Exercise4

The following 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{equation*} \begin{alignedat}{3} -x_1 \amp {}+{} \amp 2x_2 \amp {}={} \amp 3 \\ 2x_1 \amp {}-{} \amp 4x_2 \amp {}={} \amp k \\ \end{alignedat} \text{.} \end{equation*}
  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{equation*} \begin{alignedat}{3} 2x_1 \amp {}+{} \amp 4x_2 \amp {}={} \amp 3 \\ -x_1 \amp {}+{} \amp kx_2 \amp {}={} \amp l \\ \end{alignedat} \text{.} \end{equation*}
in-context