I'm having some trouble understanding about the independent rows in a basic solution. In the book Introduction to linear optimization by B&T, the authors give the definition of a basic solution as follows
where they claim that all equality constraints are active. However, in a later example, I noticed the following:
Apparently, all constraints in the later picture are inequality constraints, but the authors treat them as equality constraints and claim since they are active, we then have a basic solution.
So my question is: does inequality and equality matter when it comes to active constraints? Should I treat them differently?