1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
    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
    What are the Ui and the Vi anyway?? Vectors?? In an arbitrary vector space??
  7. Jul 10, 2012 #6
  8. Jul 10, 2012 #7
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook