Consider the quadratic form $ F(x_1, x_2, x_3) = 25x_1^2 + 34x_2^2 + 41x_3^2 - 24x_2x_3 $.a) [Struck-through text present]b) Find a set of orthonormal eigenvectors for $ A $.c) With the results of (b), form a normalized modal matrix $[Q]$ and determine the product $[Q][Q]^T$.

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Answered: Consider the quadratic form F(X₁, X₁₂,…

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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Consider the quadratic form F(X₁, X₁₂, X 3) = 25X² +34X² +41 X² - - 24 X₂ X3 at while I as = [X² [A]{X F Who A is a symmetic mat where b) Find a set of orthinormal eigen vectors for A 4) With the results of (b), form a normalized modal matri [Q] and determine the product [P] [Q]