Question

If matrix $2A+3B$ is singular, then the value of $2\lambda$ is

• A. $11$
• B. $13$
• C. $15$
• D. $17$

Answer 1

The correct option is D $17$

Here,

$2A+3B=2\left[\begin{array}{ccc}1& 3& \lambda +2\\ 2& 4& 8\\ 3& 5& 10\end{array}\right]+3\left[\begin{array}{ccc}3& 2& 4\\ 3& 2& 5\\ 2& 1& 4\end{array}\right]$
$\Rightarrow 2A+3B=\left[\begin{array}{ccc}11& 12& 2\lambda +16\\ 13& 14& 31\\ 12& 13& 32\end{array}\right]$
Since, $2A+3B$ is singular
$\Rightarrow |2A+3B|=0$
Calculating the determinant and equating it to zero, we get

$\lambda =\frac{17}{2}$
$\Rightarrow 2\lambda =17$

Hence, option D.