Question

The adjoint of the matric $A=\left[\begin{array}{ccc}1& 0& 2\\ 2& 1& 0\\ 0& 3& 1\end{array}\right]$ is

• A. $\left[\begin{array}{ccc}-1& 6& 2\\ -2& 1& -4\\ 6& 3& 1\end{array}\right]$
• B. $\left[\begin{array}{ccc}1& 6& -2\\ -2& 1& 4\\ 6& -3& 1\end{array}\right]$
• C. $\left[\begin{array}{ccc}6& 1& 2\\ 4& -1& 2\\ 6& 3& -1\end{array}\right]$
• D. $\left[\begin{array}{ccc}-6& 2& 1\\ 4& -2& 1\\ 3& 1& -6\end{array}\right]$

Answer 1

The correct option is B $\left[\begin{array}{ccc}1& 6& -2\\ -2& 1& 4\\ 6& -3& 1\end{array}\right]$

$adj\left(A\right)=cofactor(A{)}^T=\left[\begin{array}{ccc}{A}_{11}& A_{21}& A_{31}\\ A_{12}& A_{22}& A_{32}\\ A_{13}& A_{23}& A_{33}\end{array}\right]=\left[\begin{array}{ccc}1& 6& -2\\ -2& 1& 4\\ 6& -3& 1\end{array}\right]$