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