2. Consider the quadratic form Q(r)=-6s²-10st-61². (i) Find the corresponding symmetric matrix. (ii) Find the eigenvalues of the symmetric matrix in part (i). (iii) Find an orthogonal matrix P such that P-¹AP is diagonal. (iv) Find the corresponding diagonal quadratic form in terms of the variable t = C where w =pTr.
2. Consider the quadratic form Q(r)=-6s²-10st-61². (i) Find the corresponding symmetric matrix. (ii) Find the eigenvalues of the symmetric matrix in part (i). (iii) Find an orthogonal matrix P such that P-¹AP is diagonal. (iv) Find the corresponding diagonal quadratic form in terms of the variable t = C where w =pTr.
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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![2. Consider the quadratic form Q(r) = -6s² - 10st - 6t².
(i) Find the corresponding symmetric matrix.
(ii) Find the eigenvalues of the symmetric matrix in part (i).
(iii) Find an orthogonal matrix P such that P-¹AP is diagonal.
(iv) Find the corresponding diagonal quadratic form in terms of the variable w =
-C].
where w=
PT r.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54903188-3123-4405-bb5c-a094dfbdd215%2Fa71ac6e7-23d0-4216-aed6-c9c02d69d4b2%2Fibobxb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Consider the quadratic form Q(r) = -6s² - 10st - 6t².
(i) Find the corresponding symmetric matrix.
(ii) Find the eigenvalues of the symmetric matrix in part (i).
(iii) Find an orthogonal matrix P such that P-¹AP is diagonal.
(iv) Find the corresponding diagonal quadratic form in terms of the variable w =
-C].
where w=
PT r.
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