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Ques. 1. Let N be a linear space and d be a metric on N such that d(x + z,y+ z) = d(x,y), x,y € N and %3D d(ax, ay) = |a|d(x, y), a E F. Show that ||. ||: N → R defined by: ||x|| = d(x, 0),x € N, is a norm on N.

Ques. 1. Let N be a linear space and d be a metric on N such that d(x + z,y+ z) = d(x,y), x,y € N and %3D d(ax, ay) = |a|d(x, y), a E F. Show that ||. ||: N → R defined by: ||x|| = d(x, 0),x € N, is a norm on N.

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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Ques. 1. Let N be a linear space and d be a metric on N such that d(x + z,y +z) = d(x,y), x,y € N and d (аx, ay) %3Dla\d (х, у), а € F. Show that ||. ||: N → R defined by: I|x|| = d(x, 0), x E N, is a norm on N. %3D
Transcribed Image Text:Ques. 1. Let N be a linear space and d be a metric on N such that d(x + z,y +z) = d(x,y), x,y € N and d (аx, ay) %3Dla\d (х, у), а € F. Show that ||. ||: N → R defined by: I|x|| = d(x, 0), x E N, is a norm on N. %3D
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