If $P=\begin{bmatrix} 1 & \alpha & 3 \ 1 & 3 & 3 \ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a $3 imes 3$ matrix $A$ and $|A|=4$, then $\alpha$ is equal to

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If $P=\begin{bmatrix} 1 & \alpha & 3 \ 1 & 3 & 3 \ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a $3 	imes 3$ matrix $A$ and $|A|=4$, then $\alpha$ is equal to

Aicharya · Accepted Answer

$P=adjA$ $\Rightarrow |P|=|adjA|=A^2$ $\Rightarrow |adjA|=A^{n-1}$ where $n=3$ Now, $|P|=\begin{vmatrix}1 & \alpha & 3\ 1 & 3 & 3\ 2 & 4 & 4\end{vmatrix}=1(12-12)-\alpha(4-6)+3(4-6)=2\alpha-6$ $\Rightarrow 2\alpha-6=16$ $\Rightarrow \alpha=11$

If $P=\begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a $3 \times…

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