Given the linear system:
\[ \begin{align} 2x_1+x_2-x_3+x_4-3x_5&=7,\\ x_1+2x_3-x_4+x_5&=2,\\ -2x_2-x_3+x_4-x_5&=-5,\\ 3x_1+x_2-4x_3+5x_5&=6,\\ x_1-x_2-x_3-x_4+x_5&=3. \end{align} \]
Find the value of \(\lfloor\Psi\rceil\) where
\[ \Psi=1000\left|x_1+x_2+x_3+x_4+x_5\right|. \]
by
Tunk-Fey Ariawan
