In linear programming, if there are 'm' equations and 'n' variables, by making 'n-m' variables non basic(i.e. zero), we can get the corners of the feasible region. I could not understand how this works i.e., how we reach the corner points. Please explain.

Edited: I can understand that if the constraint coefficient matrix has full row rank ( m rows), keeping n-m variables zero will give a unique solution because 'm' independent vectors of 'm' dimensions combine to give a single vector of 'm' dimensions. But why should this unique solution (n dimension vector with at least n-m zero components) represent the corner point?

• I suggest consulting your textbook or notes...surely this is covered somewhere. It's pretty fundamental to the theory of linear programming. – Math1000 Mar 8 at 3:34
• @Math1000 Could you please suggest a book. My professor thought me just the simplex algorithm and no further explanation as to what happens in each step. – Mohan Mar 8 at 3:42
• Is this related? math.stackexchange.com/questions/896388/… – David K Mar 8 at 4:44
• See this thread for some recommended textbooks: math.stackexchange.com/questions/20643/linear-programming-books – Math1000 Mar 8 at 17:51
• @Math1000 Thanks man, one of the books was really good. There was a really good explanation for why the basic feasible solution (unique solution with n-m zero components) is a corner of the polyheadron feasible region. – Mohan Mar 9 at 4:17