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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
Solved Question Papers A-71
1
[2 2 1]
T
X =−
l = 6
Eigenvector corresponding to l = 6 is obtained
by solving (A 6I ) X = 0
1
2
3
12 13
22 2 3
3
12
2
324
286 0
46 7
Equivalent system is
4: 0
2:1050
[2 1 2]
212
T
x
x
x
RR xx
RR x x
x
xx
X
−−
⎡⎤
⎡⎤
⎢⎥
⎢⎥
−− =
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎣⎦
⎣⎦
−−+=
−−+=
== =
l = 9
Eigen
v
ector cor
responding to
l = −9 is
obtained by solving (A + 9I ) X = 0
1
2
3
3
12
32 2 3
31 1 2
3
12 2 4
276 0
468
Equivalent system is
2 : 20 20 0
12 2
2 : 20 10 0
[1 2 2]
T
x
x
x
x
xx
RR x x
RR x x
X
⎡⎤
⎡⎤
⎢⎥
⎢⎥
−=
⎢⎥
⎢⎥
⎢⎥
⎢⎥
⎣⎦
⎣⎦
++===
−−+=
=−
Modal matrix with normalized eigenvectors is
3
12
123
22 1
333
212
,,
333
12 2
333
X
XX
P
XX X
⎡⎤
⎢⎥
⎢⎥
⎡⎤
⎢⎥
==
⎢⎥
⎢⎥
⎣⎦
⎢⎥
⎢⎥
⎢⎥
⎣⎦
Diagonal matrix ( P
1
= P
T
)
1
( being orthogonal)
T
P
DPAPPAP
===
A
2
6A
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Publisher Resources

ISBN: 9781299446557Publisher Website