Linear programme standard form

The standard form for a linear programme with $n$ variables and $m$ constraints is given by matrices $x, c \in M_{n,1}(\mathbb{R})$, $A \in M_{m,n}(\mathbb{R})$, and $b \in M_{m,1}(\mathbb{R})$ were we want to

$$\max_x c^T x \ \mbox{ such that } \ Ax \leq b \mbox{ and } 0 \leq x.$$

Some variants may use $\min$ instead of $\max$ in the objective function or use $\geq$ instead of $\leq$ in the constraints equation however this can easily be translated using the rules from the standard form lemma.