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?

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

If the system has an unique solution the standard way is by RREF otherwise we can find an approximate solution by least squares.

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