The system of linear equations:

(a) $k \neq 0$

For a unique solution, $|A| \neq 0$.

The given system of equations can be written in matrix form as follows:

$\left[\begin{array}{ccc}1 & 1 & 1 \\ 2 & 1 & -1 \\ 3 & 2 & k\end{array}\right] \neq 0$

$\Rightarrow 1(k+2)-1(2 k+3)+1(4-3) \neq 0$

$\Rightarrow k+2-2 k-3+1 \neq 0$

$\Rightarrow k \neq 0$

So, the given system of equations has a unique solution if $k$ is not equal to 0 .