1. Show that the cube C2 = {x R2: - c 2. Suppose for any n =...
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2. Suppose for any n = 2, 3, . . . , that the cube Cn-1 Š‚ conv{(±c, ±c,. . . ±)} Š‚ Rn-1. Show that n-dimensional cube Cn Š‚ conv{(±c, ±c;. . . ,±c)} Š‚ Rn.
3. Conclude that the only extreme points of the cube
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are the points of the form (±c, ±c, . . .±c).
4. Show that Cn is the convex hull of its extreme points.
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1 F or any x 1 2 2 there exists some 1 0 1 such that 1 1 1 1 2 1 1 In fact 1 is defined by Therefore ...View the full answer
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