Maharashtra State BoardHSC Arts 12th Board Exam
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If A^-1=1/3(1,4,-2),(-2,-5,4),(1,-2,1) and | a | = 3, Then (Adj. A) = - Mathematics and Statistics

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MCQ

If `A^-1=1/3[[1,4,-2],[-2,-5,4],[1,-2,1]]` and | A | = 3, then (adj. A) = _______

Options

  • `1/9[[1,4,-2],[-2,-5,4],[1,-2,1]]`

  • `[[1,-2,1],[4,-5,-2],[-2,4,1]]`

  • `[[1,4,-2],[-2,-5,4],[1,-2,1]]`

  • `[[-1,-4,2],[2,5,-4],[1,-2,1]]`

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Solution

(C)

`A^-1=1/|A|(adjA)`

`1/3[[1,4,-2],[-2,-5,4],[1,-2,1]]=1/3(adjA)`

`(adjA)=[[1,4,-2],[-2,-5,4],[1,-2,1]]`

Concept: Determinants - Adjoint Method
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