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In simplex method, to get the initial feasible solution. We often use Big-M method. My question is can we simply use elementary row transformation to get basis fesible solution instead introduce extra variables?

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In the primal simplex method, you want an initial basic feasible solution that is feasible with respect to both the equation constraints $Ax=b$ and to lower/upper bound constraints $l \le x \le u$. Conventional row operations can easily help you find a nonsingular subset of the columns of $A$ (a basis matrix, $B$), but this wouldn't help you in finding a basic solution that is feasible with respect to the bounds constraints $l \le x \le u$.

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  • $\begingroup$ Thanks for your reply. As my understanding, we have the standard constrain, i.e. $Ax=b,x\ge0$. If we have this standard form, can we use the row operations to get the basic solution as well? $\endgroup$ – maple Apr 17 '18 at 2:31
  • $\begingroup$ You'll have the same problem with the less general nonnegativity constraints. $\endgroup$ – Brian Borchers Apr 17 '18 at 2:49

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