# Thread: Using the Wronskian to prove linear (in)dependence

1. ## Using the Wronskian to prove linear (in)dependence

Hi,

Please could someone confirm if I've does this question correctly or not?

Thanks

Find out whether or not the functions $x$, $e^x$ and $xe^x$ are linearly dependent.

So, the Wronskian of those functions works out to be:
$(x-2)e^{2x}$
which is equal to zero when $x=2$, so the functions are linearly dependent then?

2. ## Re: Using the Wronskian to prove linear (in)dependence

Yes, it's correct.

3. ## Re: Using the Wronskian to prove linear (in)dependence

Originally Posted by girdav
Yes, it's correct.
But $W=(x-2)e^{2x} \neq 0$ for all x.

4. ## Re: Using the Wronskian to prove linear (in)dependence

No. If the functions were dependent, the Wronskian would be identically 0, not just 0 at a single point.