First isomorphism theorem. The isomorphism theorems are an important class of results with versions for various algebraic structures. Here, we are concerned about the first isomorphism theorem for vector spaces-one of the most fundamental results in linear algebra. Theorem. Let V, W be vector spaces, and let T : V W be a linear map. Then the following are true: (a) ker T is a subspace of V. (b) Im T is a subspace of W. (c) Im T is isomorphic to V/ ker T. Prove parts (a) and (b) of the theorem. (The interesting result is part (c), so, if you're inclined, try it out! We promise it's a very rewarding proof :) If you are interested but unfamiliar with the language, try looking up "isomorphism" and "quotient sp