Question

Find the adjoint of the matrix A = $\left[\begin{array}{ccc}1& 4& 3\\ 4& 2& 1\\ 3& 2& 2\end{array}\right]$ .

Answer 1

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

Here,

$C_{11}=(4-2)=2$

$C_{12}=-(8-3)=-5$

$C_{13}=(8-6)=2$

$C_{21}=-(8-6)=-2$

$C_{22}=(2-9)=-7$

$C_{23}=-(2-12)=10$

$C_{31}=(4-6)=-2$

$C_{32}=-(1-12)=11$

$C_{33}=(2-16)=-14$

Hence,

$adjA=\left[\begin{array}{ccc}{C}_{11}& C_{21}& C_{31}\\ C_{12}& C_{22}& C_{32}\\ C_{13}& C_{23}& C_{33}\end{array}\right]=\left[\begin{array}{ccc}2& -2& -2\\ -5& -7& 11\\ 2& 10& -14\end{array}\right]$