1. Solve the following systems of linear equations and characterize their solution sets.(I.e., determine whether there is a unique solution, no solution, etc.) Also, write each system of linear equations as a single function $f: \mathbb{R}^{n} \rightarrow \mathbb{R}^{m}$ for appropriate choices of $m, n \in \mathbb{Z}_{+}$
(a) System of 3 equations in the unknowns $x, y, z, w:$
$$
\begin{array}{c}
x+2 y-2 z+3 w=2 \\
0.2 x+4 y-3 z+4 w=5 \\
5 x+10 y-8 z+11 w=12
\end{array}
$$
(b) System of 4 equations in the unknowns $x, y, z$ :
$$
\begin{array}{c}
x+2 y-3 z \\
x+3 y+z \\
2 x+5 y-4 z \\
2 x+6 y+2 z
\end{array}
$$
(c) System of 3 equations in the unknowns $x, y, z$ :