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find the adjoint of the matrix A=[(1,2,3...

find the adjoint of the matrix `A=[(1,2,3),(0,5,0),(2,4,3)]`

Text Solution

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if C be the matrix of cofactors of the elements in `|A|,` then
`C=[(C_(11),C_(12),C_(13)),(C_(21),C_(22),C_(23)),(C_(31),C_(32),C_(33))]`
`[{:(|(5,0),(4,3)|,-|(0,0),(2,3)|,|(0,5),(2,4)|),(|(2,3),(4,3)|,|(1,3),(2,3)|,-|(1,2),(2,4)|),(|(2,3),(5,0)|,-|(1,3),(0,0)|,|(1,2),(0,5)|):}]=[(15,0,-10),(6,-3,0),(-15,0,5)]`
`rArr adjA=C'=[(15,6,-15),(0,-3,0),(-10,0,5)]`
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