Ftv And Ftwo Of A Givea Flat F Have Paint U In Common The F4v Ftw Show That It

GEOMETRY OF CONVEX SETS

8 questions in total listed below.

M34( – Asso # 3Due Mon March &lby 5 PMProve that is two translates Ftv and Ftwo ofa givea flat F have paint u in Common, the F4v – FtwShow that it a flat cortaiss O , the I is a subspace3 Show that F-F=ix-y X,yeF? is a flat S E is a flatIf not, then yout. Gives His the hype plane in (Ry whose equation isw+ x-2y-22.=4, find the point on I that is closestthis comparito the origin5 Given the hyperplane Hi w4x-y+z=(, determine whetherp= (o,4,-3,0 and q =(4, -1,3, -1 ) are on the Same sideor on Opposite sides of the hyperplace . IS on opposite sides,find where Ep,q l intersects 4,b. Given a xt S strictly to one side of a hype place. Hexplain why Conv S cannot intersect H.Find a hyperplane H in RO which goes through the paintsX – (2 ,1,70) g= (3,0,3,0), Z = (4, 1/4 0, w = (14 4 -5)Let X+Y – Ix+yl xeX axl geY3DOPcove or disprove (a) Spaa( S+T) = SpanS + Spasb Aff( SIT) – ASSS 4 AST. (8)

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