F-Test

$\left(\begin{array}{ccc}1& -1& 0\end{array}\right)\left(\begin{array}{ccc}{\hat{V}}_{11}& {\hat{V}}_{12}& {\hat{V}}_{13}\\ {\hat{V}}_{12}& {\hat{V}}_{22}& {\hat{V}}_{23}\\ {\hat{V}}_{13}& {\hat{V}}_{23}& {\hat{V}}_{33}\end{array}\right)$

$=\left(\begin{array}{c}1\cdot {\hat{V}}_{11}+(-1)\cdot {\hat{V}}_{12}+0\cdot {\hat{V}}_{13},1\cdot {\hat{V}}_{12}+(-1)\cdot {\hat{V}}_{22}+0\cdot {\hat{V}}_{23},1\cdot {\hat{V}}_{13}+(-1)\cdot {\hat{V}}_{23}+0\cdot {\hat{V}}_{33}\end{array}\right)$