You switch the sign of a constraint simply by multiplying everything by -1. I thought that was like elementary school math. Did they change something, and put that into graduate level math classes now? ;-)
But this question is confusing.
Reading the help for linprog, we see this:
X = linprog(f,A,b) attempts to solve the linear programming problem:
min f'*x subject to: A*x <= b
So linprog assumes constraints of the form A*x<=b. And that is exactly what your problem formulation states. <= is a LESS THAN OR EQUAL to inequality, NOT GE. The only GE constraints here are the lower bounds.
So it seems you have switched the signs on those inequalties for no good reason.
However, it IS true that linprog is a MINIMIZER, and your question states that you need to maximize z.
As such, you did do the correct thing, and switched the signs on z.