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

  • Thread starter Pagless
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  • #1
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Homework Statement


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


Homework Equations


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


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.
 

Answers and Replies

  • #2
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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?
 
  • #3
Dick
Science Advisor
Homework Helper
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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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