Question

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

• A. $-2$
• B. $4$
• C. $2$
• D. $-4$

Answer 1

The correct option is C $2$

A matrix is singular if and only if it has a determinant of 0.

$\left|\begin{array}{ccc}1& 2& \lambda +2\\ 2& 4& 8\\ 3& 5& 10\end{array}\right|=0$

$(40-40)-2(20-24)+(\lambda +2)(10-12)=0$

$2\lambda =4$

$⟹\lambda =2$