4. Let T : P3 - P3 be the linear transformation given by T(p(x)) = 3p(x) - xp' (x). a) Find a basis for the kernel of T. "b) Find a basis for the image (or range) of T. 5. Let B = {v1, v2, v3} be a basis of a vector space V and let T : V - V be the linear transfor- mation with T(v1) = 3v1 + 4v2 + 5v3, T(v2) = 7v1+ 8v2 +9v3, T(v3) = -V1 - 2v2 - 3V3. Find [T]g, the matrix of T in the basis B. 6. Let B = {V1, v2, . .., Vn} be a basis of the n-dimensional vector space V. Let T : V - V be the linear transformation with T(v1) = alV1, T(V2) = Q2V2, . . . T (Vn) = an Vn, where a1, d2, . .., an are fixed scalars. Find , the matrix of T in the basis B