Determinants — Maths STD 12 Science — Question

1. Along the first row.

$|\text{A}|=2\begin{vmatrix}1&-2\\4&1 \end{vmatrix}-3\begin{vmatrix}7&-2\\-3&1\end{vmatrix}-3\begin{vmatrix}7&1\\-3&4\end{vmatrix}$

$=2(1+8)-7(3+20)-3(-6+5)$

$=18-7(23)-3(-1)$

$=21-161$

$=-140$

2. Along the first column.

$|\text{A}|=\begin{vmatrix}1&-2\\4&1 \end{vmatrix}-7\begin{vmatrix}3&-5\\4&1\end{vmatrix}-3\begin{vmatrix}3&-5\\1&-2\end{vmatrix}$

$=2(1+8)-7(3+20)-3(-6+5)$

$=18-7(23)-3(-1)$

$=18-161+3$

$=21-161$

$=-140$

We can see, the answer is same with both the methods.