Find an orthogonal matrix P that orthogonally reduces the quadratic form Q(x) = x" Ax sa} + 3.x3 + 2x3 x1x2 + 8x2x3 to the standard form y = = P-lx, 1 -1/2 07 Q(y) = A1yỉ + + \3y3, where A = |-1/2 3 4 .. 4
Find an orthogonal matrix P that orthogonally reduces the quadratic form Q(x) = x" Ax sa} + 3.x3 + 2x3 x1x2 + 8x2x3 to the standard form y = = P-lx, 1 -1/2 07 Q(y) = A1yỉ + + \3y3, where A = |-1/2 3 4 .. 4
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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![Find an orthogonal matrix P that orthogonally reduces the quadratic form Q(x) =
x" Ax
sa} + 3.x3 + 2x3
x1x2 + 8x2x3 to the standard form y =
= P-lx,
1
-1/2 07
Q(y) = A1yỉ +
+ \3y3, where A = |-1/2
3
4
..
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84a33e96-9ade-4ce8-b2bb-410c01096350%2F1a73f144-0531-4495-8596-8eed8f41e495%2F7egyvd7.bmp&w=3840&q=75)
Transcribed Image Text:Find an orthogonal matrix P that orthogonally reduces the quadratic form Q(x) =
x" Ax
sa} + 3.x3 + 2x3
x1x2 + 8x2x3 to the standard form y =
= P-lx,
1
-1/2 07
Q(y) = A1yỉ +
+ \3y3, where A = |-1/2
3
4
..
4
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