If Δ = |(a11,a12,a13),(a21,a22,a23),(a31,a32,a33)| and Aij is cofactor of aij, then value of Δ is given by: (a) a11A31 + a12A32 + a13A33

Question

If Δ = \( \begin{vmatrix} a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33} \end{vmatrix}\) and A_ij is cofactor of a_ij, then value of Δ is given by: 

(a) a₁₁A₃₁ + a₁₂A₃₂ + a₁₃A₃₃ 

(b) a₁₁A₁₁ + a₁₂A₂₁ + a₁₃A₃₁ 

(c) a₂₁A₁₁ + a₂₂A₁₂ + a₂₃A₁₃ 

(d) a₁₁A₁₁ + a₂₁A₂₁ + a₃₁A₃₁

Answer 1

(d) a₁₁A₁₁ + a₂₁A₂₁ + a₃₁A₃₁