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Solve the following equations by matrix inversion method : x + y + z = 6, 3x - y + 3z = 10 , 5x + 5y -4z = 3
1 Answer
written 5.6 years ago by |
Solution:
LetA=[1113−1355−4],B=[6103],X=[xyz]
|A|=|1113−1355−4|
|A|=1(4−15)−1(−12−15)+1(15+5)
∴|A|=36≠0
∴A−1exists
Matrixofminors=[|−135−4||335−4||3−255||115−4||115−4||1155||11−13||1133||113−1|]
Matrixofminors=[−11−2720−9−9040−4]
Matrixofcofactors=[−1127209−9040−4]
Adj.A=[−119427−90200−4]A−1=1|A| Adj. A
A−1=136[−119427−90200−4]
∴X=A−1B
[xyz]=136[−119427−90200−4][6103]
[xyz]=136[−66+90+12162−90+0120+0−12]
[xyz]=136[3672108]=[123]
∴x=1,y=2,z=3