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

To determine the definiteness of the quadratic forms subject to the given constraints, we can use…

Answered: Q(x₁, x2, x3) = x² + x² + x² + 4x₁x2 −…

Q(x₁, x2, x3) = x² + x² + x² + 4x₁x2 − 2x13 subject to x1+x2+x3 = 0 and -x₁+x2+x3 = 0, Q(x, y, z) = x² + y² - 6xz + 4yz subject to -x + y +z = 0.

Elementary Algebra

17th Edition

ISBN:9780998625713

Author:Lynn Marecek, MaryAnne Anthony-Smith

Publisher:Lynn Marecek, MaryAnne Anthony-Smith

Chapter10: Quadratic Equations

Section: Chapter Questions

Problem 332PT: Use the discriminant to determine the number of solutions of each quadratic equation. 332....

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Question

can you please provide explanations

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

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