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Is {V1, V2, V3} Linearly Independent or Dependant?

  1. Jul 10, 2012 #1
    The numbers are subscripts.

    U1 + U2 + U3 = V1 + V2 + V3

    U1 + U2 = V2

    I have tried solving for each V in terms of U, but this isn't working out too well.
     
  2. jcsd
  3. Jul 10, 2012 #2

    micromass

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    What is the exact problem?
     
  4. Jul 10, 2012 #3
    That is the exact problem. Under those conditions is {V1,V2,V3} LI or LD.
     
  5. Jul 10, 2012 #4
    I can see U3 = V1+V3

    But I'm still lost. I am trying to show one of the V's is equal to or is a multiple of another, or that they are all not equal to each other.
     
  6. Jul 10, 2012 #5

    micromass

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    What are the Ui and the Vi anyway?? Vectors?? In an arbitrary vector space??
     
  7. Jul 10, 2012 #6
    Yes.
     
  8. Jul 10, 2012 #7

    micromass

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    Begin by looking at some easy examples in vector spaces you know well, such as [itex]\mathbb{R}[/itex], [itex]\mathbb{R}^2[/itex] and [itex]\mathbb{R}^3[/itex].
     
  9. Jul 10, 2012 #8
    So I tried this out. In R^1 the vectors are Linearly Dependant due to a 0 vector.

    In R^2 I can see them being both LI or LD depending on the choices for the arbitrary vectors. For R^3 I see the same. It is possible to choose an option where V1=V3, or another where they are completely Linearly Independant.
     
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