(a) Show geometrically that the set S = {(r1, 2) E R? : r1 2.x2...

 

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(a) Show geometrically that the set S = {(r1, 2) E R? : r1 – 2.x2 > 2} is convex. (b) Prove algebraically that the set R= {(x1, x2, x3) ER : 6x1 + 3r2+ 2x3 2 6, r1 20, r2 2 0, x3 2 0} is convex. (c) State the definition of a vertex of a convex set and list all the vertices of set R from part (b). (a) Show geometrically that the set S = {(r1, 2) E R? : r1 – 2.x2 > 2} is convex. (b) Prove algebraically that the set R= {(x1, x2, x3) ER : 6x1 + 3r2+ 2x3 2 6, r1 20, r2 2 0, x3 2 0} is convex. (c) State the definition of a vertex of a convex set and list all the vertices of set R from part (b).

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Definition Lets first recall the definition of a convex function Definition 1 A function f R n R is ... View the full answer