Preview Activity 1.2.1.
In this activity, we will consider some simple examples that will guide us in finding a more general approach.
(a)
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*}
(b)
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*}
(c)
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*}
(d)
Describe the solution space to the linear equation \(0x =
0\text{.}\)
(e)
Describe the solution space to the linear equation \(0x =
5\text{.}\)