Exercise 6

The following linear systems contain either one or two parameters.

1. For what values of the parameter $k$ is the following system consistent? For which of those values is the solution unique? $$\begin{alignedat}{3} -x_1 & {}+{} & 2x_2 & {}={} & 3 \\ 2x_1 & {}-{} & 4x_2 & {}={} & k \\ \end{alignedat}$$.

2. For what values of the parameters $k$ and l is the following system consistent? For which of those values is the solution unique? $$\begin{alignedat}{3} 2x_1 & {}+{} & 4x_2 & {}={} & 3 \\ -x_1 & {}+{} & kx_2 & {}={} & l \\ \end{alignedat}$$.