Answered: In Let x, y ER" be given. (a) If ||x||…

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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.4: Complex And Rational Zeros Of Polynomials

Problem 16E

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Question

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

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