a
For the equation to be inconsistent $D=0$
$\therefore D=\left|\begin{array}{ccc}{1} & {2} & {-3} \\ {0} & {0} & {k+3} \\ {2 k+1} & {0} & {1}\end{array}\right|=0$
$\Rightarrow \quad k=-3$
and ${D_1} = \left| {\begin{array}{*{20}{c}}
1&2&{ - 3}\\
3&0&0\\
0&0&1
\end{array}} \right| \ne 0$
So that system is inconsistent for $\mathrm{k}=-3$