# Statement

Lemma

For a linear programme given by $A, b,$ and $c$ if we take the dual linear programme and then the dual of that, we get back to the original linear programme .

# Proof

Just following the definition, the dual linear programme is defined by $-A^T$, $-c$ and $-b$. Then the dual of that is given by $-(-A^T)^T$, $-(-b)$ and $-(-c)$ which by the laws of linear algebra gives us $A$, $b$ and $c$ back.

# The dual dual linear programme is the original linear programme

# Statement

# Proof