Example 3.8.2. The theorem tells you that doing the row operation 𝐫 1 ↦ 𝐫 1 + 2 𝐫 2 to a matrix with three rows is the same as left-multiplying by the 3 × 3 elementary matrix (1 2 0 0 1 0 0 0 1).

3.8 Elementary matrices Definition 3.8.1. An elementary matrix is one obtained by doing a single row operation to an identity matrix. Example 3.8.1.