1) (a) Find an orthogonal matrix P and a diagonal matrix D such that 2 -2 PDP": 5 -4 2 -2 -4 5 (b) Use your answer to part (a) to write the quadratic form Q(r, y, z) as a sum of only square terms, where Q(x, y, z) = 2x² + 5y² + 52² + 4.ry – 4rz – 8yz.

1) (a) Find an orthogonal matrix P and a diagonal matrix D such that 2 -2 PDP": 5 -4 2 -2 -4 5 (b) Use your answer to part (a) to write the quadratic form Q(r, y, z) as a sum of only square terms, where Q(x, y, z) = 2x² + 5y² + 52² + 4.ry – 4rz – 8yz.

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) (a) Find an orthogonal matrix P and a diagonal matrix D such that
2
2 -2
PDP" =
2
4
-2 -4
5
(b) Use your answer to part (a) to write the quadratic form Q(x, y, z) as a sum of only
square terms, where
Q(x, y, z) = 2x² + 5y² + 5z² + 4.xy – 4.rz – 8yz.

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