The Fourier-Motzkin elimination (FME) is a procedure that reduces an n -variable problem to an

Karina Trujillo

Karina Trujillo

Answered question

2022-06-05

The Fourier-Motzkin elimination (FME) is a procedure that reduces an n-variable problem to an equivalent ( n 1 )-variable problem. It is analogous to Gaussian elimination but for a system of inequalities. Does Fourier-Motzkin elimination also not change the solution set? Why or why not?

Answer & Explanation

Cristian Hamilton

Cristian Hamilton

Beginner2022-06-06Added 23 answers

I think the answer is affirmative. By what I know of the Fourier-Motzkin elimination: FME first classifies the inequalities into three kinds and then change the coefficient of the first variable x 1 to 1 or 0, this first step does not change the solution set apparently; then FME kicks x 1 out of the game by observing that all possible values of x 1 is already obtained for a fixed x = ( x 2 , . . . , x n ), this doesn't change the solution set too. Hence, in conclusion, Fourier-Motzkin elimination also not change the solution set.

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