Let mathrm{A}=left[begin{array}{ccc}1 & s | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$A=\left[\begin{array}{ccc}1 & \sin 	heta & 1 \ -\sin 	heta & 1 & \sin 	heta \ -1 & -\sin 	heta & 1\end{array}ight]$

Vedclass · Accepted Answer

$\operatorname{Det}(\mathrm{A}) \in[2,4]$

Vedclass · Answer

$A=\left[\begin{array}{ccc}1 & \sin 	heta & 1 \ -\sin 	heta & 1 & \sin 	heta \ -1 & -\sin 	heta & 1\end{array}ight]$

$	herefore|A|=1\left(1+\sin ^{2} 	hetaight)-\sin 	heta(-\sin 	heta+\sin 	heta)+1\left(\sin ^{2} 	heta+1ight)$

$=1+\sin ^{2} 	heta+\sin ^{2} 	heta+1$

$=2+2 \sin ^{2} 	heta$

$=2\left(1+\sin ^{2} 	hetaight)$

Now, $0 \leq 	heta \leq 2 \pi$

$\Rightarrow 0 \leq \sin 	heta \leq 1$

$\Rightarrow 0 \leq \sin ^{2} 	heta \leq 1$

$\Rightarrow 1 \leq 1+\sin ^{2} 	heta \leq 2$

$\Rightarrow 2 \leq 2\left(1+\sin ^{2} 	hetaight) \leq 4$

$	herefore \operatorname{Det}(A) \in[2,4]$

Hence, the correct answer is $B$.

Let $\mathrm{A}=\left[\begin{array}{ccc}1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1\end{array}\right],$ where $0 \leq \theta \leq 2 \pi$. Then

Similar Questions

If the system of equations

$x+y+z=2$

$2 x+4 y-z=6$

$3 x+2 y+\lambda z=\mu$ has infinitely many solutions, then

The value of $\left| {\,\begin{array}{*{20}{c}}{41}&{42}&{43}\\{44}&{45}&{46}\\{47}&{48}&{49}\end{array}\,} \right| = $

If $a, b, c$ are sides of a scalene triangle, then the value of $\left| \begin{array}{*{20}{c}}
a&b&c\\
b&c&a\\
c&a&b
\end{array} \right|$ is

Evaluate the determinants

$\left|\begin{array}{ccc}0 & 1 & 2 \\ -1 & 0 & -3 \\ -2 & 3 & 0\end{array}\right|$

If $p + q + r = 0 = a + b + c$, then the value of the determinant $\left| {\,\begin{array}{*{20}{c}}{pa}&{qb}&{rc}\\{qc}&{ra}&{pb}\\{rb}&{pc}&{qa}\end{array}\,} \right|$ is