Mathematics - Matrices Question with Solution | TestHub

$\begin{array}{rl}& |\mathrm{A}|=\frac{11}{2}\\ & {\mathrm{C}}_{11}=\sum _{\mathrm{k}=1}^2{\mathrm{a}}_{1\mathrm{k}}\cdot {\mathrm{A}}_{1\mathrm{k}}={\mathrm{a}}_{11}{\mathrm{A}}_{11}+{\mathrm{a}}_{12}{\mathrm{A}}_{12}=|\mathrm{A}|=\frac{11}{2}\\ & {\mathrm{C}}_{12}=\sum _{\mathrm{k}=1}^2{\mathrm{a}}_{1\mathrm{k}}\cdot {\mathrm{A}}_{2\mathrm{k}}=0\\ & {\mathrm{C}}_{21}=\sum _{\mathrm{k}=1}^2{\mathrm{a}}_{2\mathrm{k}}\cdot {\mathrm{A}}_{1\mathrm{k}}=0\\ & {\mathrm{C}}_{22}=\sum _{\mathrm{k}=1}^2{\mathrm{a}}_{2\mathrm{k}}\cdot {\mathrm{A}}_{2\mathrm{k}}=|\mathrm{A}|=\frac{11}{2}\\ & \mathrm{C}=\left[\begin{array}{cc}11/2& 0\\ 0& 11/2\end{array}\right]\\ & |\mathrm{C}|=\frac{121}{4}\\ & 8|\mathrm{C}|=242\end{array}$