4) Let V be the vector space of polynomials of degree < 2 and let p(x) = ax² + bx + c. Find the adjoint operator (TX@)(p) for T:V → V and p:V → R given by d) Tp(x) = x²p(x) + x³p'(x), @(p) = p"(1).

4) Let V be the vector space of polynomials of degree < 2 and let p(x) = ax² + bx + c. Find the adjoint operator (TX@)(p) for T:V → V and p:V → R given by d) Tp(x) = x²p(x) + x³p'(x), @(p) = p"(1).

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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Question

4) Let V be the vector space of polynomials of degree <2 and let p(x) = ax² + bx + c. Find the
adjoint operator (T*@)(p) for T:V → V and o:V → R given by
d) Tp(x) = x²p(x) + x³p'(x), @(p) = p"(1).

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