(2) Define T : R 3 → R 3 by T     x y z     =   0 3 −2 1 −2 2 2 −6 5     x y z   . Let V be the set of all vectors that are fixed by T, which means that V = {v ∈ R 3 : T(v) = v}. (a) Show, using the definition of subspace, that V is a subspace of R 3 . (b) Come up with an equation that also defines V. (In other words, find a linear equation ax + by + cz = d such that   x y z   ∈ V ⇔ ax + by + cz = d.) (c) Geometrically, what kind of object is V (point/line/plane etc)? (d) Find a basis for V.