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Question

Find the product of the matrices A and B where
A=513715111,B=112321213
Hence, solve the following equations by matrix method
x+y+2z=1
3x+2y+z=7
2x+y+3z=2

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Solution

A=513715111,B=112321213

AB=5+3+65+2+310+1+97+3107+2514+11513+212+121+3

AB=400040004

AB=4100010001

AB=4I3

B(14A)=I3

B1=14A

B1=14513715111

The given system of equation is
x+y+2z=1
3x+2y+z=7
2x+y+3z=2

This system can be written as
112321213xyz=172 or BX=C

where X=xyz,C=172

As B1 exists, the given system has a unique solution
X=B1C

X=14513715111172

xyz=145+7+67+71017+2

xyz=211x=2,y=1,z=1

Hence, the solution of given system of equation is x=2,y=1,z=1.

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