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  • Please solve RD Sharma class 12 chapter Determinants exercise multiple choise question 13 maths textbook solution

Please solve RD Sharma class 12 chapter Determinants exercise multiple choise question 13 maths textbook solution

Answers (1)

Answer:

Correct option (a)

Hint:

Simply solve this determinant.

Given:

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

We have to find \Delta

Solution:

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

Applying C1→C1+C2+C3

        \Rightarrow \Delta=\left|\begin{array}{ccc} 1+\omega^{n}+\omega^{2n} & \omega^{n} & \omega^{2 n} \\ 1+\omega^{n}+\omega^{2n} & 1 & \omega^{n} \\ 1+\omega^{n}+\omega^{2n} & \omega^{2 n} & 1 \end{array}\right|

        \Rightarrow \Delta=\left|\begin{array}{ccc} 0 & \omega^{n} & \omega^{2 n} \\ 0 & 1 & \omega^{n} \\ 0 & \omega^{2 n} & 1 \end{array}\right|                            [\because 1+\omega ^{n}+\omega ^{2n}=0]

        \Rightarrow \Delta=0

Posted by

Gurleen Kaur

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