V21. Show that there exist constants M and N such that M||x||| < ||||2< N ||x|| -
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 15BEXP
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feeb7cc3b-3eb0-4cab-88e0-fc777da30e6a%2Fcf9f5595-a2d3-4f45-a964-716437f328e7%2Flhswogc_processed.png&w=3840&q=75)
Transcribed Image Text: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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