Answer
a.
$\left\{\begin{array}{l}
2w+17x-23y+40z=0\\
2w+5x+y+3z=0\\
x-2y+3z=0
\end{array}\right.$
b.
$\{(-5.5y, \ 2y, \ y, \ 0), \ \ y\in \mathbb{R}\}$.
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:
$\left\{\begin{array}{l}
2w+17x-23y+40z=0\\
2w+5x+y+3z=0\\
x-2y+3z=0
\end{array}\right.$
b.
The reduced system: $\left\{\begin{array}{l}
w+5.5y=0\\
x-2y=0\\
z=0
\end{array}\right.$
Taking y as a parameter,
express w and x in terms of y.
$w+5.5y=0 \Rightarrow w=-5.5y$
$x-2y=0=0 \Rightarrow x=2y$
The solution set is $\{(-5.5y, 2y, y, 0), y\in \mathbb{R}\}$.
