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. Let A = -3 the matrix A. 93). Is it true that A is orthogonally diagonalizable? If yes, orthogonally diagonalize

. Let A = -3 the matrix A. 93). Is it true that A is orthogonally diagonalizable? If yes, orthogonally diagonalize

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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1. Let A = -3 5). Is it true that A is orthogonally diagonalizable? If yes, orthogonally diagonalize the matrix A. 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 = D where w = PT r.
Transcribed Image Text:1. Let A = -3 5). Is it true that A is orthogonally diagonalizable? If yes, orthogonally diagonalize the matrix A. 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 = D where w = PT r.
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