Question: 2. Consider the bases & = {1, t, t' } and B = {1 +t, t+th, t' } for P2 and the linear transformation T

2. Consider the bases & = {1, t, t' } and B = {1 +t, t+th, t' } for P2 and the linear transformation T : P2 -+ P2 defined by T(p(t)) = tp'(t), where p'(t) is the derivative of p(t). (a) (5 pts) Find the coordinate vector of t relative to B. (b) (5 pts) Find the change-of-coordinates matrix P from B to E. (c) (5pts) Find [Tje, the E-matrix of T. (d) (3 pts) We know that the two matrix representations [The and [T']g are similar; that is [T]B = P-[T]&P for some invertible matrix P. What is P? (e) (2 pts) What is the kernel of T

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