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How to tell if a pair of functions are linearly dependent or linearly independent

  1. Mar 5, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine if the pair of functions given are linearly independent or linearly dependent on the interval 1<x<∞, and give a reason for your answer.
    y1=|x| y2=-3x


    2. Relevant equations
    I'm pretty sure this has something to do with the Wronskian.
    W(f,g)=fg'-f'g


    3. The attempt at a solution
    f=y1, g=y2
    f'=1, g'=-3
    I can assume that the derivative of the abs. value of x is just 1, because the question says that x is greater than 1, right?
    So then W(f,g)=-3|x|+3x
    can i assume x is positive again, so therefore the Wronskian is equal to zero? Would this then make my solution linearly independent?

    Thanks.
     
  2. jcsd
  3. Mar 5, 2012 #2
    Maybe I'm misunderstanding the question, but it seems to me that all you have to do is see whether they are linear combinations of each other. does y1(x) = a*y2(x) for all x in the domain, for some constant a?
     
  4. Mar 5, 2012 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Technically just showing that the Wronskian is zero doesn't tell you the functions are linearly dependent. There are exceptions to that. Follow the suggestion 80past2 gave.
     
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