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Let x, y € R" be given. (a) If ||z||||y||=1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and ||y|| ≤ 1, prove that √1- ||1||² √/1 − ||y||² ≤ 1 − |x · y|. /1

Let x, y € R" be given. (a) If ||z||||y||=1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and ||y|| ≤ 1, prove that √1- ||1||² √/1 − ||y||² ≤ 1 − |x · y|. /1

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 15BEXP
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1. Let z, y € R" be given. (a) If ||z|| = ||y|| = 1 and z-y = 1, show that x = y. (b) If ||z|| ≤ 1 and ||y|| ≤ 1, prove that √√1 - ||1||²√√/1 – ||y||² ≤1 − |z · y|.
Transcribed Image Text:1. Let z, y € R" be given. (a) If ||z|| = ||y|| = 1 and z-y = 1, show that x = y. (b) If ||z|| ≤ 1 and ||y|| ≤ 1, prove that √√1 - ||1||²√√/1 – ||y||² ≤1 − |z · y|.
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