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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
1-36 Mathematical Methods
111
222
333
Let
abc
Aabc
abc
⎡⎤
⎢⎥
=
⎢⎥
⎢⎥
⎣⎦
and A
i
, B
i
, C
i
denote the cofactors of elements a
i
, b
i
,
c
i
(i = 1, 2, 3), respectively.
12
31
23
12
52 12
21; 21
77 77
12 2 2
12; 12;
52 17
12 12
9; 6;
17 22
25 11
9; 6;
17 17
AA
AB
BB
CC
=+ =− =− =+
−−
=+ =− =− =
−−
=+ =− =− =
−−
=+ = =− =−
3
11
3;
25
C =+ =
det A = a
1
A
1
+ a
2
A
2
+ a
3
A
3
= 1· (21) + 2 · 21 + 1 ·
(12) = 9 0
So,
1
det
Adj A
A
A
=
exists and is equal to
1
21 21 12
1
12 9 6
9
963
77 4
1
432
3
321
A
−−
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎣⎦
−−
⎡⎤
⎢⎥
=−
⎢⎥
⎢⎥
⎣⎦
Solution is
1
1
2
3
77 44 9
1
4 3 2 3 17 3
3
3 2 1 5 11 3
x
Xx AB
x
−−
⎡⎤
⎡⎤⎡⎤⎡⎤
⎢⎥
⎢⎥⎢⎥⎢⎥
== == =
⎢⎥
⎢⎥⎢⎥⎢⎥
⎢⎥
⎢⎥⎢⎥⎢⎥
⎣⎦⎣⎦⎣⎦
⎣⎦
i.e., x
1
= 9; x
2
= 17/3; x
3
= 11/3.
1.15.3 Method 3: Gauss’s
Elimination Method ...
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Publisher Resources

ISBN: 9781299446557Publisher Website