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# Gauss-Jordan procedure to put a matrix into reduced row echelon form

Put content here**Gauss-Jordan elimination** transforms a matrix into **reduced row echelon form** (RREF).
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**Algorithm:**
1. **Forward elimination:** Find the leftmost nonzero column. Use row swaps and row operations to create zeros below the pivot. Repeat for each subsequent row.
2. **Scale pivots to 1:** Divide each row by its pivot value.
3. **Backward elimination:** Starting from the rightmost pivot, create zeros above each pivot.
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**Example:** For $\begin{pmatrix} 1 & 2 & 3 \\ 0 & 1 & 2 \end{pmatrix}$, after backward elimination ($R_1 \leftarrow R_1 - 2R_2$): $\begin{pmatrix} 1 & 0 & -1 \\ 0 & 1 & 2 \end{pmatrix}$.
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The result is unique: every matrix has exactly one RREF.

# Parents

* Echelon matrices