Consider the vector space Pg. We define linear functionalsJ(p(x)) = p(-1), J2{p(x)) = p'(-1), J3(p(x)) = p(1), J4(P(x)) = p'(1),for all P(x) and P3. Show that B* ={J1, is a basis for the dual space (P3)*, and find abase B to space P3 so that B'is its dual base.

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Answered: Consider the vector space Pg. We define…

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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Consider the vector space Pg. We define linear functionals J«(p(z)) = p(-1), J2(p(x)) = p'(–1), Ja(P(x)) = P(1), Ja(p(x)) = p'(1), for all P(x) and P3. Show that B* ={J,J is a basis for the dual space (P3)*, and find a base B to space P3 so that B'is its dual base.