Question

If the Wronskian of a set of functions is identically zero at every point of an interval I, then the set of functions is linearly dependent. True or False. If false, give a counterexample
Please, help

Answer 1

I have no idea how to do this, but you could try yahoo answers, the physics forum, the physicsforum (Website), or search google for a similar problem. Just some advice. Sorry for not being able to help.

Answer 2

Thanks anyway. I appreciate any response

Answer 3

False. Take, for example ,the functions, \(x^2\) and \(|x|x\) , which are continuous and linearly independent near x=0. Yet, their Wronkians are zero.

http://en.wikipedia.org/wiki/Wronskian
http://www.wolframalpha.com/input/?i=wronskian%28x^2%2C |x|x%29