(19) In this problem, we will use the ordered bases B: 1, x, x? B': - 2', 2x - 12, 3 - 2x + 2? for Pz, the vector space of polynomials of degree _ 2....

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(19) In this problem, we will use the ordered basesB: 1, x, x?B': - 2', 2x - 12, 3 - 2x + 2?for Pz, the vector space of polynomials of degree _ 2.4(a) Find the change of basis matrices P and PB'+BB+ B'(b) Find (#2 - 2z + 3)> and (-2z? + 1 - 7)s using the formula VB =B'+-B(c) Let L: P2 -+ Pa denote the linear operator that takes the derivative # of a poly-nomial. Verify that0)LB,B =0 00(d) Find LE'B' using the formulaLB',B' = P LB.B PB'+ BB+ B'