7 20 -10 Let A = 20 7 10 Find an orthogonal matrix P with rational entries and a diagonal matrix D -10 10 22 such that DPTAP.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.4: Orthogonal Diagonalization Of Symmetric Matrices
Problem 27EQ
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Question
7
20
-10]
Let A =
20
7
10
-10
10
22
such that DPTAP.
Find an orthogonal matrix P with rational entries and a diagonal matrix D
2
1
12
-18
0
0
P =
D =
0
27
0
-2
1
0
Note: You'll probably need to do a little bit of
0
0
27
1
0
1
extra work to ensure that each entry in P is a rational number.
Transcribed Image Text:7 20 -10] Let A = 20 7 10 -10 10 22 such that DPTAP. Find an orthogonal matrix P with rational entries and a diagonal matrix D 2 1 12 -18 0 0 P = D = 0 27 0 -2 1 0 Note: You'll probably need to do a little bit of 0 0 27 1 0 1 extra work to ensure that each entry in P is a rational number.
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