Question

Find the Adjoint matrix of the matrix $\left|\begin{array}{ccc}1& 2& 3\\ 2& 3& 2\\ 3& 3& 4\end{array}\right|$

Answer 1

Given matrix:

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

Cofactor matrix:

$cof\left(A\right)=\left[\begin{array}{ccc}6& -2& -3\\ 1& -5& 3\\ -5& 4& -1\end{array}\right]$

Adjoint matrix is the transpose of the cofactor matrix:

$adj\left(A\right)=\left[\begin{array}{ccc}6& 1& -5\\ -2& -5& 4\\ -3& 3& -1\end{array}\right]$