(adsbygoogle = window.adsbygoogle || []).push({}); 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.

y_{1}=|x| y_{2}=-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=y_{1}, g=y_{2}

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.

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

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