Write a system of linear equations with 5 unknowns and 3 equations.
See development and solution
Development:
$$$\left\{ \begin{array} {rcl} 2x+3y-z+u-2v & = & 1 \\ x-3y+2z-8+2v &=& -1 \\ -2x+y-2z-u+2v &=& 3 \end{array}\right.$$$
or we can also write it in the matricial form: $$$\begin{pmatrix} 2 & 3 & -1 & 1 & -2 & | & 1 \\ 1 & -3 & 2 & 1 & 1 & | & -1 \\ -2 & 1 & -2 & -1 & 2 & | & 3 \end{pmatrix}$$$
Solution:
$$$\left\{ \begin{array} {rcl} 2x+3y-z+u-2v & = & 1 \\ x-3y+2z-8+2v &=& -1 \\ -2x+y-2z-u+2v &=& 3 \end{array}\right.$$$