Suppose that A is a 3 x 3. Use the information in the table below to find the characteristic polynomial of A and to determine if A is diagonalizable. If it is, find P, D so that A = PDP-. If not, explain why. Eigenvalue Basic Eigenvectors 0. d1= 0 12 = 1 (1) So CA(x) = (ii) Circle and complete one of the following options.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
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Suppose that A is a 3 x 3. Use the information in the table below to find the characteristic polynomial of A
and to determine if A is diagonalizable. If it is, find P, D so that A = PDP-. If not, explain why.
Eigenvalue Basic Eigenvectors
0.
d1 = 0
1
1
0.
d2 = 1
1
1
(1) So C'a(x) =
(ii) Circle and complete one of the following options.
• A is diagonalizable with P =
D =
A is not diagonalizable because... (Complete the sentence to provide an explanation for your
selection.)
Transcribed Image Text:Suppose that A is a 3 x 3. Use the information in the table below to find the characteristic polynomial of A and to determine if A is diagonalizable. If it is, find P, D so that A = PDP-. If not, explain why. Eigenvalue Basic Eigenvectors 0. d1 = 0 1 1 0. d2 = 1 1 1 (1) So C'a(x) = (ii) Circle and complete one of the following options. • A is diagonalizable with P = D = A is not diagonalizable because... (Complete the sentence to provide an explanation for your selection.)
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