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Consider the following. A = A₁ = 5 50 0 -9 1 1 1 (a) Compute the characteristic polynomial of A. det(A-AI)=-23-32² A3 = -1 0 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) (LF) has eigenspace span has eigenspace span ALF has eigenspace span (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A has algebraic multiplicity and geometric multiplicity A₂ has algebraic multiplicity and geometric multiplicity A3 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)

Consider the following. A = A₁ = 5 50 0 -9 1 1 1 (a) Compute the characteristic polynomial of A. det(A-AI)=-23-32² A3 = -1 0 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) (LF) has eigenspace span has eigenspace span ALF has eigenspace span (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A has algebraic multiplicity and geometric multiplicity A₂ has algebraic multiplicity and geometric multiplicity A3 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)

Advanced Engineering Mathematics
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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Consider the following. A₁ = A = (a) Compute the characteristic polynomial of A. det (A-AI)=-23-32² d₂= 5 50 0 -9 1 1 1 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) ^3 = -1 0 (LF has eigenspace span has eigenspace span has eigenspace span ↓1 1 (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A₁ has algebraic multiplicity and geometric multiplicity λ₂ has algebraic multiplicity and geometric multiplicity 13 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)
Transcribed Image Text:Consider the following. A₁ = A = (a) Compute the characteristic polynomial of A. det (A-AI)=-23-32² d₂= 5 50 0 -9 1 1 1 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) ^3 = -1 0 (LF has eigenspace span has eigenspace span has eigenspace span ↓1 1 (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A₁ has algebraic multiplicity and geometric multiplicity λ₂ has algebraic multiplicity and geometric multiplicity 13 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)
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