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The adjoint of a matrix A=[(3,1,2),(4,5,...

The adjoint of a matrix `A=[(3,1,2),(4,5,-1),(3,2,-1)]` is

A

`[(-7,1,-7),(5,-9,-3),(-11,11,11)]`

B

`[(-7,5,-11),(1,-9,11),(-7,-3,11)]`

C

`[(-7,5,-11),(1,-9,11),(-7,3,11)]`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Now cofactors of matrix A are
`C_(11)=(-1)^(2)|(5,-1),(2,-1)|=+(-5-2)=-7`
`C_(12)=(-1)^(3)|(4,-1),(3,-1)|=-(-4+3)=1`
`C_(13)=(-1)^(4)|(4,5),(3,2)|=+(8-15)=-7`
`C_(21)=(-1)^(3)|(1,2),(2,-1)|=-(-1-4)=5`
`C_(22)=(-1)^(4)|(3,2),(3,-1)|=+(3-6)=-9`
`C_(23)=(-1)^(5)|(3,1),(3,2)|=-(6-3)=-3`
`=C_(31)=(-1)^(4)|(1,2),(5,-1)|=+(-1-10)=-11`
`C_(32)=(-1)^(5)|(3,2),(4,-1)|=-(3-8)=11`
`C_(33)=(-1)^(6)|(3,1),(4,5)|=+(15-4)=11`
`:. adjA=[(C_(11),C_(12),C_(13)),(C_(21),C_(22),C_(23)),(C_(31),C_(32),C_(33))]^(T)=[(-7,1,-7),(5,-9,-3),(-11,11,11)]^(T)`
`=[(-7,5,-11),(1,-9,11),(-7,-3,11)]`
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