Veronese image not contained in proper linear subspace I'm studying the Veronese Map from Shafarevich Book. And I want to prove the following problem (Ex 10 Section 4.4 Shafarevich Basic Algebraic Geometry)
Prove that the Veronese image $v_m(\mathbb{P}^n)\subset \mathbb{P}^N$ is not contained in any linear subspace of $\mathbb{P}^N$.
I don't know how to start this problem because I need to know more about this map. Someone could teach me some tool that can help me in this problem? I don't want a solution at first but help.
Thanks!

Note that the coordinates of the Veronese embedding consist of all monomials in $n+1$ variables of degree $m$. You just need to show that they are linearly independent.
