Linear Dependence of f and g on 1<x<∞

[Pagless]

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.

 

[80past2]

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?

 

[Dick]

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.