#### Preview Activity 1.2.1.

In this activity, we will consider some simple examples that will guide us in finding a more general approach.

- Give a description of the solution space to the linear system:\begin{equation*} \begin{alignedat}{3} x \amp = \amp 2 \\ y \amp = \amp -1. \\ \end{alignedat} \end{equation*}
- 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*}
- Give a description of the solution space to the linear system:\begin{equation*} \begin{alignedat}{3} x \amp {} + {} \amp 3y \amp {}={} \amp -1 \\ 2x\amp {}+{} \amp y \amp {}={} \amp 3. \\ \end{alignedat} \end{equation*}
- Describe the solution space to the linear equation \(0x = 0\text{.}\)
- Describe the solution space to the linear equation \(0x = 5\text{.}\)