Basic Maths Grand Test - Q18

0 votes

Let A =\begin{bmatrix} 1 & \sin\theta &1 \\ -\sin\theta& 1 & \sin\theta \\ -1 & -\sin\theta & 1 \end{bmatrix} , where \ 0 \leq \theta \leq 2\pi , then

 

A. Det(A) = 0

B. Det(A) \in (2,\infty)

C. Det(A) \in [2,4]

D. Det(A) \in (2,4)

asked Nov 18, 2019 in Basic Maths by gbmentor (90,880 points)
edited Jun 11 by deepak-gatebook

1 Answer

+1 vote

Det(A)=2+2\sin ^{2}\Theta=2(1+\sin ^{2}\Theta)

\sin ^{2}\Theta\in [0,1]

1+\sin ^{2}\Theta \in [1,2]

2(1+\sin ^{2}\Theta)\in [2,4]

Det(A)\in [2,4]

So option C is correct

answered Nov 20, 2019 by (2,920 points)
Answer:
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