Question

If the matrix $\left[\begin{array}{ccc}1& 2& \lambda +2\\ 2& 4& 8\\ 3& 5& 10\end{array}\right]$ is singular, then value of $\lambda$ is

• A. $4$
• B. $-4$
• C. $5$
• D. $3$

Answer 1

Answer: (A)

$4$

Since, given matrix is a singular matrix.
$\therefore \left|\begin{array}{ccc}1& 3& \lambda +2\\ 2& 4& 8\\ 3& 5& 10\end{array}\right|=0$
$\Rightarrow 1(40-40)-3(20-24)+(\lambda +2)(10-12)=0$
$\Rightarrow 12-2\lambda -4=0$
$\Rightarrow \lambda -4=0$
$\Rightarrow \lambda =4$