the diagonal matrix containing the eigenvalues 2 and
5 of A as the principal diagonal elements.
T
o find A
6
6
661
6
112011
1
2121
3
05
1164011
1
210625021
3
641562511
1
12811562521
3
3131415561104385187
1
3112215753103745251
3
APDP
−
⎡⎤
−
⎡⎤⎡⎤
==
⎢⎥
⎢⎥⎢⎥
−
⎣⎦⎣⎦
⎢⎥
⎣⎦
−
⎡⎤⎡⎤⎡⎤
=
⎢⎥⎢⎥⎢⎥
−
⎣⎦⎣⎦⎣⎦
−
⎡⎤⎡⎤
=
⎢⎥⎢⎥
−
⎣⎦⎣⎦
⎡⎤⎡⎤
==
⎢⎥⎢⎥
⎣⎦⎣⎦
Example 2.15
Diagonalise
161
120
003
A
⎡⎤
⎢⎥
=
⎢⎥
⎢⎥
⎣⎦
and hence find A
8
. Find
the modal matrix.
SolutionThe matrix A can be diagonalised ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month, and much more.