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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Determinants

NDA 2022 · Mathematics · Determinants

For what value of k is the matrix [ array ccc 2 2 θ & 2 2 θ & 6 1-2...

For what value of kk is the matrix \left[2cos⁡2θ2cos⁡2θ61−2sin⁡2θ2cos⁡2θ−13k2k1\begin{array}{ccc}2 \cos 2 \theta & 2 \cos 2 \theta & 6 \\ 1-2 \sin ^2 \theta & 2 \cos ^2 \theta-1 & 3 \\ k & 2 k & 1\end{array}\right] singular?

Options

  1. A0 only
  2. B1 only
  3. C2 only
  4. DAny real value

Correct answer

D. Any real value

Step-by-step solution

\left|2cos⁡2θ2cos⁡2θ61−2sin⁡2θ2cos⁡2θ−13k2k1\begin{array}{ccc}2 \cos 2 \theta & 2 \cos 2 \theta & 6 \\ 1-2 \sin ^2 \theta & 2 \cos ^2 \theta-1 & 3 \\ k & 2 k & 1\end{array}\right|=\left|2cos⁡2θ2cos⁡2θ6cos⁡2θcos⁡2θ3k2k1\begin{array}{ccc}2 \cos ^2 \theta & 2 \cos ^2 \theta & 6 \\ \cos ^2 \theta & \cos ^2 \theta & 3 \\ k & 2 k & 1\end{array}\right|=0\left(\because R_1\right. and R_2 are identical )) Hence, for any real value of kk the given matrix is singular.
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