(Solved): Let \( V \) be a finite dimensional vector space over \( \mathbb{R} \), and let \( T: V \rightarro ...

Let \( V \) be a finite dimensional vector space over \( \mathbb{R} \), and let \( T: V \rightarrow V \) be a linear map. a) (4 points) Prove that if \( T \) is injective then \( T \) is surjective. HINT: Use the Rank-Nullity Theorem. b) (4 points) Prove that if \( T \) is surjective then \( T \) is injective. c) ( 2 points) Prove that \( T \) is bijective if and only if \( T \) is injective.