Q77 / 150 · MHT CET 2023 (11 May Shift 1) · Mathematics

If $P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$ is the adjoint of a $3 \times 3$ matrix A and $|A|=4$, then value of $\alpha$ is

  • A
    $4$
  • Correct answer
    B
    $11$
  • C
    $5$
  • D
    $0$

Solution

$\begin{aligned} & P=\operatorname{adj} A \\ \therefore \quad & |\mathrm{P}|=|\mathrm{A}|^2 \\ & \Rightarrow\left|\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right|=4^2 \\ & \Rightarrow 2 \alpha-6=16 \\ & \Rightarrow \alpha=11\end{aligned}$

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

Relevant Questions