A) 0
B) 1
C) \[\omega \]
D) \[{{\omega }^{2}}\]
Correct Answer: A
Solution :
\[\left| \,\begin{matrix} 1 & \omega & -{{\omega }^{2}}/2 \\ 1 & 1 & 1 \\ 1 & -1 & 0 \\ \end{matrix}\, \right|=-\frac{1}{2}\left| \,\begin{matrix} 1 & \omega & {{\omega }^{2}} \\ 1 & 1 & -2 \\ 1 & -1 & 0 \\ \end{matrix}\, \right|\] = \[-\frac{1}{2}\left| \,\begin{matrix} 0 & \omega & {{\omega }^{2}} \\ 0 & 1 & -2 \\ 0 & -1 & 0 \\ \end{matrix}\, \right|=0\],(Apply \[{{C}_{1}}\to {{C}_{1}}+{{C}_{2}}+{{C}_{3}})\].
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