If \(\omega\) is the cube root of unity, then the system of equations \[\] \(x+\omega^{2} y+\omega z=0, \omega x+y+\omega^{2} z=0\) and \(\omega^{2} x+\omega y+z=0\) is
Step-by-step Solution:
Let us check determinant of coefficients. \[\] \(\left|\begin{array}{ccc}1 & \omega^{2} & \omega \\ \omega & 1 & \omega^{2} \\ \omega^{2} & \omega & 1\end{array}\right|=\left|\begin{array}{ccc}1+\omega+\omega^{2} & \omega^{2} & \omega \\ 1+\omega+\omega^{2} & 1 & \omega^{2} \\ 1+\omega+\omega^{2} & \omega & 1\end{array}\right|=0\) \[\] Hence there are many solutions. \[\] Choice (B)\[\]