Today was my first course of linear programing, I've just read again my notes and I'm not sure how does this array of equations actually transformed itself.
\begin{equation*} \begin{cases} \max a^Tx+b^Ty+c^Tz \\ \\ Ax + By+ Cz \le d\\ Dx + Ey + Fz \ge e\\ Gx + Hy + Iz =f\\ \\ a\ge0,b\le 0 \end{cases} \end{equation*}
Is it transformed as a canonical form as
\begin{equation*} \begin{cases} \max a^Tx-b^Ty+c^Tz \\ \\ Ax - By+ Cz \le d\\ -Dx + Ey - Fz \le -e\\ \\ Gx - Hy + Iz \le f\\ -Gx + hy -Iz \le -f\\ \\ a\ge0,b\le 0 \end{cases} \end{equation*}
