Let $f_1,...,f_m \in V^*$ be a linearly independent family ,and F a field. Show that for each $1\leq j\leq m$ there is a $v\in V$ such that $ f_i (v)= \delta_{i j} $ for any $1\leq j\leq m$
I thought about defining a linear map $T: V\to F^m$ such that $T(v) = (f_1(v),...,f_m(v)) $ and proving that T is surjective using the fact that T is surjective $ \iff Ker(T^t) = 0$ where $T^t$ is the transpose of T. Is it the right way to do it?
Ps: The exercise doesn't say anything about the dimension of V