Indicate whether each statement is true or false. If true, prove the result. If false, provide a counterexample. (i) (2 points) There is a linearly independent subset of P2(R) consisting of four elements.

(ii) (2 points) If T : V W is an isometry between finite dimensional vector spaces, then T is an isomorphism.

(iii) (2 points) If V is a non-trivial vector space and T : V R is a linear transformation, then T is either surjective or the zero map. (iv) (2 points) If V, W are finite dimensional vector spaces with dim(V ) = dim(W), and T : V W is an injective linear transformation, then T is an isomorphism. (v) (2 points)

If V and W are finite dimensional vector spaces and T : V W is an isomorphism, then det(T) = 1.