Let 3 4. 3. A = -3 -5 -3 and B -4 -6 -3 3 3 1 3 3 1 For this problem, you may use the fact that both matrices have the same characteristic polynomial: PA(A) = PB(A) = -( – 1)(A+ 2)°. (a) Find all eigenvectors of A. (b) Find all eigenvectors of B. (c) Which matrix A or Bis diagonalizable?

Let 3 4. 3. A = -3 -5 -3 and B -4 -6 -3 3 3 1 3 3 1 For this problem, you may use the fact that both matrices have the same characteristic polynomial: PA(A) = PB(A) = -( – 1)(A+ 2)°. (a) Find all eigenvectors of A. (b) Find all eigenvectors of B. (c) Which matrix A or Bis diagonalizable?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let
1
3
4.
A =
-5
-3 and B =
-4
-6
-3
3
1
3
1
For this problem, you may use the fact that both matrices have the same characteristic polynomial:
PA(A) = PB(A) = -(A – 1)(A+2)².
(a) Find all eigenvectors of A.
(b) Find all eigenvectors of B.
(C) Which matrix A or Bis diagonalizable?
(d) Diagonalize the matrix stated in (C), i.e., find an invertible matrix P and a diagonal matrix D such that A = PDP
B= PDP 1.
1
or
%3D
%3D

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