a) Let D be the differential operator on the vector space P2(R). Given two ordered bases a = (1. y Rand B = { 1, 2x, 4x-2} for P2(R). Find the matrix [D]a and matrix [D]g using similarity lineartransformation method.b)Let T, : R > R? and T2: R R be defined by T1(a, b, c) = (3a, b+c) and T2(a, b, c) = (2a- 3c, b)%3DCompute T + T2, 5T1, 4T1-5T2, TT2 and T2T1, if possible.

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Answered: a) Let D be the differential operator…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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a) Let D be the differential operator on the vector space P2(R). Given two ordered bases a = (1, x. %3D and B = {1, 2x, 4x - 2} for P2(R). Find the matrix [D], and matrix [D]a using similarity linear transformation method.