WBJEE · Maths · Determinants
The value of det \(A\), where \(A=\left(\begin{array}{ccc}1 & \cos \theta & 0 \\ -\cos \theta & 1 & \cos \theta \\ -1 & -\cos \theta & 1\end{array}\right)\), lies
- A in the closed interval [1,2]
- B in the closed interval [0,1]
- C in the open interval (0,1)
- D in the open interval (1, 2)
Answer & Solution
Correct Answer
(A) in the closed interval [1,2]
Step-by-step Solution
Detailed explanation
We have, \(|A|=\left|\begin{array}{ccc}1 & \cos \theta & 0 \\ -\cos \theta & 1 & \cos \theta \\ -1 & -\cos \theta & 1\end{array}\right|\) \(=1[1-(-\cos \theta)(\cos \theta)]\) \(-\cos \theta[-\cos \theta+\cos \theta]+0\left(\cos ^{2} \theta+1\right)\) \(=1+\cos ^{2} \theta\)…
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