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

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

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$3\sqrt{3}i$

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(A) माना $D = \left| \begin{array}{ccc} 1 & 1 & 1 \ 1 & \omega^2 & \omega \ 1 & \omega & \omega^2 \end{array} ight|$.$C_1 	o C_1 - C_2$ और $C_2 	o C_2 - C_3$ लागू करने पर:$D = \left| \begin{array}{ccc} 0 & 0 & 1 \ 1-\omega^2 & \omega^2-\omega & \omega \ 1-\omega & \omega-\omega^2 & \omega^2 \end{array} ight|$.प्रथम पंक्ति के अनुदिश विस्तार करने पर:$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)$चूंकि $\omega^3 = 1$ और $\omega^4 = \omega$:$D = 3\omega - 3\omega^2 = 3(\omega - \omega^2)$.$\omega = \frac{-1 + i\sqrt{3}}{2}$ और $\omega^2 = \frac{-1 - i\sqrt{3}}{2}$ रखने पर:$D = 3 \left( \frac{-1 + i\sqrt{3}}{2} - \frac{-1 - i\sqrt{3}}{2} ight) = 3 \left( \frac{2i\sqrt{3}}{2} ight) = 3i\sqrt{3}$.

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

Similar Questions

$x$ के किन मानों के लिए दिया गया आव्यूह $\left[\begin{array}{ccc}-x & x & 2 \\ 2 & x & -x \\ x & -2 & -2\end{array}\right]$ व्युत्क्रमणीय (non-singular) होगा?

सारणिक का मान ज्ञात कीजिए: $\left|\begin{array}{cc}x^{2}-x+1 & x-1 \\ x+1 & x+1\end{array}\right|$

यदि $\left|\begin{array}{ccc}x & 4 & 6 \\ 2 & 3 & -9 \\ 5 & 6 & 1\end{array}\right|+\left|\begin{array}{ccc}5 & 6 & 1 \\ 6 & 4 & 5 \\ 2 & 3 & -9\end{array}\right|=\left|\begin{array}{ccc}2 & 3 & -9 \\ 1-2 x & -8 & -11 \\ 5 & 6 & 1\end{array}\right|$ है,तो $x=$ . . . . . .

यदि $a, b, c$ वास्तविक हैं,तो सारणिक $\left| {\begin{array}{*{20}{c}} {{a^2} + 1}&{ab}&{ac}\\{ab}&{{b^2} + 1}&{bc}\\{ac}&{bc}&{{c^2} + 1}\end{array}}\right| = 1$ है यदि

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