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A = 0 0 be a symmetric matrix. (1) Orthogonally diagonalize A (that is, find an orthogonal matrix P and a diagonal matrix D such that P-¹AP = D. (2) Write the quadratic form Q(x) given by A in terms of a function in 1, 2, 3. Determine the type of this quadratic form (for the type, you only need to give an answer as positive-definite, negative-definite or indefinite).

A = 0 0 be a symmetric matrix. (1) Orthogonally diagonalize A (that is, find an orthogonal matrix P and a diagonal matrix D such that P-¹AP = D. (2) Write the quadratic form Q(x) given by A in terms of a function in 1, 2, 3. Determine the type of this quadratic form (for the type, you only need to give an answer as positive-definite, negative-definite or indefinite).

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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Must solve both the questions strictly. Dont solve it partially. 

1 4 --09 A = 4 -50 003 be a symmetric matrix. (1) Orthogonally diagonalize A (that is, find an orthogonal matrix P and a diagonal matrix D such that P-¹AP = D. (2) Write the quadratic form Q(x) given by A in terms of a function in 1, 2, 3. Determine the type of this quadratic form (for the type, you only need to give an answer as positive-definite, negative-definite or indefinite).
Transcribed Image Text:1 4 --09 A = 4 -50 003 be a symmetric matrix. (1) Orthogonally diagonalize A (that is, find an orthogonal matrix P and a diagonal matrix D such that P-¹AP = D. (2) Write the quadratic form Q(x) given by A in terms of a function in 1, 2, 3. Determine the type of this quadratic form (for the type, you only need to give an answer as positive-definite, negative-definite or indefinite).
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