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!

Linear Independence

  1. Oct 8, 2007 #1
    1. The problem statement, all variables and given/known data
    Using the wronskian (determinant basically), determine if e^x, sin(x), cos(x) are linearly independent

    2. Relevant equations
    I used this:
    | e^{x} sin(x) \:cos(x)|[/tex]
    |e^{x} cos(x) -sin(x)|[/tex]
    [tex]|e^{x} -sin(x) -cos(x)|[/tex]

    But pretend that's just a 3x3 matrix and you take the determinant of it

    3. The attempt at a solution

    After finding the determinant I get -2e^x which is never 0 so they're linearly independent. Am I right in this?
  2. jcsd
  3. Oct 8, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    Yes, but you know the wronskian only has to be nonvanishing someplace for the functions to be linearly independent, right?
  4. Oct 8, 2007 #3
    Oh wow, I thought it was at all points. If possible, would you mind telling me why that is?
  5. Oct 8, 2007 #4


    User Avatar
    Science Advisor
    Homework Helper

    Sure. If f1(x), f2(x) and f3(x) are linearly dependent, then there are nonzero constants such that c1*f1(x)+c2*f2(x)+c3*f3(x) is identically zero over some interval. So a linear combination of columns in your matrix is zero. This tells you det=0 over the interval. So if det is non-zero anywhere, you know they aren't linearly dependent.
    Last edited: Oct 8, 2007
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Linear Independence
  1. Linear Independence (Replies: 1)

  2. Linear independence (Replies: 2)

  3. Linear independence (Replies: 6)

  4. Linear independance (Replies: 3)

  5. Linear independence (Replies: 3)