Answered: Problem 65 Let Z be a subspace of a… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section: Chapter Questions

Problem 5RQ

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Problem 65
Let Z be a subspace of a normed space X, and y E X. Let d = d(y, Z). Prove
that there exists A e X* such that ||A|| < 1, A(y) = d and A(z)
z E Z.
= 0 for all
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