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Determinants and Matrices — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDeterminants and Matrices1 Mark
Question
Evaluate : $\left|\begin{array}{cr}\log _4^2 & \log _4^2 \\ 2 & 4\end{array}\right|$
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Answer

$\begin{array}{rr}\left|\begin{array}{rr}\log _4^2 & \log _4^2 \\ 2 & 4\end{array}\right| & =4 \times \log _4 2-2 \times \log _4{ }^2 \\ & =\log _4 2^4-\log _4 2^2\end{array}$

$\begin{aligned} & =\log _4 16-\log _4 4 \\ & =2 \log _4 4-\log _4 4 \\ & =2 \times 1-1=2-1=1\end{aligned}$

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