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# Definition of reduced row echelon form of a matrix

Put content here**Definition:** The **reduced row echelon form** of a matrix $A$ is the **unique** matrix $R$ in RREF that is row-equivalent to $A$.
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**Uniqueness Theorem:** Every matrix is row-equivalent to exactly one matrix in reduced row echelon form.
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**Why this matters:** The RREF is a canonical form — it provides a unique "fingerprint" for the row space of a matrix. Two matrices have the same row space if and only if they have the same RREF.
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**Computation:** The RREF is found by applying Gauss-Jordan elimination: forward elimination to reach REF, then scaling pivots to 1, then backward elimination to clear entries above pivots.

# Parents

* Echelon matrices