Let V and V' be vector spaces over the same field F, and let ∅ : V → V' be a linear transformation. 

a. To what concept that we have studied for the algebraic structures of groups and rings does the concept of a linear transformation correspond? 

b. Define the kernel (or nullspace) of ∅, and show that it is a subspace of V. 

c. Describe when ∅ is an isomorphism of V with V'.