The vector space V = P2 (R) admits for bases A = {1, x, x2} and B = {1, x + 2, (x + 2) 2 }.

The vector space V = P2 (R) admits for bases

A = {1, x, x2} and B = {1, x + 2, (x + 2)2}.

(i) Determine matrices P and Q such that, for every polynomial p (x) ∈ V, we have

[p (x)] A = P [p (x)] B and [p (x)] B = Q [p (x)] A.

(ii) Let T: V → V be the linear map given by T (p (x)) = p (x + 2) for all p (x) ∈ V.

Determine the matrices [T]BA and [T]BA