A) \[3\omega \]
B) \[3\omega (\omega -1)\]
C) \[3{{\omega }^{2}}\]
D) \[3\omega (1-\omega )\]
Correct Answer: B
Solution :
\[D=\left| \begin{matrix} 1 & 1 & 1 \\ 1 & -1-{{\omega }^{2}} & {{\omega }^{2}} \\ 1 & {{\omega }^{3}} & {{\omega }^{4}} \\ \end{matrix} \right|=\left| \begin{matrix} 1 & 1 & 1 \\ 1 & +\omega & {{\omega }^{2}} \\ 1 & {{\omega }^{2}} & \omega \\ \end{matrix} \right|\] \[=\left| \begin{matrix} 3 & 0 & 0 \\ 1 & \omega & {{\omega }^{3}} \\ 1 & {{\omega }^{2}} & \omega \\ \end{matrix} \right|\] \[=3[{{\omega }^{2}}-{{\omega }^{4}}]=3({{\omega }^{2}}-\omega )=3\omega (\omega -1)\]
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