Determinants and Matrices — Maths STD 11 Science — Question

Expansion along the second column

$\begin{aligned} & =a_{12} C_{12}+a_{22} C_{22}+a_{32} C_{32} \\ & =(-1) \times(-1)^{1+2}\left|\begin{array}{rr}3 & -2 \\ 0 & -2\end{array}\right| \\ & +(2) \times(-1)^{2+2}\left|\begin{array}{rr}1 & 2 \\ 0 & -2\end{array}\right|+(1) \times(-1)^{3+2}\left|\begin{array}{rr}1 & 2 \\ 3 & -2\end{array}\right|\end{aligned}$

$\begin{aligned} & =1(-6-0)+2(-2-0)-1(-2-6) \\ & =1(-6)+2(-2)-1(-8)\end{aligned}$

$\begin{aligned} & =-6-4+8 \\ & =-2\end{aligned}$