Let $\mathrm{a}, \mathrm{b}$ and c be three real numbers satisfying $\left[\begin{array}{lll}\mathrm{a} & \mathrm{b} & \mathrm{c}\end{array}\right]\left[\begin{array}{lll}1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7\end{array}\right]=\left[\begin{array}{lll}0 & 0 & 0\end{array}\right]$

Let $\omega$ be a solution of $x^3-1=0$ with $\operatorname{Im}(\omega)>0$. If $a=2$ with $b$ and $c$ satisfying (E), then the value of $\frac{3}{\omega^{\mathrm{a}}}+\frac{1}{\omega^{\mathrm{b}}}+\frac{3}{\omega^{\mathrm{c}}}$ is equal to