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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}. ∞

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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}. ∞
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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