1. -2 -2 Let A = -2 -2 -2 -2 1 Determine the characteristic polynomial of A: I-1 2 XA(x) = det(rI3 – A) = det 2 I-1 2 2 I-1, b) multiplicity. Factor XA(1) and determine the eigenvalues and their algebraic c) For each eigenvalue a find a basis of the eigenspace, E.(A). d) Explain why the matrix is diagonaizable. Write down a diagonal form, D, of A and a diagonalizing matrix P such that P-1AP = D.

1. -2 -2 Let A = -2 -2 -2 -2 1 Determine the characteristic polynomial of A: I-1 2 XA(x) = det(rI3 – A) = det 2 I-1 2 2 I-1, b) multiplicity. Factor XA(1) and determine the eigenvalues and their algebraic c) For each eigenvalue a find a basis of the eigenspace, E.(A). d) Explain why the matrix is diagonaizable. Write down a diagonal form, D, of A and a diagonalizing matrix P such that P-1AP = D.

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

1.
-2 -2
Let A =
-2
1
-2
-2 -2
1.
a)
Determine the characteristic polynomial of A:
2
2
XA(1) = det(rl3 – A) = det
2
I - 1
2
2
2
I - 1
b)
multiplicity.
Factor XA(r) and determine the eigenvalues and their algebraic
c)
For each eigenvalue a find a basis of the eigenspace, E.(A).
d)
Explain why the matrix is diagonaizable.
e)
P such that P-1AP = D.
Write down a diagonal form, D, of A and a diagonalizing matrix

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