Consider R'\" = {(xo,x1, .--) = x;- E R} the vector space of countably infinite sequences of reals. We define the following maps: LOCO, x1, x2, ---) = (x1, 172,-\") R(x0, x1, 162,-\") = (0, x0, x1, x2, ---) we call L the left shift transformation and we call R the right shift transformation. 1. Prove that L is onto but not one-to-one. 2. Prove that R is onetoone but not onto. 3. Why are these transformations special? Could such maps exist for a finite dimensional space