[20] 3. Let T: R³ → R³ be defined by T((x,y,z))=(x+2y, 2x − z,x−2y-z), for (x,y,z) = R³. a. Prove T is a linear operator. b. Find the kernel and image of T, bases for the kernel and image of T, and the dimensions of the kernel and image of T. c. Describe the kernel and image of T geometrically.