The matrix \(A\) is given by \(A = \begin{pmatrix} 1 & 2 & 3 \\ 4 & k & 6 \\ 7 & 8 & 9 \end{pmatrix}\).

1. Find the set of values of \(k\) for which \(A\) is non-singular.
2. Given that \(A\) is non-singular, find, in terms of \(k\), the entries in the top row of \(A^{-1}\).
3. Given that \(B = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \end{pmatrix}\), give an example of a matrix \(C\) such that \(BAC = \begin{pmatrix} 2 & 1 \\ k & 4 \end{pmatrix}\).
4. Find the set of values of \(k\) for which the transformation in the \(x-y\) plane represented by \(\begin{pmatrix} 2 & 1 \\ k & 4 \end{pmatrix}\) has two distinct invariant lines through the origin.