Last question for the night!

Let V and W be vector spaces and T: V --> W be linear.

a) Prove that T is 1-1 if and only if T carries linearly independent subsets of V onto linearly independent subsets of W.

b) Suppose that T is 1-1 and that S is a subset of V. Prove that S is linearly independent if and only if T(S) is linearly independent.

c) Suppose B {v1, v2,...,vn} is a basis for V and T is 1-1 and onto. Prove that T(B) = {T(v1), T(v2),...,T(vn)} is a basis for W