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If $A=\left[\begin{array}{ccc}0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x\end{array}\right]$ is singular, then the possible values of $x$ are
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Verified Answer
The correct answer is:
$0,+12-12$
Since, $A$ is singular matrix, then
$$
\begin{aligned}
\left|\begin{array}{ccc}
0 & x & 16 \\
x & 5 & 7 \\
0 & 9 & x
\end{array}\right|=0 \\
\Rightarrow-x\left[x^{2}\right.&-144]=0 \Rightarrow x=0, \pm 12
\end{aligned}
$$
$$
\begin{aligned}
\left|\begin{array}{ccc}
0 & x & 16 \\
x & 5 & 7 \\
0 & 9 & x
\end{array}\right|=0 \\
\Rightarrow-x\left[x^{2}\right.&-144]=0 \Rightarrow x=0, \pm 12
\end{aligned}
$$
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