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Consider the following. 1 2₂ = A = (a) Compute the characteristic polynomial of A. det(A-AI) = -2³ +22² + 192-20 22= 0 0 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) 46 23= 10 4 1 05 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 3 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)

Consider the following. 1 2₂ = A = (a) Compute the characteristic polynomial of A. det(A-AI) = -2³ +22² + 192-20 22= 0 0 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) 46 23= 10 4 1 05 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 3 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section: Chapter Questions
Problem 9RQ
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Consider the following. 1 2₂ = A = (a) Compute the characteristic polynomial of A. det(A-AI) = -2³ +22² + 192-20 22= 0 0 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) 46 23= 10 4 1 05 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 3 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)
Transcribed Image Text:Consider the following. 1 2₂ = A = (a) Compute the characteristic polynomial of A. det(A-AI) = -2³ +22² + 192-20 22= 0 0 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) 46 23= 10 4 1 05 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 3 has algebraic multiplicity and geometric multiplicity (smallest λ-value) (largest λ-value)
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