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: Linear independence

  1. Jan 18, 2010 #1
    1. The problem statement, all variables and given/known data
    If the set {v1,v2,v3} of vectors in R^(m) is linearly dependent, then argue that the set {v1,v2,v3,v4} is also linearly dependent for every choice of v4 in R^(m).


    2. Relevant equations
    Definitions would be more relevant so...

    Linearly Independent: If the only solution is the trivial solution

    Linearly Dependent: If there are more solutions than he trivial solution.

    3. The attempt at a solution

    I started out by writing out three vectors that are a dependent set, and I noticed that no matter what I added for v4 there would still be that non trivial solution, therefore making it remain dependent.

    Is that sound reasoning?
     
  2. jcsd
  3. Jan 18, 2010 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi EV33! :smile:

    (try using the X2 and X2 tags just above the Reply box :wink:)
    If I'm guessing correctly what you mean, then yes that's sound.

    But you should write it properly, starting "if v1 v2 and v3 are dependent, then there exist …" :wink:
     
  4. Jan 18, 2010 #3
    Thank you very much
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook