Given a set A such that A consists of an overdetermined system of linear equation.
Find $$ B \subset A $$ such that B has x equations and x unknowns and has an exact solution.
In a system where you have 4 unknowns and 7 equations, you can solve this by trying all 4 distinct equations you can create from the 7 equations, and then see if it's solvable.
But the permutations become really big as your overdetermined system grows.
Is there a correct way to do this? Is Linear Programming an option? & if so, how to change this into a linear programming problem?