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: Spanning of vectors

  1. Jan 27, 2013 #1
    1. The problem statement, all variables and given/known data
    Suppose u,v,w are linearly independent, is it true that <u,v,w> does not equal <u,v>

    2. Relevant equations

    3. The attempt at a solution
    I started by defining what it meant to be linearly independent but am unsure where to go from there. I think the statement is true since the span <u,v> won't include any multiple of w but i can't give a solid proof
  2. jcsd
  3. Jan 27, 2013 #2
    Assume by contradiction that <u,v,w>=<u,v>. Then [itex]w\in <u,v>[/itex]. Thus...
  4. Jan 27, 2013 #3
    oh i think i get it, by assuming that we can say by definition

    w=λ1u + λ2v
    then there is now a non trivial solution to
    λ1u + λ2v + λ3w=0 which contradicts the statement that u,v,w are linearly independent, is that right?
  5. Jan 27, 2013 #4
    That's right!
  6. Jan 27, 2013 #5
    Sweet, cheers
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook