# Definition of matrix in reduced row echelon form

Put content here**Definition:** A matrix is in **reduced row echelon form (RREF)** if:
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1. It is in row echelon form.
2. Every leading entry is 1 (these are called **leading 1s**).
3. Each leading 1 is the only nonzero entry in its column.
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**Example:**
$$\begin{pmatrix} 1 & 0 & 0 & 3 \\ 0 & 1 & 0 & -2 \\ 0 & 0 & 1 & 5 \end{pmatrix}$$
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This is in RREF: each leading 1 is the only nonzero entry in its column.
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**Contrast with REF:** A matrix in (plain) row echelon form may have nonzero entries above pivots and pivots other than 1. RREF adds the uniqueness property.

# Parents

* Echelon matrices