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JEE Main 201912 AprilMorning Shift
Exam
JEE Main
Year
2019
Date
12 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Matrices

JEE Main 2019 · 12 April · Morning Shift · Mathematics · Matrices

If B = [ cases 5 & 2α & 1 0 & 2 & 1 α & 3 & - 1 cases ] is the...

If B = \left[\begin{cases}5 & 2\alpha & 1 \\ 0 & 2 & 1 \\ \alpha & 3 & - 1\end{cases}\right] is the inverse of a3 \times 3matixmatixA, then the sum of all values of α\alpha for which det(A)+1=0,det\left(A\right) + 1 = 0, is:

Options

  1. A22
  2. B11
  3. C00
  4. D−1- 1

Correct answer

B. 11

Step-by-step solution

Since, ∣A∣=−1\left|A\right| = - 1
Hence, \left|B\right| = \dfrac{1}{| A |} = - 1<br/><br />⇒ \left|B\right| = 5\left(- 5\right) - 2\alpha\left(- \alpha\right) - 2\alpha<br/><br />= 2{\alpha}^{2} - 2\alpha - 25</p><p></p><p>1 + \left|A\right| = 0<br/><br />{\alpha}^{2} - \alpha - 12 = 0<br/>Sum<br />Sum= 1

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