Please solveusing information of 19,20solve 21 19. LetX=and define ||x|,=|x||+... +|x„|. Show that(i) ||x||, >0 and ||x||, 0 only if x-0(ii) ||Ax||=A||li(iii) ||x+y||1< ||x|+ |[y||1Va.V20. LetX=and define ||x||2 =[|x||²+... + |x,|]'/2. Show that(i) |x||2>0 and ||x||2=0 only if x-0(ii) ||Ax||2=|N||l2(iii) ||x+y|l2< ||x||2+ ||y||2%3DV21. Show that there exist constants M and N such that|x||N > ||x|| >|x||W

Given ||x||1=∑i=1n|xi|=|x1|+|x2|+...+|xn| ||x||2=∑i=1n|xi|2=|x1|2+|x2|2+...+|xn|2 Now we have…

Answered: V21. Show that there exist constants M…

Math

Advanced Math

V21. Show that there exist constants M and N such that M||x||| < ||||2< N ||x|| -

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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Question

Please solve

using information of 19,20

solve 21

19. Let
X=
and define ||x|,=|x||+... +|x„|. Show that
(i) ||x||, >0 and ||x||, 0 only if x-0
(ii) ||Ax||=A||li
(iii) ||x+y||1< ||x|+ |[y||1
Va.
V20. Let
X=
and define ||x||2 =[|x||²+... + |x,|]'/2. Show that
(i) |x||2>0 and ||x||2=0 only if x-0
(ii) ||Ax||2=|N||l2
(iii) ||x+y|l2< ||x||2+ ||y||2
%3D
V21. Show that there exist constants M and N such that
|x||N > ||x|| >|x||W

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