1. Consider the linear map T : R[X]deg<3 –→ Mat2,2(R) given byT(f) =f(0) f'(1)(f"(-1) f(2)$(2) ).Let B = {X, X², 1, X³} be a basis for R[X]deg<3 and-{( :). (; ?) - (: )- (: )}:=1 1a basis for Mat2,2 (R). Find [T]c+B, and determine whether T is injectiveand/or surjective.

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Answered: 1. Consider the linear map T :…

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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1. Consider the linear map T : R[X]deg<3 → Mat2,2(IR) given by f(0) f'(1) T(f) = (-1) F(2) Let B = {X, X², 1, X³} be a basis for R[X]deg<3 and - {(' :) (: ) - (6 :). ( )} (6 ) · (: )} C : a basis for Mat22(R). Find [T]c-8, and determine whether T is injective and/or surjective.