# Detached coefficient form

### From Glossary

Given the system , we augment the objective equation: . Then, detaching the variables, the form is:

Upon multiplying by the inverse of a basis, say , where
, the *detached coefficient form* becomes

where (conformal with the partition of the columns of ). Now if we subtract times the first rows from the last row, this becomes

Recognizing that is the vector of basic levels, and the associated objective value is , we can drop the first columns plus column (corresponding to ) and form the tableau associated with this basis (adding labels to identify the basic variables in the rows and nonbasic variables in the columns).