# Definition of echelon form of a linear system

Put content here**Theorem:** All echelon forms of a given linear system have the same pivot positions, and therefore the same free variables.
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While the exact numerical entries in different echelon forms may vary (depending on the sequence of row operations), the **positions of the pivots** are uniquely determined by the system itself. This means the classification of variables into basic and free variables is invariant.
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**Why this matters:** When solving a system, you can use any valid sequence of row operations — the set of free variables you identify will always be the same.
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**Note:** The *reduced* row echelon form (RREF) is unique for a given matrix, but ordinary echelon forms are not unique.

# Parents

* Linear systems of equations