B = 5 3 -3 -2 1\ 0 1 2 1
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
Only (ii) please.
Transcribed Image Text:4. Let
A =
3
-1
6
2 2
0 −1
6 7
2
B =
5
3
-3
-2
2
1
1
1
.
(i) Show that A is diagonalizable. Find a basis of R³ consisting of eigenvectors of A. Write
down an invertible matrix P and a diagonal matrix D such that D = P-¹AP.
(ii) Find the eigenvalues and bases of the eigenspaces of B, and show that B is not diagonalizable.
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