On expanding d 1strow d value of a 3rd order determinant is a11A11+a12A12+a13A13 Write d expansion for its value on - Maths - Vector Algebra

Question

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
PLSSSSSSSSSSANSWER DIS FAST

Manbar Singh · Accepted Answer

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

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.PLSSSSSSSSSSANSWER DIS FAST ...

On expanding d 1^strow d value of a 3^rd order determinant is a₁₁A₁₁+a₁₂A₁₂+a₁₃A_13.Write d expansion for its value on expanding by 2^nd column, where A_ij is d cofactor of element a_ij.
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