Consider the following. *-[49] A = (a) Compute the characteristic polynomial of A. det(A-AI) = (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) A₁ = 2₂= has eigenspace span has eigenspace span (c) Compute the algebraic and geometric multiplicity of each eigenvalue. (smallest λ-value) (largest λ-value)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the following.
A =
det(A - AI) =
(a) Compute the characteristic polynomial of A.
16
2₂₁ = [
2₂=
8
(b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.)
has eigenspace span
has eigenspace span
11
(c) Compute the algebraic and geometric multiplicity of each eigenvalue.
A has algebraic multiplicity
and geometric multiplicity
A has algebraic multiplicity
and geometric multiplicity
(smallest λ-value)
(largest λ-value)
Transcribed Image Text:Consider the following. A = det(A - AI) = (a) Compute the characteristic polynomial of A. 16 2₂₁ = [ 2₂= 8 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) has eigenspace span has eigenspace span 11 (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A has algebraic multiplicity and geometric multiplicity A has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)
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