Preview Activity1.2.1

Let's begin by considering some simple examples that will guide us in finding a more general approach.

  1. Give a description of the solution space to the linear system:

    \begin{equation*} \begin{alignedat}{3} x \amp \amp \amp {}={} \amp 2 \\ \amp \amp y \amp {}={} \amp -1. \\ \end{alignedat} \end{equation*}
  2. Give a description of the solution space to the linear system:

    \begin{equation*} \begin{alignedat}{4} -x \amp {} + {} \amp 2y \amp {}-{} \amp z \amp {}={} \amp -3 \\ \amp \amp 3y \amp {}+{} \amp z \amp {}={} \amp -1. \\ \amp \amp \amp \amp 2z \amp {}={} \amp 4. \\ \end{alignedat} \end{equation*}
  3. Give a description of the solution space to the linear system:

    \begin{equation*} \begin{alignedat}{3} x \amp {} + {} \amp 2y \amp {}={} \amp 2 \\ 2x\amp {}+{} \amp 2y \amp {}={} \amp 0. \\ \end{alignedat} \end{equation*}
  4. Describe the solution space to the linear equation \(0x = 0\text{.}\)
  5. Describe the solution space to the linear equation \(0x = 5\text{.}\)
in-context