(a) Show that the following sets are not convex: - i. S = {x € R²: x² = x² + x₁ + x₂ ≤ 4}. ii. T = {x € R²: x²-x² + x₁ + x₂ ≥ 4}.

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Chapter2: Second-order Linear Odes
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(a) Show that the following sets are not convex:
i. S = {x € R²: x² = x² + x₁ + x₂ ≤ 4}.
-
ii. T
{x € R²: x²-x² + x₁ + x₂ ≥ 4}.
=
(b) Let C be a convex set.
Prove that x ES is an extreme point of C if and only if C - {x} is convex.
Transcribed Image Text:(a) Show that the following sets are not convex: i. S = {x € R²: x² = x² + x₁ + x₂ ≤ 4}. - ii. T {x € R²: x²-x² + x₁ + x₂ ≥ 4}. = (b) Let C be a convex set. Prove that x ES is an extreme point of C if and only if C - {x} is convex.
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