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

Answer: (B)

| A | = 0 as the matrix A is singular
$\therefore |A|=\left|\begin{array}{ccc}1& 3& \lambda +2\\ 2& 4& 8\\ 3& 5& 10\end{array}\right|=0$
Apply $R_2\to R_2-2R_1$
and $R_3\to R_3-3R_1$ and expand.
$-2(4-3\lambda )+4(4-2\lambda )=0$
$\Rightarrow 8-2\lambda =0\Rightarrow \lambda =4$
For $\lambda =4$, the second and the third column are proportional.