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

Question

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

Aicharya · Accepted Answer

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

If $P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$ is the adjoint of…

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