Consider the following. (a) Compute the characteristic polynomial of A. det(A-AI) = 801 -106 A₁ = (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) A₂ = has eigenspace span has eigenspace span 11 has eigenspace span 11 13 41 (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A, has algebraic multiplicity and geometric multiplicity A has algebraic multiplicity and geometric multiplicity A has algebraic multiplicity and geometric multiplicity (smallest A-value) (largest X-value)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the following.
A =
801
-106
(a) Compute the characteristic polynomial of A.
det(A-AI) =
λ₂ =
(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
has eigenspace span
11
22 has algebraic multiplicity
A has algebraic multiplicity
11
11
(c) Compute the algebraic and geometric multiplicity of each eigenvalue.
A, has algebraic multiplicity
and geometric multiplicity
and geometric multiplicity
and geometric multiplicity
(smallest λ-value)
(largest λ-value)
Transcribed Image Text:Consider the following. A = 801 -106 (a) Compute the characteristic polynomial of A. det(A-AI) = λ₂ = (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 has eigenspace span 11 22 has algebraic multiplicity A has algebraic multiplicity 11 11 (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A, has algebraic multiplicity and geometric multiplicity and geometric multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)
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