left| begin{array}{ccc} 1 & 1 & 1 1 & omega^ | vedclass

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(A) ધારો કે $D = \left| \begin{array}{ccc} 1 & 1 & 1 \ 1 & \omega^2 & \omega \ 1 & \omega & \omega^2 \end{array} ight|$.$C_1 	o C_1 - C_2$ અને $C

Vedclass · Accepted Answer

$3\sqrt{3}i$

Vedclass · Answer

(A) ધારો કે $D = \left| \begin{array}{ccc} 1 & 1 & 1 \ 1 & \omega^2 & \omega \ 1 & \omega & \omega^2 \end{array} ight|$.$C_1 	o C_1 - C_2$ અને $C_2 	o C_2 - C_3$ લેતા:$D = \left| \begin{array}{ccc} 0 & 0 & 1 \ 1-\omega^2 & \omega^2-\omega & \omega \ 1-\omega & \omega-\omega^2 & \omega^2 \end{array} ight|$.પ્રથમ હાર મુજબ વિસ્તરણ કરતા:$D = 1 \cdot [(1-\omega^2)(\omega-\omega^2) - (1-\omega)(\omega^2-\omega)]$$D = (\omega - \omega^2 - \omega^2 + \omega^4) - (\omega^2 - \omega - \omega^3 + \omega^2)$અહીં $\omega^3 = 1$ અને $\omega^4 = \omega$ હોવાથી:$D = 3\omega - 3\omega^2 = 3(\omega - \omega^2)$.$\omega = \frac{-1 + i\sqrt{3}}{2}$ અને $\omega^2 = \frac{-1 - i\sqrt{3}}{2}$ મુકતા:$D = 3 \left( \frac{-1 + i\sqrt{3}}{2} - \frac{-1 - i\sqrt{3}}{2} ight) = 3 \left( \frac{2i\sqrt{3}}{2} ight) = 3i\sqrt{3}$.

$\left| \begin{array}{ccc} 1 & 1 & 1 \\ 1 & \omega^2 & \omega \\ 1 & \omega & \omega^2 \end{array} \right| = $

Similar Questions

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ગુણાકાર $xyz$ ની ન્યૂનતમ કિંમત શોધો જેના માટે નિશ્ચાયક $\left| \begin{array}{ccc} x & 1 & 1 \\ 1 & y & 1 \\ 1 & 1 & z \end{array} \right|$ અ-ઋણ (non-negative) હોય.

જો $\left|\begin{array}{ll}2 & 4 \\ 5 & 1\end{array}\right|=\left|\begin{array}{cc}2x & 4 \\ 6 & x\end{array}\right|$ હોય,તો $x$ ની કિંમતો શોધો.

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