$(10$ pts$.)$ The stiffness constants for hexagonal magnesium are given as $C_{11}=6\mathrm{.}0$GPa, $C_{12}=2\mathrm{.}6$GPa,$C_{13}=2\mathrm{.}2$GPa,$C_{33}=6\mathrm{.}2$GPa and $C_{44}=1\mathrm{.}6$GPa. Determine the stress matrix $({}_{ij})$ based on the measured strain: ${}_{ij}=\left[\begin{array}{ccc}0\mathrm{.}012& 0\mathrm{.}006& 0\\ 0\mathrm{.}006& 0& 0\\ 0& 0& -0\mathrm{.}005\end{array}\right].$