Chapter 4.2, Problem 33E

Find out which of the transformations in Exercises 1 through 50 are linear. For those that are linear, determine whether they are isomorphisms.

33. $T\left(x_0,x_1,x_2,x_3,x_4,\mathrm{...}\right)=\left(x_0,x_2,x_4,\mathrm{...}\right)$ from V (we are dropping every other term)