Practicing Success
Let $D=\begin{vmatrix}1&\sin θ&1\\-\sin θ&1&\sin θ\\-1&-\sin θ&1\end{vmatrix};0≤θ<2π$, then |
$D=0$ $D ∈ (0,∞)$ $D ∈ [2,4]$ $D ∈ [2,∞]$ |
$D ∈ [2,4]$ |
We have, $D=\begin{vmatrix}1&\sin θ&1\\-\sin θ&1&\sin θ\\-1&-\sin θ&1\end{vmatrix}$ $⇒D=\begin{vmatrix}2&\sin θ&1\\0&1&\sin θ\\0&-\sin θ&1\end{vmatrix}$ [Applying $C_1→C_1+C_3$] $⇒D=2(1 + \sin^2θ)$ Now, $0 ≤ \sin^2θ ≤1$ $⇒2 ≤2 (1 + \sin^2θ) ≤ 4 ⇒ D∈ [2,4]$ |