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  • Please solve RD Sharma solution for Maths Class 12 Chapter 5 Determinants Exercise Very short question Question 11 for maths textbook solution.

Please solve RD Sharma solution for Maths Class 12 Chapter 5 Determinants Exercise Very short question Question 11 for maths textbook solution.

Answers (1)

Answer: 0

Hint: Here we use basic concept of determinant of matrix

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

Solution :

C_{1} \rightarrow C_{1}+C_{2}+C_{3}

So,

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

\rightarrow We know that  1+\omega+\omega^{2}=0

So,

\Delta=\left|\begin{array}{ccc} 0 & \omega & \omega^{2} \\ 0 & \omega^{2} & 1 \\ 0 & 1 & \omega \end{array}\right|

\rightarrow Here whole 1st column is zero

So, the value of determinant is also zero

 

Posted by

infoexpert23

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