Problem

(a) Find the values of $k$ for which the system of equations

$$\begin{aligned} x + 2y + 3z &= 1,\\ kx + 5y + 6z &= 2,\\ 7x + 2ky + 9z &= 3 \end{aligned}$$

does not have a unique solution.

(b) Given that $k = 1$, show that the system of equations in part (a) is consistent. Interpret this situation geometrically.