QJEEM19Mafc8e: JEE Main 2019 Mathematics - Class 12 JEEM19Mafc8e Solution: If B = [ 5 2 α 1 0 2 1 α 3 − 1 ] is the inverse of a 3 × 3…

Question

Verified Solution • 2025–26 Session moderate

If

B = [\begin{matrix} 5 & 2 α & 1 \\ 0 & 2 & 1 \\ α & 3 & - 1 \end{matrix}]

is the inverse of a 3 × 3 matrix A, then the sum of all values of

α

for which det(A) + 1 = 0, is :

Accepted Answer

Given |A| + 1 = 0

\Rightarrow

|A| = -1

| B | = | A^{- 1} | = \frac{1}{| A |} = - 1

| \begin{matrix} 5 & 2 α & 1 \\ 0 & 2 & 1 \\ α & 3 & - 1 \end{matrix} |

= -1

\Rightarrow

5 (- 2 - 3) + 2 α (α) + 1 (- 2 α) = - 1

\Rightarrow

2 α^{2} - 2 α - 24 = 0

∴

sum of value of

α

=

\frac{- (- 2)}{2} = 1

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