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Determine the definiteness of the following constrained quadratics: a) Q(x₁, x₂) = x² + 2x₁x2x2, subject to x₁ + x₂ = 0.

Determine the definiteness of the following constrained quadratics: a) Q(x₁, x₂) = x² + 2x₁x2x2, subject to x₁ + x₂ = 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Determine the definiteness of the following constrained quadratics:

Determine the definiteness of the following constrained quadratics: a) Q(x₁, x₂) = x² + 2x₁x₂x2, subject to x₁ + x₂ = 0. b) Q(x₁, x₂) = 4x + 2x₁x2x2, subject to x₁ + x₂ = 0. c) Q(x₁, x2, x3) = x² + x² − x} + 4x₁x3 − 2x₁x2, subject to x₁ + x₂ + x3 = 0 and x₁ + x₂x3 = 0. d) Q(x1, x2, X3) = x² + x² + x² + 4x₁x3 - 2x₁x2, subject to x₁ + x₂ + x3 = 0 and x₁ + x₂x3 = 0. e) Q(x₁, x2, x3) = x² − x² + 4x₁x₂ − 6x2x3, subject to x₁ + x₂ - x3 = 0. -
Transcribed Image Text:Determine the definiteness of the following constrained quadratics: a) Q(x₁, x₂) = x² + 2x₁x₂x2, subject to x₁ + x₂ = 0. b) Q(x₁, x₂) = 4x + 2x₁x2x2, subject to x₁ + x₂ = 0. c) Q(x₁, x2, x3) = x² + x² − x} + 4x₁x3 − 2x₁x2, subject to x₁ + x₂ + x3 = 0 and x₁ + x₂x3 = 0. d) Q(x1, x2, X3) = x² + x² + x² + 4x₁x3 - 2x₁x2, subject to x₁ + x₂ + x3 = 0 and x₁ + x₂x3 = 0. e) Q(x₁, x2, x3) = x² − x² + 4x₁x₂ − 6x2x3, subject to x₁ + x₂ - x3 = 0. -
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