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

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 20EQ

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Problem 6 (Orthogonal Complement). Consider the vector space P2 along with the inner product
(f(x), 9(x)) = [] f (x)g(x)dx
(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 WCW+.

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