Question

Adj $\left[\begin{array}{ccc}1& 0& 2\\ -1& 5& -2\\ 0& 2& 1\end{array}\right]=\left[\begin{array}{ccc}9& a& -2\\ -1& 1& 0\\ -2& 2& b\end{array}\right]\Rightarrow \left[\begin{array}{cc}a& b\end{array}\right]=$

• A. $\left[\begin{array}{cc}-4& 5\end{array}\right]$
• B. $\left[\begin{array}{cc}-4& -1\end{array}\right]$
• C. $\left[\begin{array}{cc}4& 1\end{array}\right]$
• D. $\left[\begin{array}{cc}4& -1\end{array}\right]$

Answer 1

The correct option is A $\left[\begin{array}{cc}-4& 5\end{array}\right]$

$\begin{array}{c}A=\left(\begin{array}{ccc}1& 0& 2\\ -1& 5& -2\\ 0& 2& 1\end{array}\right)\\ \Rightarrow cofactorofA\\ \Rightarrow C_{11}=9,C_{12}=-1,C_{13}=-2\\ \Rightarrow C_{21}=-4,C_{22}=1,C_{23}=2\\ \Rightarrow C_{31}=-10,c_{32}=0.c_{33}=5\\ \Rightarrow adJ\left(\begin{array}{ccc}1& 0& 2\\ -1& 5& -2\\ 0& 2& 1\end{array}\right)=\left(\begin{array}{ccc}9& -4& -10\\ -1& 1& 0\\ -2& 2& 5\end{array}\right)=\left(\begin{array}{ccc}9& a& -10\\ -1& 1& 0\\ -2& 2& b\end{array}\right)\end{array}$

hence by compearing $a=-4,b=5$