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1. Show that the definition (x1, x2) · (Y1, Y2) = x1Y2 is not an inner product on R?.

1. Show that the definition (x1, x2) · (Y1, Y2) = x1Y2 is not an inner product on R?.

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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Answer any ONE of these questions

1. Show that the definition (x1, 12) · (y1, 42) = x142 is not an inner product on R². 2. If r = (x1, 12) E R², define ||x||. by ||||∞ = sup {|x1], |x2l}. Prove that ||x||. is a norm on R².
Transcribed Image Text:1. Show that the definition (x1, 12) · (y1, 42) = x142 is not an inner product on R². 2. If r = (x1, 12) E R², define ||x||. by ||||∞ = sup {|x1], |x2l}. Prove that ||x||. is a norm on R².
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