On expanding d 1strow d value of a 3rd order determinant is a11A11+a12A12+a13A13.Write d expansion for its value on expanding by 2nd column, where Aij​ is d cofactor of element aij.
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Let A = aij =a11a12a13a21a22a23a31a32a33Now, A = a11a12a13a21a22a23a31a32a33Let Aij be the cofactors of aij in A. Then the cofactors of elements of A are :A11 = -12a22.a33-a23.a32 = a22.a33-a23.a32A12 = -13a21.a33-a23.a31 = -a21.a33-a23.a31A13 = -14a21.a32-a31.a22 = a21.a32-a31.a22A21 = -13a12.a33-a13.a32 = -a12.a33-a13.a32A22 = -14a11.a33-a13.a31 = a11.a33-a13.a31A23 = -15a11.a32-a12.a31 = -a11.a32-a12.a31A31 = -14a12.a23-a13.a22 = a12.a23-a13.a22A32 = -15a11.a23-a13.a21 = -a11.a23-a13.a21A33 = -16a11.a22-a12.a21 = a11.a22-a12.a21Now, expanding the determinant along C2, we get-a12a21.a33-a23.a31 + a22a11.a33-a13.a31 - a32a11.a23-a13.a21= a12 × A12 + a22 ×A22 + a32 × A32

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a21 A21 + a22 A22 + a23 A23
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Sorry, a21 A21 + a22 A22 + a32 A32 is the correct answer
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Sorry again, I got it wrong
a12 A12 + a22 A22 + a32 A32
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