# Is a matrix in row echelon form if the leading ones do not have a perfectly diagonal shape?

I'm slightly confused by the definition of row echelon form. For example, is this matrix considered to be in row echelon form?

$$\begin{pmatrix} 1 & 2 & 5 & 8 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 1 \\ \end{pmatrix}$$

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2. All rows begin with a leading $1$.
Your matrix satisfies 1. because there are no zero rows. It satisfies 2. because all the entries begin with leading $1$s. It also satisfies 3. The leading entry of the second row is in position $3$ which is to the right of the leading entry in row $1$. The leading entry of row $3$ is also to the right of the leading ones above it.