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JEE Main 202117 MarchMorning Shift
Exam
JEE Main
Year
2021
Date
17 March
Shift
Morning Shift
Subject
Mathematics
Chapter
Matrices

JEE Main 2021 · 17 March · Morning Shift · Mathematics · Matrices

If A = [ cases 0 & sinα sinα & 0 cases ] and det( A ^ 2 - (1)/(2)I)...

If A = \left[\begin{cases}0 & sin\alpha \\ sin\alpha & 0\end{cases}\right] anddet\left({A}^{2} - \dfrac{1}{2}I\right) = 0, then a possible value of α\alpha is

Options

  1. Aπ2\dfrac{\pi}{2}
  2. Bπ3\dfrac{\pi}{3}
  3. Cπ4\dfrac{\pi}{4}
  4. Dπ6\dfrac{\pi}{6}

Correct answer

C. π4\dfrac{\pi}{4}

Step-by-step solution

{A}^{2} = \sin^{2}\alphaI</p><p>So,∣A2−I2∣=(sin⁡2α−12)2=0</p><p>So, \left|{A}^{2} - \dfrac{I}{2}\right| = {\left(\sin^{2}\alpha - \dfrac{1}{2}\right)}^{2} = 0

⇒sinα=12⇒ sin\alpha = \dfrac{1}{\sqrt{2}}

⇒α=π4⇒ \alpha = \dfrac{\pi}{4}

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