-1 3 3 -1 0 0 0 0 3 Find the eigenvalues and an orthonormal basis for each eigenspace. A₁ = -4 The matrix M = = 0 0 0 0 -1 3 has two distinct eigenvalues λι < λ Orthonormal basis of eigenspace: [1,1,0,0], [0,0,1,1] A₂ = 2₁ A2 Orthonormal basis of eigenspace: [-1,1,0,0], [0,0,-1,1]

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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3
3
-1
0
0
0 0
Find the eigenvalues and an orthonormal basis for each eigenspace.
A₁ = -4
The matrix M = =
0
0
-1
0
0
3
3 -1
has two distinct eigenvalues λι <dg
Orthonormal basis of eigenspace: [1,1,0,0], [0,0,1,1]
A₂ = 2.
A2
Orthonormal basis of eigenspace: [-1,1,0,0], [0,0,-1,1]
Transcribed Image Text:3 3 -1 0 0 0 0 Find the eigenvalues and an orthonormal basis for each eigenspace. A₁ = -4 The matrix M = = 0 0 -1 0 0 3 3 -1 has two distinct eigenvalues λι <dg Orthonormal basis of eigenspace: [1,1,0,0], [0,0,1,1] A₂ = 2. A2 Orthonormal basis of eigenspace: [-1,1,0,0], [0,0,-1,1]
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