It really depends how much linear algebra you know. There are so many answers to this question depending on implicit knowledge.
The simplest way is to do the following:
Pick elements with . Then , so T cannot be injective.
This works for both finite and infinite dimensional vector spaces. If your vector space is finite, there are other ways of looking at this:
For example, if T is projection of V onto a proper subset W, then the associated matrix of T is not square and cannot be invertible.
Alternatively, if T is an isomorphism, there is a 1-1 correspondence between a basis of V and a basis of W. If your vector space V is finite dimensional, then you are looking for a 1-1 correspondence between two finite sets of different cardinality, but this is impossible.