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) %3D lald(х, у), а є F. Show that ||. ||: N → R defined by: ||x|| = d(x,0),x E 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 d(аx, ay) %3D lald(х, у), а є F. Show that ||. ||: N → R defined by: ||x|| = d(x,0),x E N, is a norm on N.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 67E

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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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

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