Question

Using cofactors of elements of second row, evaluate$△=\left|\begin{array}{ccc}5& 3& 8\\ 2& 0& 1\\ 1& 2& 3\end{array}\right|$

Answer 1

We have to evaluate $\Delta =\left|\begin{array}{ccc}5& 3& 8\\ 2& 0& 1\\ 1& 2& 3\end{array}\right|$ using the cofactors of elements of second row.

$\therefore \Delta =a_{21}{A}_{21}+a_{22}{A}_{22}+a_{23}{A}_{23}$ where $A_{21},A_{22},A_{23}$ are the cofactors of second row.

$A_{21}=(-1)(9-16)=-(-7)=7$

$A_{22}=(+1)(15-8)=7$

$A_{23}=(-1)(10-3)=-7$

$\therefore \Delta =2\times 7+0\times 7+1\times (-7)$

$=14+0-7$

$=7$

$\therefore \Delta =7$