(i) State the rank-nullity theorem for a linear map between finite-dimensional vector spaces.

(ii) Show that a linear transformation $f: V \rightarrow V$ of a finite-dimensional vector space $V$ is bijective if it is injective or surjective.

(iii) Let $V$ be the $\mathbb{R}$-vector space $\mathbb{R}[X]$ of all polynomials in $X$ with coefficients in $\mathbb{R}$. Give an example of a linear transformation $f: V \rightarrow V$ which is surjective but not bijective.