Find an orthogonal matrix P that diagonalizes matrix A. 1 0 1 0 1 0 1 0 1 Also, find the diagonal matrix D: D = P-¹AP A = SCH
Find an orthogonal matrix P that diagonalizes matrix A. 1 0 1 0 1 0 1 0 1 Also, find the diagonal matrix D: D = P-¹AP A = SCH
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 26CM: Find an orthogonal matrix P such that PTAP diagonalizes the symmetric matrix A=[1331].
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Explanation along with answer is appreciated, thank you.
Transcribed Image Text:Find an orthogonal
matrix P that diagonalizes matrix A.
1 0 1
0 1 0
1 0 1
Also, find the diagonal matrix D: D = P-¹AP
A =
Transcribed Image Text:0
0
P= 0 1
0
D =
P=
D
||
||
P=
D =
√2
00
000
00
2
5 0 13 0oo
0
1
0
00
00
√5
0
1
SM
訂
120
「言。
1
V3
0.10
J
02.
0
信】
0 1
0
2
1
0
計
V2
000
010
V3
0 1 0
0
V2
00
02 0
0
,
2
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