Consider the following. 1 1 0 A = 0-3 1 0 04 (a) Compute the characteristic polynomial of A. det(AAI) = -3,1,4 × (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) 1 -4 -> λη = -3 has eigenspace span (smallest -value) 0 1 0 12 = 1 has eigenspace span 0 1 3 23 = 4 has eigenspace span (largest A-value) 21 λ, has algebraic multiplicity 1 (c) Compute the algebraic and geometric multiplicity of each eigenvalue. and geometric multiplicity 1 2 has algebraic multiplicity 1 and geometric multiplicity 1 13 has algebraic multiplicity 1 and geometric multiplicity 1
Consider the following. 1 1 0 A = 0-3 1 0 04 (a) Compute the characteristic polynomial of A. det(AAI) = -3,1,4 × (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) 1 -4 -> λη = -3 has eigenspace span (smallest -value) 0 1 0 12 = 1 has eigenspace span 0 1 3 23 = 4 has eigenspace span (largest A-value) 21 λ, has algebraic multiplicity 1 (c) Compute the algebraic and geometric multiplicity of each eigenvalue. and geometric multiplicity 1 2 has algebraic multiplicity 1 and geometric multiplicity 1 13 has algebraic multiplicity 1 and geometric multiplicity 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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Transcribed Image Text:Consider the following.
1
1 0
A =
0-3 1
0 04
(a) Compute the characteristic polynomial of A.
det(AAI) = -3,1,4
×
(b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.)
1
-4
->
λη
= -3
has eigenspace span
(smallest -value)
0
1
0
12 = 1
has eigenspace span
0
1
3
23
= 4
has eigenspace span
(largest A-value)
21
λ, has algebraic multiplicity 1
(c) Compute the algebraic and geometric multiplicity of each eigenvalue.
and geometric multiplicity 1
2 has algebraic multiplicity 1
and geometric multiplicity 1
13 has algebraic multiplicity 1
and geometric multiplicity 1
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