(a) Find the transition matrix S from B' to B. (b) Use the matrices S and A to find [v], and [T(v)], where [V]B/ = (-1,4) T. (c) Find S" and A' (the matrix for T relative to B' ). (d) Find [T(v)]B, in two different ways. Problem 13 a. Consider the linear map L: P2 -> P2 defined by L(p(x)) =3p(x+1). a) Find the matrix A of L relative to the basis B= (1, x, x2}. b) Show that the inverse of L is defined by L-' (p(x)) = =p(x - 1). c) Find the matrix A' of L-1 relative to B. Problem 14 a) Suppose {u, v, w} spans the vector space V. Prove that {u + v, u + w, v + w} also spans V. b) Suppose that the set of vectors {u, v, W} is linearly independent in a vector space V. Prove that the set of vectors {u tv + w, utv, u + W} must be linearly independent. Problem 15 Expand the set ! = 1 5 2 to a basis for R