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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 10EQ

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Q. 6. (a) If M is a closed linear subspace of a
normed linear space X, and x, be a vector not in
M. Let d be the distance from x, to M, then there
exists a functional f, in X' such that
fo (M)= 0, fo (x₁) = 1, and ||fo||=1/d.

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