Question

The value of $\left| \begin{matrix} 1 + \omega & \omega^{2} & - \omega \\ 1 + \omega^{2} & \omega & - \omega^{2} \\ \omega^{2} + \omega & \omega & - \omega^{2} \end{matrix} \right|$ is equal to

• A. 0
• B. 2w
• C. 2w²
• D. – 3w²

Answer 1

Answer: (D)

– 3w²

Answer 2

Sol. Operating (C₁ ® C₁ + C₂)

1 + \omega + \omega^{2} & \omega^{2} & - \omega \\ 1 + \omega^{2} + \omega & \omega & - \omega^{2} \\ \omega^{2} + 2\omega & \omega & - \omega^{2} \end{matrix} \right|$$ = w(–w) $\left| \begin{matrix} 0 & \omega & 1 \\ 0 & 1 & \omega \\ \omega - 1 & 1 & \omega \end{matrix} \right|$ = – w² (1 + 1 + 1) = – 3w²