(N2) (Homogeneity) ||ax || = |a| ||x || for all a eR %3D
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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please provide N2 and N3 answer only.
Transcribed Image Text:Prove that l', 12 and lº norms satisfy the properties (N1)-(N3).
(N1) (Positivity) |||| = 0, and ||x || =0 =x= 0
(N2) (Homogeneity) ||ax || = |a| ||x || for all a E R
(N3) (Triangle inequality) ||x + y || < ||x || + ||y ||
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