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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 ||

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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Prove that 1', 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 ER (N3) (Triangle inequality) ||x + y || < ||æ || + ||Y ||
Transcribed Image Text:Prove that 1', 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 ER (N3) (Triangle inequality) ||x + y || < ||æ || + ||Y ||
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