Answer any ONE of these questions 1. Show that the definition (x1, 12) · (y1, 42) = x142 is not an inner product on R².2. If r = (x1, 12) E R², define ||x||. by ||||∞= sup {|x1], |x2l}. Prove that ||x||. is anorm on R².

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Answered: 1. Show that the definition (x1, x2) ·…

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1. Show that the definition (x1, x2) · (Y1, Y2) = x1Y2 is not an inner product on R?.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 17E: If e is the unity in an integral domain D, prove that (e)a=a for all aD. [Type here][Type here]

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Question

Answer any ONE of these questions

1. Show that the definition (x1, 12) · (y1, 42) = x142 is not an inner product on R².
2. If r = (x1, 12) E R², define ||x||. by ||||∞
= sup {|x1], |x2l}. Prove that ||x||. is a
norm on R².

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