Assume that you are solving a LP using Simplex method.
You reach a point and know that at this point, $x_j$ (one of the decision variables) should leave the basis.
So, you perform a ratio test to see which variable should enter the basis and fill the place of $x_j$.
But, In this state, the result of your ratio test is not unique. For example, you can arbitrarily choose $x_k$ or $x_l$ to enter the basis.
Regardless of which one you choose for entering the basis, Can you conclude that the new basic feasible solution, which is achieved by choosing $x_k$ or $x_l$ as the entering variable, Is degenerate?
If yes, Prove it.
If no, give a counterexample.
Note: I believe this claim is true... But writing a formal proof is what i need. The problem is that i always saw tables in Simplex method and proving such things seems a bit strange to me. I don't know how this proof can be started.
Any hints or answers will be appreciated.
