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If Delta=|(a(11), a(12), a(13) ),(a(21)...

If `Delta=|(a_(11), a_(12), a_(13) ),(a_(21), a_(22), a_(23)),(a_(31), a_(32), a_(33))|` and `A_(i j)` is cofactors of `a_(i j)` , then value of `Delta` is given by
(A) `a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33)`
(B) `a_(11)A_(11)+a_(12)A_(21)+a_(13)A_(31)`
(C) `a_(21)A_(11)+a_(22)A_(12)+a_(23)A_(13)`
(D) `a_(11)A_(11)+a_(21)A_(21)+a_(31)A_(31)`

Text Solution

Verified by Experts

The correct Answer is:
(d)
The value o a determinant is equal to the sum of the product of the elements of a row or columen and their corresponding cofactors.
`Delta=a_(11)A_(11)++a_(21)A_(21)+a_(31)A_(31)`
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