Answered: Problem 6 (Orthogonal Complement).… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.9: Properties Of Determinants

Problem 34E

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Problem 6 (Orthogonal Complement). Consider the vector space P2 along with the inner product
(f(x), g(x)) = [ f(x)g(x)dr
(a) Find the orthogonal complement of W₁
=
span(1 + x).
(b) Find the orthogonal complement of W₂ = span(1+x, x²).
(c) Verify that WCW.
(d) The observation made in (c) is true in full generality: prove that if W₁ C W2 are two subspaces of an
inner product space, then WC W.

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