Let a b and n Let A- (a.az, as), B- (b. b, ba).S- conv (aa a) and T-conv (b, by, by). (a) Find a hyperplane H with normal n that separates A and B. (b) Is there a hyperplane parallel to H that strictly separates A and B (e) Find the maximum and minimum of the linear functional on S and T respectively and indicate at which x these maxinua and minium are attained

Let a b and n Let A- (a.az, as), B- (b. b, ba).S- conv (aa a) and T-conv (b, by, by). (a) Find a hyperplane H with normal n that separates A and B. (b) Is there a hyperplane parallel to H that strictly separates A and B (e) Find the maximum and minimum of the linear functional on S and T respectively and indicate at which x these maxinua and minium are attained

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

Let a
by
by
by=
and n
Let A- {a, az, as}, B- (b, b2, ba). S- conv {a.a a) and T- conv (b, b,, bs).
(a) Find a hyperplane H with normal n that separates A and B.
(b) Is there a lhyperplane parallel to H that strictly separates A and B?
(e) Find the maximum and minimum of the linear functional
f(r, a, ra) 3r, + - 2rs
on S nnd T respectively and indicate at which x these maximun and minimm are attained.

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