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B = 5 3 -3 -2 1\ 0 1 2 1

B = 5 3 -3 -2 1\ 0 1 2 1

Advanced Engineering Mathematics
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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Only (ii) please.

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.
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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