Question

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. $2$

Answer 1

The correct option is C $3$

For matrix to be non invertible $detA=0$
$\left(\begin{array}{ccc}12& 24& 5\\ x& 6& 2\\ -1& -2& 3\end{array}\right)|A|=2\left|\begin{array}{ccc}12& 12& 5\\ x& 3& 2\\ -1& -1& 3\end{array}\right|=0\Rightarrow x=3\cdots \left(C_1\&C_2\text{are identical}\right)$