Answer
a. $\left\{\begin{array}{l}
w+y+z=0\\
w-x+2y+3z=0\\
3w-2x+5y+7z=0
\end{array}\right.$
b. $\{(-y-z, y+2z, y, z),\ \ y,z\in \mathbb{R}\}$
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:
$\left\{\begin{array}{l}
w+y+z=0\\
w-x+2y+3z=0\\
3w-2x+5y+7z=0
\end{array}\right.$
b.
The reduced system: $\left\{\begin{array}{l}
w+y+z=0\\
x-y-2z=0
\end{array}\right.$
Taking y and z as parameters,
express w and x in terms of z.
$w+y+z=0 \Rightarrow w=-y-z$
$x-y-2z=0 \Rightarrow x=y+2z$
The solution set is
$\{(-y-z, y+2z, y, z),\ \ y,z\in \mathbb{R}\}$.
