(i) Find the value of \(k\) for which the set of linear equations
\(\begin{aligned} x+3 y+k z & =4 \\ 4 x-2 y-10 z & =-5 \\ x+y+2 z & =1 \end{aligned}\)
has no unique solution.

(ii) For this value of \(k\), find the set of possible solutions, giving your answer in the form
\(\left(\begin{array}{l} x \\ y \\ z \end{array}\right)=\mathbf{a}+t \mathbf{b},\)
where \(\mathbf{a}\) and \(\mathbf{b}\) are vectors and \(t\) is a scalar.