Consider the following. 4 05 A = 6-16 5 04 (a) Compute the characteristic polynomial of A. det(AAI) = 0 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) 21 = has eigenspace span 12 = has eigenspace span - I t (smallest -value) 13 = has eigenspace span (largest A-value) (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A₁ has algebraic multiplicity 12 has algebraic multiplicity 13 has algebraic multiplicity | and geometric multiplicity and geometric multiplicity and geometric multiplicity

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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need help 4.3

Consider the following.
4
05
A =
6-16
5
04
(a) Compute the characteristic polynomial of A.
det(AAI) = 0
(b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.)
21
=
has eigenspace
span
12
=
has eigenspace span
-
I t
(smallest -value)
13 =
has eigenspace
span
(largest A-value)
(c) Compute the algebraic and geometric multiplicity of each eigenvalue.
A₁ has algebraic multiplicity
12 has algebraic multiplicity
13 has algebraic multiplicity |
and geometric multiplicity
and geometric multiplicity
and geometric multiplicity
Transcribed Image Text:Consider the following. 4 05 A = 6-16 5 04 (a) Compute the characteristic polynomial of A. det(AAI) = 0 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) 21 = has eigenspace span 12 = has eigenspace span - I t (smallest -value) 13 = has eigenspace span (largest A-value) (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A₁ has algebraic multiplicity 12 has algebraic multiplicity 13 has algebraic multiplicity | and geometric multiplicity and geometric multiplicity and geometric multiplicity
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