Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the following matrix. [ ] 2 -3 2 0 The characteristic equation is The eigenvalue X is A = A basis for the eigenspace is ?) = 0

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CR: Review Exercises
Problem 15CR: For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of...
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Suppose that a 4 x 4 matrix A has eigenvalues A₁ = 1, A2= -7, A3-9, and A4-9. Use the following method to find det (A).
If
So, on setting A = 0, we obtain that
det (A) = i
Find the characteristic equation, the eigenvalues,
and bases for the eigenspaces of the following matrix.
A
=
[
The characteristic equation is
2 -3
2
1
p(A) = det (Al-A) = A +₁^²-¹ ++ Cn
0
det (-A) = C₁ or det (A) = (-1)^cn
The eigenvalue A is
A basis for the eigenspace is
?
= 0
Transcribed Image Text:Suppose that a 4 x 4 matrix A has eigenvalues A₁ = 1, A2= -7, A3-9, and A4-9. Use the following method to find det (A). If So, on setting A = 0, we obtain that det (A) = i Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the following matrix. A = [ The characteristic equation is 2 -3 2 1 p(A) = det (Al-A) = A +₁^²-¹ ++ Cn 0 det (-A) = C₁ or det (A) = (-1)^cn The eigenvalue A is A basis for the eigenspace is ? = 0
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