# Isomorphism of Linear space of polynomials with degree less than n and $V_n(R)$

I need to show that there is an Isomorphism of Linear space of polynomials with real coefficients with degree less than n and $V_n(R)$. Now $V_n(R)$ is the linear space where the vectors are n-tuples of real numbers and the scalars are real numbers with addition and scalar multiplication defined by $$(\alpha^1,....,\alpha^n)+(\beta^1,....,\beta^n)=(\alpha^1+\beta^1,....,\alpha^n+\beta^n)$$ and $$\gamma(\alpha^1,....,\alpha^n)=(\gamma\alpha^1,....,\gamma\alpha^n)$$

So, I need to either find a linear transformation from $V_n(R)$ to the set of polynomials of degree less than n, or show that their dimensions are the same. Which one is easier to show? How do I start? I am asking these questions to myself first of all and I appreciate all your input.

$T(P_{n-1})=(\alpha^1,....,\alpha^n)$ seems like the linear transformation I am looking for, right? I know both of these spaces have degree n, but how does one show that?

Let $P_h$ and $P_m$ be two polynomials of power less than n-1.

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