Question:
Linear transformation
For each of the following functions decide whether or not the function is a linear transformation. Prove your answer in each case:
(a) F: V3(R) --> V2(R) defined by F(a1, a2, a3) = (2a1 - a2, 3a3)
(b) G: V3(R) --> V2(R) defined by G(a1, a2, a3) = (a1 - a2 + a3, a1 + a2a3)