Question

Find the adjoint of $\left[\begin{array}{ccc}1& -1& 2\\ 3& 0& -2\\ 1& 0& 3\end{array}\right]$

Answer 1

Let,

$A=\left|\begin{array}{ccc}1& -1& 2\\ 3& 0& -2\\ 1& 0& 3\end{array}\right|$

Let the minors,

$M_{11}=0,M_{12}=-11,M_{13}=0$

$M_{21}=3,M_{22}=1,M_{23}=-1$

$M_{31}=2,M_{32}=4,M_{33}=4$

Therefore,

$adjA=\left[\begin{array}{ccc}{M}_{11}& M_{21}& M_{31}\\ M_{12}& M_{22}& M_{32}\\ M_{13}& M_{23}& M_{33}\end{array}\right]$

$=\left[\begin{array}{ccc}0& 3& 2\\ -11& 1& 4\\ 0& -1& 4\end{array}\right]$