b
(b) The matrix $\left[ {\begin{array}{*{20}{c}}1&3&{\lambda + 2}\\2&4&8\\3&5&{10}\end{array}} \right]$ is singular,
If $\,\left| {\,\begin{array}{*{20}{c}}1&3&{\lambda + 2}\\2&4&8\\3&5&{10}\end{array}\,} \right| = 0$
==> $1(40 - 40) - 3(20 - 24) + (\lambda + 2)(10 - 12) = 0$
==> $2(\lambda + 2) = 12 \Rightarrow \lambda = 4.$