he symmetric matrix A below has distinct eigenvalues −3, -6 ar ind an orthogonal matrix P and a diagonal matrix D such that TAP-DUse the square root symbol 'V' where needed to give ar Exact value for your answer. 1: = 1 1 5 1 -5 -1 5 -1 1 000 P=000 000 000 D= 000 000

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 16EQ
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The symmetric matrix A below has distinct eigenvalues −3, −6 and 6.
Find an orthogonal matrix P and a diagonal matrix D such that
PTAP-DUse the square root symbol 'V' where needed to give an
exact value for your answer.
1 1 5
A = 1 -5 -1
5 -1 1
000
P=000
000
000
000
000
D = 0
Transcribed Image Text:The symmetric matrix A below has distinct eigenvalues −3, −6 and 6. Find an orthogonal matrix P and a diagonal matrix D such that PTAP-DUse the square root symbol 'V' where needed to give an exact value for your answer. 1 1 5 A = 1 -5 -1 5 -1 1 000 P=000 000 000 000 000 D = 0
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