Question

Let $A$ and $B$ are two matrices of same order $3\times 3$ given by $A=\left[\begin{array}{ccc}1& 3& \lambda +2\\ 2& 4& 6\\ 3& 5& 8\end{array}\right]$ $B=\left[\begin{array}{ccc}3& 2& 4\\ 3& 2& 5\\ 2& 1& 4\end{array}\right]$If $2A+B$ is singular, then $2\lambda$ equals

• A. $3$
• B. $5$
• C. $7$
• D. $9$

Answer 1

The correct option is A $3$

Here, $2A+B=\left[\begin{array}{ccc}2& 6& 2\lambda +4\\ 4& 8& 12\\ 6& 10& 16\end{array}\right]+\left[\begin{array}{ccc}3& 2& 4\\ 3& 2& 5\\ 2& 1& 4\end{array}\right]$
$\Rightarrow 2A+B=\left[\begin{array}{ccc}5& 8& 2\lambda +8\\ 7& 10& 17\\ 8& 11& 20\end{array}\right]$
Given , $|2A+B|=0$

$\left|\begin{array}{ccc}5& 8& 2\lambda +8\\ 7& 10& 17\\ 8& 11& 20\end{array}\right|=0$

$\Rightarrow 9-6\lambda =0$

$\Rightarrow 2\lambda =3$