Let $\displaystyle a_0,...,a_n $be distinct real numbers.

Let the linear map $\displaystyle T: R[X]_{\leq n} \rightarrow R^{n+1}$ be defined by $\displaystyle T(q(x)) = [q(a_0),....,q(a_n)]^T$ for all $\displaystyle q(x)$ in $\displaystyle R[X]_{\leq n} $

Prove that $\displaystyle T$ is an isomorphism

For this question is it enough to say that $\displaystyle R[X]_{\leq n}$ and $\displaystyle R^{n+1}$ are both of dimension $\displaystyle n+1 $and therefore isomorphic? Im not sure i can apply this to a transformation. Thanks for any help!