Answer
a.
$\left\{\begin{array}{l}
4w-2x+2y-3z=0\\
7w-x-y-3z=0\\
w+x-y-z=0
\end{array}\right.$
b.
$\{(0.5z,\ 0,\ 0.5z$, $z), z \in R\}$.
Work Step by Step
a.
The augmented matrix has 5 columns, so there are 4 variables.
Let the variables be w,x,y, and z.
System of equations:
$\left\{\begin{array}{l}
4w-2x+2y-3z=0\\
7w-x-y-3z=0\\
w+x-y-z=0
\end{array}\right.$
b.
The reduced system: $\left\{\begin{array}{l}
w-0.5z=0\\
x=0\\
y-0.5z=0
\end{array}\right.$
Taking z as a parameter,
express $w$ and $y$ in terms of $z$.
$w-0.5z=0 \Rightarrow w=0.5z$
$y-0.5z=0 \Rightarrow y=0.5z$
The solution set is $\{(0.5z,\ 0,\ 0.5z$, $z), z \in R\}$.
