Question

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

• A. $[-4,1]$
• B. $[-4,-1]$
• C. $[4,1]$
• D. $[4,-1]$

Answer 1

The correct option is C $[4,1]$

$\begin{array}{c}Adj\left(\begin{array}{ccc}1& 0& 2\\ -1& 1& -2\\ 0& 2& 1\end{array}\right)=\left(\begin{array}{ccc}5& 9& -2\\ 1& 1& 0\\ -2& -2& b\end{array}\right),\\ \left[a,b\right]=2\\ Firstlyfindoutcofactor\\ A_{11}=\left(1+4\right),A_{12}=1,A_{13}=-2,A_{21}=4,A_{22}=1,A_{23}=2,A_{31}=-2,A_{32}=0,A_{33}=1\\ ThenAdj\left(\begin{array}{ccc}1& 0& 2\\ -1& 1& -2\\ 0& 2& 1\end{array}\right)=\left(\begin{array}{ccc}5& 4& -2\\ 1& 1& 0\\ -2& 2& 1\end{array}\right)=\left(\begin{array}{ccc}5& a& -2\\ 1& 1& 0\\ -2& 2& b\end{array}\right)\\ Bycomparingweget\left(a\right)and\left(b\right)\\ a=4\\ b=1\\ Therefore\left[a,b\right]=\left[4,1\right]Ans.\end{array}$