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Let $\mathrm{A}=\left(\begin{array}{ccc}12 & 24 & 5 \\ \mathrm{x} & 6 & 2 \\ -1 & -2 & 3\end{array}\right) .$ The value of $\mathrm{x}$ for which the matrix $\mathrm{A}$ is not invertible is
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Verified Answer
The correct answer is:
3
Hint:
If matrix is not invertible $\Rightarrow|\mathrm{A}|=0$
$\therefore|\mathrm{A}|=\left|\begin{array}{ccc}12 & 24 & 5 \\ \mathrm{x} & 6 & 2 \\ -1 & -2 & 3\end{array}\right|=0 \Rightarrow \mathrm{x}=3$
If matrix is not invertible $\Rightarrow|\mathrm{A}|=0$
$\therefore|\mathrm{A}|=\left|\begin{array}{ccc}12 & 24 & 5 \\ \mathrm{x} & 6 & 2 \\ -1 & -2 & 3\end{array}\right|=0 \Rightarrow \mathrm{x}=3$
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