Exercise 4 (The max norm ||||). Recall from class that the max norm ||· || isdefined on Rn as== max{|x₁|, ...,|xn|}.||x||∞ :Show that | || is a norm on R". More precisely, show that the following hold.(i) |||| ≥0 for all x € Rn and ||x|| 0 holds if and only if x is the zero=∞vector.(ii) ||ax||∞ = |a|||x||∞ for all a € R and for all x € R”.(iii) ||x+y||∞ ≤ ||x||∞ + ||y||∞ for all x, y = R".

Answered: Image /qna-images/answer/5f03da91-905f-4235-84d5-36b4d70591a4.jpg

Exercise 4 (The max norm ||· ||). Recall from class that the max norm ||· ||∞ is defined on Rn as ||x||∞ : = = max{|x₁,..., |xn|}. Show that | || is a norm on R. More precisely, show that the following hold. : 0 holds if and only if x is the zero (i) |||| ≥0 for all x € Rn and ||x|| = ∞ vector. (ii) ||ax||∞ = |a|||x||∞ for all a € R and for all x € R”. (iii) ||x+y||∞ ≤ ||x||∞ + ||y||∞ for all x, y ≤ Rn.

Exercise 4 (The max norm ||· ||). Recall from class that the max norm ||· ||∞ is defined on Rn as ||x||∞ : = = max{|x₁,..., |xn|}. Show that | || is a norm on R. More precisely, show that the following hold. : 0 holds if and only if x is the zero (i) |||| ≥0 for all x € Rn and ||x|| = ∞ vector. (ii) ||ax||∞ = |a|||x||∞ for all a € R and for all x € R”. (iii) ||x+y||∞ ≤ ||x||∞ + ||y||∞ for all x, y ≤ Rn.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 64E

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