I am a bit confused... Linear combination means
$$F(X)=af(x_1)+bf(x_2) + \cdots$$
and linearly independent means
$$af(x_1)+bf(x_2) + \cdots=0$$
where $a=b=\cdots=0$
My question: is a linear combination linearly independent or linearly dependent as $F(x)$ is not $0$?