Let $\left(\begin{array}{ccc}1 & \cos heta & 1 \ -\cos heta & 1 & \cos heta \ -1 & -\cos h

Question

Let $\left(\begin{array}{ccc}1 & \cos 	heta & 1 \ -\cos 	heta & 1 & \cos 	heta \ -1 & -\cos 	heta & 1\end{array}ight)$, where $0 \leq 	heta \leq 2 \pi$. Then

Professor PC Thomas Classes · Answer

$\det(A) = 1(1+\cos^2	heta) - \cos	heta(-\cos	heta+\cos	heta) + 1(\cos^2	heta+1) = 2(1+\cos^2	heta) \in [2,4]$.