Results 1 to 2 of 2

Math Help - Linear Dependence/Independence

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    19

    Linear Dependence/Independence

    The question asks me to determine whether the given set of functions is linearly dependent or linearly independent. If they are linearly dependent I must find a linear relation among them.

    f_{1}(t)=2t-3, f_{2}(t)=t^2+1, f_{3}(t)=2t^2-1, f_{4}(t)=t^2+t+1

    So I computed to the 4th derivative of each one of these, and then put them in a 4x4 matrix, in order to solve the Wronskian and see if its nonzero. My only question is, how do I go about solving this 4x4 matrix?

    Is there an easier way to do this problem/finding linear dependence and independence?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Mentia's Avatar
    Joined
    Dec 2008
    From
    Bellingham, WA
    Posts
    134
    Row reduction would be the easiest way I think. Row reduce the 4x4 and see if you get a row of all zeroes. If you do, then you have a dependent system. If you do not get a row of all zeroes, then you have linear independence.

    In your case it looks like you have linear independence.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Independence/Dependence
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 19th 2010, 04:33 AM
  2. linear dependence/independence
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 7th 2010, 06:18 PM
  3. Linear dependence/independence
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: July 27th 2010, 08:34 AM
  4. Linear Dependence & independence
    Posted in the Advanced Algebra Forum
    Replies: 11
    Last Post: March 20th 2009, 02:39 AM
  5. Linear dependence and independence
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 2nd 2008, 11:51 PM

Search Tags


/mathhelpforum @mathhelpforum