Let's say that we have a system of linear inequalities:
It can be represented in a matrix form:
Does it hold that:
and that is invertible if and only if the whole system is solvable?
P.S. All the numbers are real. Would restricting them to be integers change the answer?
EDIT 1: for matrices and it holds that if and only if every element of is to corresponding element in .
EDIT 2: the are bounded to .