TS EAMCET · Maths · Determinants
The system of linear equations \((\sin \theta) x+y-2 z=0,2 x-y+(\cos \theta) z=0\) and \(-3 x+(\sec \theta) y+3 z=0\), where \(\theta \neq(2 n+1) \frac{\pi}{2}\), has non-trivial solution for
- A no value of \(\theta\)
- B \(\theta=n \pi+\frac{\pi}{4}, n \in z\)
- C \(\theta=\operatorname{Tan}^{-1}\left(\frac{3}{4}\right)\)
- D \(\theta=\operatorname{Tan}^{-1}\left(\frac{4}{3}\right)\)
Answer & Solution
Correct Answer
(A) no value of \(\theta\)
Step-by-step Solution
Detailed explanation
\( \det(A) = \begin{vmatrix} \sin \theta & 1 & -2 \\ 2 & -1 & \cos \theta \\ -3 & \sec \theta & 3 \end{vmatrix} = 0 \) \( \sin \theta(-3-\cos \theta \sec \theta) - 1(6+3 \cos \theta) - 2(2 \sec \theta - 3) = 0 \)…
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