Let T: P2 (R) -› P2 (R) be a transformation defined as: T(f(x)) = f'(x) ∀ f(x) E P2 (R), and S: P1 (R) - P2 (R) be transformation defined as: S(g(x)) = xg(x) ∀ g(x) E P2 (R). Prove that S and T are linear transformations and also find the matrix representation of ToS w.r.t. standard bases a = (1,x,x^2} of P2(R) and ß = (1,x) of P1 (R), i.e., find [ToS] ß

Let T: P2 (R) -› P2 (R) be a transformation defined as: T(f(x)) = f'(x) ∀ f(x) E P2 (R), and S: P1 (R) - P2 (R) be transformation defined as: S(g(x)) = xg(x) ∀ g(x) E P2 (R). Prove that S and T are linear transformations and also find the matrix representation of ToS w.r.t. standard bases a = (1,x,x^2} of P2(R) and ß = (1,x) of P1 (R), i.e., find [ToS] ß

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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