Consider the following. -4 32 0 HEB A = -1 91 0 (a) Compute the characteristic polynomial of A. det(A - AI) = (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) 2₁ = 11 2₂ = has eigenspace span has eigenspace span 11 41 (smallest λ-value)

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
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Consider the following.
21
A =
22
32 0
9 1
0 1 1
(a) Compute the characteristic polynomial of A.
det(A - AI) =
23
-1
(b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.)
C
has eigenspace span
has eigenspace span
has eigenspace span
11
(c) Compute the algebraic and geometric multiplicity of each eigenvalue.
A has algebraic multiplicity 1
2, has algebraic multiplicity 1
1, has algebraic multiplicity 11
(smallest λ-value)
(largest λ-value)
X and geometric multiplicity 1
X and geometric multiplicity 1
and geometric multiplicity 1
Transcribed Image Text:Consider the following. 21 A = 22 32 0 9 1 0 1 1 (a) Compute the characteristic polynomial of A. det(A - AI) = 23 -1 (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) C has eigenspace span has eigenspace span has eigenspace span 11 (c) Compute the algebraic and geometric multiplicity of each eigenvalue. A has algebraic multiplicity 1 2, has algebraic multiplicity 1 1, has algebraic multiplicity 11 (smallest λ-value) (largest λ-value) X and geometric multiplicity 1 X and geometric multiplicity 1 and geometric multiplicity 1
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