# Example of row reducing a 3-by-3 matrix

Put content here**Example:** Row-reduce a 3-by-3 matrix to RREF:
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$$A = \begin{pmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 5 & 8 \end{pmatrix}$$
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**Step 1:** Swap $R_1 \leftrightarrow R_2$:
$$\begin{pmatrix} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 2 & 5 & 8 \end{pmatrix}$$
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**Step 2:** $R_3 \leftarrow R_3 - 2R_1$:
$$\begin{pmatrix} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 & 1 & 2 \end{pmatrix}$$
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**Step 3:** $R_3 \leftarrow R_3 - R_2$:
$$\begin{pmatrix} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{pmatrix}$$
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**Step 4:** $R_1 \leftarrow R_1 - 2R_2$:
$$\begin{pmatrix} 1 & 0 & -1 \\ 0 & 1 & 2 \\ 0 & 0 & 0 \end{pmatrix}$$
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This is the RREF. Rank = 2, one free variable ($x_3$).

# Parents

* Echelon matrices