> [!Definition] Definition (Reduced row echelon form/ RREF) > A [[Real Matrices|real matrix]] $A$ is said to be in **reduced row echelon form** (or **RREF**) if: > 1. The leftmost non-zero entry of any non-zero row is $1$ (leading $1$ or pivot); > 2. The leading $1$ of a non-zero row appears strictly to the right of leading $1$s of the nonzero rows above it; > 3. any zero rows appear below the non-zero rows; > 4. in a column that contains a pivot, all other entries of that column are zero. > >If only ($(1)-(3)$) hold, we say that the matrix is in **row echelon form**. If $(4)$ holds as well, we say the matrix is in **reduced row echelon form**. ^9f9c22 # Properties By [[Existence of Reduced Row Echelon Form of Real Matrix]], ....