1. Not finding help here? Sign up for a free 30min 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!

Dimension of subspace

  1. Feb 28, 2010 #1
    C[-pi, pi]
    Span(1, cos (2x), cos2 (x))

    Doing the Wronskian here is pain so what other method would be more appropriate?
     
    Last edited: Feb 28, 2010
  2. jcsd
  3. Feb 28, 2010 #2

    Mark44

    Staff: Mentor

    One of the functions is a linear combination of the other two, so the three functions can't be linearly independent.
     
  4. Feb 28, 2010 #3
    How can I go about identifying if one is?
     
  5. Feb 28, 2010 #4
    Use a trig identity for cos2x
     
  6. Feb 28, 2010 #5
    cos2x=2cos^2 x-1 but I don't see how that is a multiple of cos2x sine it doesn't = cos^2 x outright.
     
  7. Feb 28, 2010 #6
    Can cos2x can be written as a linear combination of cos2x and 1?
     
  8. Feb 28, 2010 #7
    I see now.
     
  9. Feb 28, 2010 #8
  10. Mar 1, 2010 #9

    Mark44

    Staff: Mentor

    I realize that you already figured this out, but if you look at what I said, I didn't say that one of the functions was a multiple of another. I said that one function was a linear combination of the other two.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Dimension of subspace
  1. Dimensions of subspaces (Replies: 24)

  2. Subspaces & dimension (Replies: 9)

Loading...