Matrices And Determinants

Let a, b and c be three real numbers satisfying

\([\matrix{ a & b & c \cr } ]\left[ {\matrix{ 1 & 9 & 7 \cr 8 & 2 & 7 \cr 7 & 3 & 7 \cr } } \right] = [\matrix{ 0 & 0 & 0 \cr } ]\) ........(E)

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