4.2. Let x be an element of a convex set S. Assume that x = x...

 

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4.2. Let x be an element of a convex set S. Assume that x₁ = x + 1 = Sand x₂ = x - €₂p E S, where p = 0 and 1, 2 > 0. Prove that x is a convex combination of x₁ and x2. That is, prove that x = ax₁ + (1 - α)x₂, where 0 < a < 1, and determine the value of a. 4.2. Let x be an element of a convex set S. Assume that x₁ = x + 1 = Sand x₂ = x - €₂p E S, where p = 0 and 1, 2 > 0. Prove that x is a convex combination of x₁ and x2. That is, prove that x = ax₁ + (1 - α)x₂, where 0 < a < 1, and determine the value of a.

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ANS WER We have x x1 P and x ... View the full answer