The value of \( \left|\begin{array}{ccc}1 & \omega & 2 \omega^{2} \\ 2 & 2 \omega^{2} & 4 \omega...

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If \( A=\left[\begin{array}{ccc}1 & \omega & \omega^{2} \\ \omega & \omega^{2} & 1 \\ \omega^{2}... If \( A=\left[\begin{array}{ccc}1 & \omega & \omega^{2} \\ \omega & \omega^{2} & 1 \\ \omega^{2}...
The value of the expression `1.(2-omega).(2-omega^2)+2.(3-omega)(3-omega^2)+.+(n-1)(n-omega)(n-o... The value of the expression `1.(2-omega).(2-omega^2)+2.(3-omega)(3-omega^2)+.+(n-1)(n-omega)(n-o...
If \( \omega \) is an imaginary cube root of unity and \( \left|\begin{array}{ccc}x+\omega)^{2} ... If \( \omega \) is an imaginary cube root of unity and \( \left|\begin{array}{ccc}x+\omega)^{2} ...
\[ \left|\begin{array}{ccc} 1 & \omega^{3} & \omega^{5} \\ \omega^{3} & 1 & \omega^{4} \\ \omega... \[ \left|\begin{array}{ccc} 1 & \omega^{3} & \omega^{5} \\ \omega^{3} & 1 & \omega^{4} \\ \omega...
The value of \( \left|\begin{array}{ccc}-1 & 2 & 1 \\ 3+2 \sqrt{2} & 2+2 \sqrt{2} & 1 \\ 3-2 \sq.... The value of \( \left|\begin{array}{ccc}-1 & 2 & 1 \\ 3+2 \sqrt{2} & 2+2 \sqrt{2} & 1 \\ 3-2 \sq....
The value of the determinant \( \left|\begin{array}{ccc}1 & \omega^{3} & \omega^{5} \\ \omega^{3... The value of the determinant \( \left|\begin{array}{ccc}1 & \omega^{3} & \omega^{5} \\ \omega^{3...
If \( \omega \) is an imaginary cube root of unity, then the value of \( \left|\begin{array}{ccc... If \( \omega \) is an imaginary cube root of unity, then the value of \( \left|\begin{array}{ccc...
The value of `|(1,1,1),(1,omega,omega^2), (1,omega^2,omega)|`is The value of `|(1,1,1),(1,omega,omega^2), (1,omega^2,omega)|`is