(a) Let x1,.., Xn+2 € R". Show that there must exist some sets A and B such tha i. ANB=Ø, ii. AUB= {x1,..., Xn+2} , and iii. conv(A) N conv(B) + Ø. (Hint: Use the idea of linear dependence.) %3D

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 23E
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(a) Let x1,· ..,
Xn+2 € R". Show that there must exist some sets A and B such that
i. ANB= Ø,
ii. AUB = {x1, ... , Xn+2} , and
iii. conv(A) N conv(B) # Ø.
(Hint: Use the idea of linear dependence.)
(b) Show that Part (a) is not necessarily true if we only have n +1 points in R".
Transcribed Image Text:(a) Let x1,· .., Xn+2 € R". Show that there must exist some sets A and B such that i. ANB= Ø, ii. AUB = {x1, ... , Xn+2} , and iii. conv(A) N conv(B) # Ø. (Hint: Use the idea of linear dependence.) (b) Show that Part (a) is not necessarily true if we only have n +1 points in R".
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