A) 0
B) \[\omega \]
C) \[{{\omega }^{2}}\]
D) 1
Correct Answer: A
Solution :
\[\left| \begin{matrix} 1 & {{\omega }^{n}} & {{\omega }^{2n}} \\ {{\omega }^{2n}} & 1 & {{\omega }^{n}} \\ {{\omega }^{n}} & {{\omega }^{2n}} & 1 \\ \end{matrix} \right|\] \[=\left| \begin{matrix} 1+{{\omega }^{n}}+{{\omega }^{2n}} & {{\omega }^{n}} & {{\omega }^{2n}} \\ {{\omega }^{2n}}+1+{{\omega }^{n}} & 1 & {{\omega }^{n}} \\ 1+{{\omega }^{n}}+{{\omega }^{2n}} & {{\omega }^{2n}} & 1 \\ \end{matrix} \right|\]\[[{{C}_{1}}\to {{C}_{1}}+{{C}_{2}}+{{C}_{3}}]\] \[=\left| \begin{matrix} 0 & {{\omega }^{n}} & {{\omega }^{2n}} \\ 0 & 1 & {{\omega }^{n}} \\ 0 & {{\omega }^{2n}} & 1 \\ \end{matrix} \right|\] \[[\because 1+\omega +{{\omega }^{2}}=0,n=3k]\] \[=0\]
You need to login to perform this action.
You will be redirected in
3 sec
