082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

8.9 Application to the solution of simultaneous equations 283
EXERCISES8.8
1 Find adj(A), |A| and, ifitexists,A −1 ,if
⎛ ⎞
2 −3 1
(a) A= ⎝5 4 1⎠
2 −2 −1
⎛ ⎞
3 1 0
(b) A= ⎝2 −1 1⎠
5 5 −7
⎛ ⎞
2 −1 4
(c) A= ⎝5 −2 9⎠
3 2 −1
⎛ ⎞
10 −5 −4
2 IfP= ⎝−5 10 −3⎠,find adj(P)and |P|.
−4 −3 8
DeduceP −1 .
Solutions
1 (a) |A| = −43
⎛ ⎞
−2 −5 −7
adj(A) = ⎝ 7 −4 3 ⎠ ,
−18 −2 23
⎛ ⎞
A −1 = 1 25 7
⎝ −74 −3 ⎠
43
18 2 −23
(b) |A| = 25
⎛ ⎞
2 7 1
adj(A) = ⎝19 −21 −3⎠,
15 −10 −5
⎛ ⎞
A −1 = 1 2 7 1
⎝19 −21 −3⎠
25
15 −10 −5
(c) |A| = 0
⎛
⎞
−16 7 −1
adj(A) = ⎝ 32 −14 2 ⎠
16 −7 1
A −1 does notexist.
2 |P| = 230
⎛ ⎞
71 52 55
adj(P) = ⎝52 64 50⎠
55 50 75
⎛ ⎞
P −1 = 1 71 52 55
⎝52 64 50⎠
230
55 50 75
8.9 APPLICATIONTOTHESOLUTIONOFSIMULTANEOUS
EQUATIONS
Thematrixtechniqueswehavedevelopedallowthesolutionofsimultaneousequations
tobefound inasystematic way.
Example8.31 Useamatrix methodtosolve the simultaneousequations
2x+4y=14
x−3y=−8
(8.6)
Solution We first notethatthe systemofequationscan bewritteninmatrix form asfollows:
( ( ) 2 4 x
=
1 −3)
y
( ) 14
−8
(8.7)