Problem 3. Consider the matrices 2 0 0 0 0 1 3 -1 3 -1 A = В 0 -1 0 0 -1 3 3 0 0 2 (a) Show that A and B have the same eigenvalues, but have different eigenspaces. (b) Find invertible matrices P and Q and a diagonal matrix A such that A and B factor as A = PAP¯' and B = QAQ-', or explain why this is not possible.
Problem 3. Consider the matrices 2 0 0 0 0 1 3 -1 3 -1 A = В 0 -1 0 0 -1 3 3 0 0 2 (a) Show that A and B have the same eigenvalues, but have different eigenspaces. (b) Find invertible matrices P and Q and a diagonal matrix A such that A and B factor as A = PAP¯' and B = QAQ-', or explain why this is not possible.
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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Linear Methods
Transcribed Image Text:Problem 3. Consider the matrices
0 0
3 -1
0 -1
0 0
2
2
1
3 -1
A =
B =
0 1
3
3
2
2
(a) Show that A and B have the same eigenvalues, but have different eigenspaces.
(b) Find invertible matrices P and Q and a diagonal matrix A such that A and B
factor as A = PAP-' and B = QAQ¬', or explain why this is not possible.
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