To find a 8-100p in B U {(P,q)} , place an entry of +8 in the nonbasic cell (p,q).
Then make alternating entries of -8 and +8 among the basic cells, such that each row and
column contains a +8 and -8 or none at all. The cells marked by +8 and -8 creates a
unique 8-100p. Cells marked +8 are called recipient cells and cells marked -8 are called
donor cells. 8-100ps can be used to change the basis, which is shown in the next theorem.
Theorem (2.g). Let B be a basis from A (ignoring one row) and let d be another column
corresponding to a nonbasic variable which is entering the basis. The vector y=B-1 d will
give the changes in the current basic variables when the new variable is entered. The
components of the vector y=B-1 dare + 1, -lor O.