1. define For R", one can consider the following norm structures. For all x = (1,,n) R", we • == |||||= max {1,, n} (a) Prove that (R", || ||1) and (R", || ||∞) satisfy the triangle inequality. (b) Draw figures for S₁ = {r R² ||||₁ = 1} and S = {x € R² : ||r||∞ = 1}. ∞
1. define For R", one can consider the following norm structures. For all x = (1,,n) R", we • == |||||= max {1,, n} (a) Prove that (R", || ||1) and (R", || ||∞) satisfy the triangle inequality. (b) Draw figures for S₁ = {r R² ||||₁ = 1} and S = {x € R² : ||r||∞ = 1}. ∞
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
Question
![1.
define
For R", one can consider the following norm structures. For all x = (1,,n) R", we
•
==
|||||= max {1,, n}
(a) Prove that (R", || ||1) and (R", || ||∞) satisfy the triangle inequality.
(b) Draw figures for S₁ = {r R² ||||₁ = 1} and S = {x € R² : ||r||∞ = 1}.
∞](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c20c826-ea82-4ac8-bc3d-0227ad67ebcb%2F9d82dbf0-da35-41c4-9624-e015386e3786%2Fq5cl29e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.
define
For R", one can consider the following norm structures. For all x = (1,,n) R", we
•
==
|||||= max {1,, n}
(a) Prove that (R", || ||1) and (R", || ||∞) satisfy the triangle inequality.
(b) Draw figures for S₁ = {r R² ||||₁ = 1} and S = {x € R² : ||r||∞ = 1}.
∞
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