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A2. Use Bordered Hessians to determine the sign properties (definiteness) of the following con- strained quadratic forms: (i) Q(x₁, x2, x3) = −x² + x² + x² + 4x1x2 – 2x1x3 subject to x₁+x2+x3 = 0 and −x1+x2+x3 = 0, (ii) Q(x, y, z) = −x² + y² − 6xz + 4yz subject to −x + y + z = 0.

A2. Use Bordered Hessians to determine the sign properties (definiteness) of the following con- strained quadratic forms: (i) Q(x₁, x2, x3) = −x² + x² + x² + 4x1x2 – 2x1x3 subject to x₁+x2+x3 = 0 and −x1+x2+x3 = 0, (ii) Q(x, y, z) = −x² + y² − 6xz + 4yz subject to −x + y + z = 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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A2. Use Bordered Hessians to determine the sign properties (definiteness) of the following con- strained quadratic forms: (i) Q(x₁, x2, x3) = −x² + x² + x² + 4x1x2 − 2x1x3 subject to x₁+x2+x3 0, (ii) Q(x, y, z) = −x² + y² − 6xz + 4yz subject to −x + y + z = 0. 0 and -x1+x2+x3 =
Transcribed Image Text:A2. Use Bordered Hessians to determine the sign properties (definiteness) of the following con- strained quadratic forms: (i) Q(x₁, x2, x3) = −x² + x² + x² + 4x1x2 − 2x1x3 subject to x₁+x2+x3 0, (ii) Q(x, y, z) = −x² + y² − 6xz + 4yz subject to −x + y + z = 0. 0 and -x1+x2+x3 =
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