First slide

Introduction to Determinants

Question

Let $Δ = |\begin{array}{ccc} 1 & \sin θ & 1 \\ - \sin θ & 1 & \sin θ \\ - 1 & - \sin θ & 1 \end{array}|, 0 \leq θ \leq 2 π$ . The

Moderate

A

$∆ = 0$
B

$Δ \in (2, \infty)$
C

$Δ \in (2, 4)$
D

$Δ \in [2, 4]$

Solution

Applying $R_{1} \to R_{1} + R_{3}$ to obtain
$Δ = |\begin{array}{ccc} 0 & 0 & 2 \\ - \sin θ & 1 & \sin θ \\ - 1 & - \sin θ & 1 \end{array}| = 2 (\sin^{2} θ + 1)$
As, $0 \leq \sin^{2} θ \leq 1,$ we get $Δ \in [2, 4]$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App