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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)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 35EQ
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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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