Let T : R3 → R3 be the linear operator T(x, y, z) = (4x + 2y y 2z, 4y, 2y + 2z) (b) Determine whether T is diagonalizable or not. If so, find a basis γ of R3 such that [T]γ is diagonal. (c) A linear...

Let T : R3 → R3 be the linear operator
T(x, y, z) = (4x + 2y y 2z, 4y, 2y + 2z)

(b) Determine whether T is diagonalizable or not. If so, find a basis γ of R3 such that [T]γ is diagonal.
(c) A linear operator N : V → V is called nilpotent if there exists a positive integer k such that Nk = 0. Is T nilpotent?