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Solve the following equations by matrix inversion method : x + y + z = 6, 3x - y + 3z = 10 , 5x + 5y -4z = 3
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Solution:

LetA=[111313554],B=[6103],X=[xyz]

|A|=|111313554|

|A|=1(415)1(1215)+1(15+5)

|A|=360

A1exists

Matrixofminors=[|1354||3354||3255||1154||1154||1155||1113||1133||1131|]

Matrixofminors=[112720990404]

Matrixofcofactors=[112720990404]

Adj.A=[119427902004]A1=1|A| Adj. A

A1=136[119427902004]

X=A1B

[xyz]=136[119427902004][6103]

[xyz]=136[66+90+1216290+0120+012]

[xyz]=136[3672108]=[123]

x=1,y=2,z=3

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