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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]

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]

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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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 \([Q][Q]^T\).
Transcribed Image Text: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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