Differential Equations and Linear Algebra (4th Edition)

A matrix is a row-echelon matrix if: 1. If there are any rows consisting only of zeros, they are all together at the bottom of the matrix. 2. The first nonzero element in any nonzero row is a $1$. 3. The leading $1$ of any row below the first row is to the right of the leading $1$ of the row above it. A matrix is a reduced row-echelon matrix if it is a row-echelon matrix and any column that contains a leading $1$ has zeros everywhere else. Hence here because the second row has its leading $1$ not to the right of the above row's it is neither.