Prove that ', 12 and lº norms satisfy the properties (N1)-(N3). (N1) (Positivity) ||x|| > 0, and ||x || = 0 +x = 0 (N2) (Homogeneity) ||ax || = |a| ||x || for all a E R (N3) (Triangle inequality) ||æ + y || < ||æ || + ||Y ||
Prove that ', 12 and lº norms satisfy the properties (N1)-(N3). (N1) (Positivity) ||x|| > 0, and ||x || = 0 +x = 0 (N2) (Homogeneity) ||ax || = |a| ||x || for all a E R (N3) (Triangle inequality) ||æ + y || < ||æ || + ||Y ||
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 3E
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