3. The eigenvalues of the matrix A= 8 5 4 are A₁ = A₂ = -3, A3 = 15. 4 I (a) (b) (c) Find the corresponding eigenspace for each eigenvalue of A. Is the matrix A diagonalizable? Explain your reasons. If A is a diagonalizable matrix, find the matrices P and D such that A = PDP-1 where D is dagonal.

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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3. The eigenvalues of the matrix A= 8 5 4 are A₁ = A₂ = -3, A3 = 15.
|4 4 −1|
Find the corresponding eigenspace for each eigenvalue of A.
I
(a)
(b)
(c)
Is the matrix A diagonalizable? Explain your reasons.
If A is a diagonalizable matrix, find the matrices P and D such that A = PDP-1 where D is dagonal.
Transcribed Image Text:8 3. The eigenvalues of the matrix A= 8 5 4 are A₁ = A₂ = -3, A3 = 15. |4 4 −1| Find the corresponding eigenspace for each eigenvalue of A. I (a) (b) (c) Is the matrix A diagonalizable? Explain your reasons. If A is a diagonalizable matrix, find the matrices P and D such that A = PDP-1 where D is dagonal.
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