A) \[3\omega \]
B) \[3\omega (\omega -1)\]
C) \[3{{\omega }^{2}}\]
D) \[3\omega (1-\omega )\]
Correct Answer: B
Solution :
\[D=\left| \begin{matrix} 1 & 1 & 1 \\ 1 & -1-{{w}^{2}} & {{w}^{2}} \\ 1 & {{w}^{2}} & {{w}^{4}} \\ \end{matrix} \right|=\left| \begin{matrix} 1 & 1 & 1 \\ 1 & +w & {{w}^{2}} \\ 1 & {{w}^{2}} & w \\ \end{matrix} \right|\] \[=\left| \begin{matrix} 3 & 0 & 0 \\ 1 & w & {{w}^{2}} \\ 1 & {{w}^{2}} & w \\ \end{matrix} \right|\] \[=3[{{w}^{2}}-{{w}^{4}}]=3({{w}^{2}}-w)=3w(w-1)\]You need to login to perform this action.
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