Let A = left[ {begin{array}{*{20}{c}}1&{s | vedclass

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Question

$| A | =$ $\left| {\,\begin{array}{*{20}{c}}1&{\sin 	heta }&1\{ - \sin 	heta }&1&{\sin 	heta }\{ - 1}&{ - \sin 	heta }&1

Vedclass · Accepted Answer

$Det\, (A) \in [2, 4]$

Vedclass · Answer

$| A | =$ $\left| {\,\begin{array}{*{20}{c}}1&{\sin 	heta }&1\{ - \sin 	heta }&1&{\sin 	heta }\{ - 1}&{ - \sin 	heta }&1\end{array}\,} ight|$

$= 1(1 + \sin^2	heta ) - \sin	heta (- \sin	heta + \sin	heta ) + (1 + \sin^2	heta ) = 2\, (1 + \sin^2	heta )$ $| \sin	heta | \le 1$

$==> -1 \le \sin	heta \le 1$

$==> 0 \le \sin^2	heta \le 1$

==> $1 \le 1 + \sin^2	heta \le 2$

$==> 2 \le 2(1 + \sin2	heta ) \le 4$

==> $| A | \in [2, 4]$

Let $A =$ $\left[ {\begin{array}{*{20}{c}}1&{\sin \theta }&1\\{ - \sin \theta }&1&{\sin \theta }\\{ - 1}&{ - \sin \theta }&1\end{array}} \right]$, where $0 \le \theta < 2\pi$ , then

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