If A = $$\left[ {\matrix{ 1 & {\sin \theta } & 1 \cr { - \sin \theta } & 1 & {\sin \theta } \cr { - 1} & { - \sin \theta } & 1 \cr } } \right]$$; then for all $\theta $ $ \in $ $\left( {{{3\pi } \over 4},{{5\pi } \over 4}} \right)$, det (A) lies in the interval :

Question

If A = $$\left[ {\matrix{ 1 & {\sin \theta } & 1 \cr { - \sin \theta } & 1 & {\sin \theta } \cr { - 1} & { - \sin \theta } & 1 \cr } } \right]$$;

then for all $\theta $ $ \in $ $\left( {{{3\pi } \over 4},{{5\pi } \over 4}} \right)$, det (A) lies in the interval :

$\left( {{3 \over 2},3} \right]$

$\left( {0,{3 \over 2}} \right]$

$\left[ {{5 \over 2},4} \right)$

$\left( {1,{5 \over 2}} \right]$

Solution

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