Results 1 to 3 of 3

Math Help - Please help solving Linearly Dependent question for 4 variation

  1. #1
    Junior Member
    Joined
    Sep 2012
    From
    NY
    Posts
    32

    Please help solving Linearly Dependent question for 4 variation

    cosx, sinx, ex, and e-x are LI or LD ( 0 =or< x =or< 1)

    I can see without calculation that it is LI but I do not know how to prove it.

    I tried to use Wronskian Determinant but it gets really messy

    W(x) =

    cosx sinx ex e-x
    -sinx cosx ex -ex

    -cosx -sinx ex e-x
    sinx -cosx ex e-x


    Someone please suggest a better and quicker way...

    Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    GJA
    GJA is offline
    Member
    Joined
    Jul 2012
    From
    USA
    Posts
    109
    Thanks
    29

    Re: Please help solving Linearly Dependent question for 4 variation

    Hi angelme,

    I will call the Wronskian matrix W. To start, we should have W_{4,4}=-e^{-x}; in other words the entry in the fourth row, fourth column should be -e^{-x}, not e^{-x}. I'm guessing you actually have this and missed a minus sign in your post.

    To make life simpler, using the fact that the determinant is not affected when you add a row to another will make things easier. For example, adding row 1 to row 3 makes row 3 become 0, 0, 2 e^{x}, 2e^{-x}. If you use this fact a couple of times you should be able to get a row that has 3 zeros and one nonzero entry. You then expand your determinant about this nonzero entry and go from there.

    Give it another shot with this in mind. I ended up getting det(W)=-6 when all was said and done. Since -6\neq 0 the vectors are linearly independent. Let me know if you still get stuck. Good luck!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2012
    From
    NY
    Posts
    32

    Re: Please help solving Linearly Dependent question for 4 variation

    sorry I'm still not getting it Could you please explain me step by step?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linearly Dependent
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: May 21st 2011, 05:15 AM
  2. linearly dependent in Q, linearly independent in R
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: April 12th 2011, 01:44 PM
  3. Linearly dependent
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 9th 2011, 05:46 PM
  4. linearly dependent
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: April 21st 2009, 05:35 AM
  5. linearly dependent
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 20th 2008, 05:37 PM

Search Tags


/mathhelpforum @mathhelpforum