Find cofactors of a21 and a31 of the matrix A=[aij]=[ beginmatrix1&3&-2 4&-5&6 3&5&2 endmatrix]

Question

Find cofactors of a21 and a31 of the matrix A=[aij]=[ beginmatrix1&3&-2 4&-5&6 3&5&2 endmatrix] (A) -16, 8 (B) -16, -8 (C) 16, 8 (D) 16 , -8

Tardigrade Admin · Accepted Answer

Let Mij and Cij respectively denote the minor and cofactor of element aij in A. Then, M21=| beginmatrix3&-2 5&2 endmatrix|=6+10=16 ⇒ c21=-M21=-16 M31=| beginmatrix3&-2 -5&6 endmatrix|=18-10=8 ⇒ c31=M31=8

Q. Find cofactors of $a_{21}$ and $a_{31}$ of the matrix
$A = [a_{ij}] = ⎣ ⎡ 143 3 - 5 5 - 2 62 ⎦ ⎤$

$- 16, 8$

$- 16, - 8$

$16, 8$

$16, - 8$

Let $M_{ij}$ and $C_{ij}$ respectively denote the minor and cofactor of element $a_{ij}$ in A. Then,

$M_{21} = ∣ ∣ 35 - 2 2 ∣ ∣ = 6 + 10 = 16 \Rightarrow c_{21} = - M_{21} = - 16$

$M_{31} = ∣ ∣ 3 - 5 - 2 6 ∣ ∣ = 18 - 10 = 8 \Rightarrow c_{31} = M_{31} = 8$

Q. Find cofactors of a21​ and a31​ of the matrix A=[aij​]=⎣⎡​143​3−55​−262​⎦⎤​

−16,8

−16,−8

16,8

16,−8