If the Wronskian is non-zero at some point in an interval, then the associated functions are linearly independent on the interval.
For (a) though, is one element a linear combination of the others? If so, then they are dependent.
a)V is the vector space of all real valued functions defined on R. A = {2,sin^2(x), cos^2(x)}
Is A linearly independent?
b) V=C([-PI, PI]).
A={sin x , sin 2x, .... sin nx}, where n is some natural number. Is A linealy independent?
I am not sure how to work them out.