3. Use the definition of a convex set to show that if S₁ and S₂ are convex sets in R+", then so is their partial sum S = {(x,y₁ + y₂) | ER",3₁,32 € R"; (a; y₁) € S₁, (x, y2) € S₂}.

Elementary Linear Algebra (MindTap Course List)
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ISBN:9781305658004
Author:Ron Larson
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Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 48E: Let R be the set of all infinite sequences of real numbers, with the operations...
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3. Use the definition of a convex set to show that if S₁ and S₂ are convex sets in Rm+n, then so is their
partial sum
S = {(x, y₁ + y2) | ER",1,32 € R"; (2; y₁) € S₁, (x, y2) € S₂}.
Transcribed Image Text:3. Use the definition of a convex set to show that if S₁ and S₂ are convex sets in Rm+n, then so is their partial sum S = {(x, y₁ + y2) | ER",1,32 € R"; (2; y₁) € S₁, (x, y2) € S₂}.
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