Consider the following. (a) Compute the characteristic polynomial of A. det(A - AI) = -2³ +72² +172 +9 A₁ = A = (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) ^₂ = 4 05 6-1 6 5 04 23 = has eigenspace span has eigenspace span has eigenspace span ↓↑ (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A₁ has algebraic multiplicity and geometric multiplicity ₂ has algebraic multiplicity and geometric multiplicity 13 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)
Consider the following. (a) Compute the characteristic polynomial of A. det(A - AI) = -2³ +72² +172 +9 A₁ = A = (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) ^₂ = 4 05 6-1 6 5 04 23 = has eigenspace span has eigenspace span has eigenspace span ↓↑ (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A₁ has algebraic multiplicity and geometric multiplicity ₂ has algebraic multiplicity and geometric multiplicity 13 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question

Transcribed Image Text:Consider the following.
(a) Compute the characteristic polynomial of A.
det(A - AI) = -2³ +72² +172 +9
A₁ =
A =
(b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.)
^₂ =
4 05
6-1 6
5 04
23 =
has eigenspace span
has eigenspace span
has eigenspace span
↓ 1
(c) Compute the algebraic and geometric multiplicity of each eigenvalue.
A₁ has algebraic multiplicity
and geometric multiplicity
₂ has algebraic multiplicity
and geometric multiplicity
13 has algebraic multiplicity
and geometric multiplicity
(smallest λ-value)
(largest λ-value)
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