A) \[0\]
B) \[1\]
C) \[\omega \]
D) \[{{\omega }^{2}}\]
E) \[1+\omega \]
Correct Answer: A
Solution :
Let\[\Delta =\left| \begin{matrix} 1+2{{\omega }^{100}}+{{\omega }^{200}} & {{\omega }^{2}} \\ 1 & 1+{{\omega }^{100}}+2{{\omega }^{200}} \\ \omega & {{\omega }^{2}} \\ \end{matrix} \right.\] \[\left. \begin{matrix} 1 \\ \omega \\ 2+{{\omega }^{100}}+{{\omega }^{200}} \\ \end{matrix} \right|\] \[=\left| \begin{matrix} 1+2\omega +{{\omega }^{2}} & {{\omega }^{2}} & 1 \\ 1 & 1+\omega +2{{\omega }^{2}} & \omega \\ \omega & {{\omega }^{2}} & 2+\omega +{{\omega }^{2}} \\ \end{matrix} \right|\] \[=\left| \begin{matrix} \omega & {{\omega }^{2}} & 1 \\ 1 & {{\omega }^{2}} & \omega \\ \omega & {{\omega }^{2}} & 1 \\ \end{matrix} \right|\] \[=0\] (\[\because \]Rows\[{{R}_{1}}\]and\[{{R}_{3}}\]are identical)You need to login to perform this action.
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