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  4. If A=[0 x 16 x 5 7 0 9 x] is singular, then the possible values of x are

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Q. If $A=\begin{bmatrix}0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x\end{bmatrix}$ is singular, then the possible values of $x$ are

Solution:

$\begin{bmatrix}0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x\end{bmatrix}=0$
$\Rightarrow -x\left(x^{2}-144\right)=0$
$\Rightarrow x\left(x^{2}-144\right)=0$
$\Rightarrow x=0, x=\pm 12$