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