero. But how do I go about finding what scalar fits in front of the scalar?oh wait wouldnt it be linear dependent since the scalars(4) in front of vectors r,d,u are 4?
     
  5. Sep 10, 2012 #4

    Dick

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    You are overthinking this. Try putting 1 in front of x.
     
  6. Sep 10, 2012 #5
    That I tried. All I know if I divide it i'm left with the same equation as I started with.
     
  7. Sep 10, 2012 #6

    Dick

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    Mmm. I just noticed your algebra is a bit off. If you do it right you have 0=-4*r-4*d-4*u+1*x. All of the scalars in front of the vectors are nonzero and the sum is 0. Linearly dependent or independent??
     
  8. Sep 10, 2012 #7
    ok thanks
     
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