Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 4 / 18H / a / Solution

A vector $x$ is a basic feasible solution whenand the columns $A_i$ for which $x_i>0$ are linearly independent. Equivalently, after extending those columns to a basis of the column space of $A$, one sets all nonbasic variables to zero and solves for the basic variables, obtaining a nonnegative vector.