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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
2-18 Mathematical Methods
The modal matrix which diagonalises A is
11
21
P
⎡⎤
=
⎢⎥
⎣⎦
.
V
erifi cation
1
1
11
1
21
3
1141 11
1
21 23 21
3
2211
1
05 21
3
60 20
1
,
015 05
3
P
PAP
D
⎡⎤
=
⎢⎥
⎣⎦
⎡⎤⎡⎤⎡⎤
⇒=
⎢⎥⎢⎥⎢⎥
−−
⎣⎦⎣⎦⎣⎦
⎡⎤⎡⎤
=
⎢⎥⎢⎥
⎣⎦⎣⎦
⎡⎤⎡⎤
===
⎢⎥⎢⎥
⎣⎦⎣⎦
the diagonal matrix containing the eigenvalues 2 and
5 of A as the principal diagonal elements.
T
o find A
6
6
661
6
112 0 1 1
1
21 2 1
3
05
1 1 64 0 1 1
1
2 1 0 6250 2 1
3
64 15625 1 1
1
128 115625 2 1
3
31314 15561 10438 5187
1
31122 15753 10374 5251
3
APDP
⎡⎤
⎡⎤ ⎡⎤
==
⎢⎥
⎢⎥ ⎢⎥
⎣⎦ ⎣⎦
⎢⎥
⎣⎦
⎡⎤⎡ ⎤⎡⎤
=
⎢⎥⎢ ⎥⎢⎥
⎣⎦⎣ ⎦⎣⎦
⎡⎤⎡⎤
=
⎢⎥⎢⎥
⎣⎦⎣⎦
⎡⎤⎡⎤
==
⎢⎥⎢⎥
⎣⎦⎣⎦
Example 2.15
Diagonalise
161
120
003
A
⎡⎤
⎢⎥
=
⎢⎥
⎢⎥
⎣⎦
and hence find A
8
. Find
the modal matrix.
Solution The matrix A can be diagonalised ...
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Publisher Resources

ISBN: 9781299446557Publisher Website