Q50 / 124 · NTA Abhyas (JEE Main) 2020 · Mathematics · Determinants

If $A = [\begin{array}{l} 1 & - 2 & 1 \\ 2 & λ & - 2 \\ 1 & 3 & - 3 \end{array}]$ be the adjoint matrix of matrix $B$ such that $|B| = 9$ , then the value of $λ$ is equal to

A
$1$
Correct answer
B
$\frac{- 77}{4}$
C
$\frac{23}{2}$
D
$\frac{- 39}{2}$

Solution

A = a d j (B)

|A| = {|B|}^{2}

|\begin{array}{l} 1 & - 2 & 1 \\ 2 & λ & - 2 \\ 1 & 3 & - 3 \end{array}| = 81

\Rightarrow 1 (- 3 λ + 6) + 2 (- 6 + 2) + 1 (6 - λ) = 81

\Rightarrow - 4 λ + 4 = 81

\Rightarrow λ = - \frac{77}{4}

Hence, the correct answer is option: 'B'.

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