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EE364a Winter 2007-08 Prof. S. Boyd EE364a Homework 1 solutions 2. 1 Let C Rn be a convex set with x1. xk C and let 1. k R satisfy i 0 1 k 1. Show that 1 x1 k xk C. The definition of convexity is that this holds for k 2 you must show it for arbitrary k. Hint* Use induction on k. Solution* This is readily shown by induction from the definition of convex set. We illustrate the idea for k 3 leaving the general case to the reader. Suppose that x1 x2 x3 C and 1 2 3 1 with 1 2 3 0....

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