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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.

    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?

  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


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    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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