# Given an overdetermined system of linear equation, find a subset that can be solved with exact solution

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.

For example:

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?

• By RREF we can select the independent equations. – user Apr 14 '18 at 20:37