Definition of (echelon matrix/matrix in (row) echelon form)
Created almost 9 years ago, updated 5 months ago
ID23539
Definition: A matrix is in row echelon form if:
All nonzero rows are above any rows of all zeros.
The leading entry (first nonzero entry from the left, also called the pivot) of each nonzero row is in a column to the right of the leading entry of the row above it.
All entries in a column below a leading entry are zeros.
Note: Some definitions additionally require the leading entry to be 1, but this is not universal. When leading entries are all 1 and are the only nonzero entries in their column, the matrix is in reduced row echelon form.
**Definition:** A matrix is in **row echelon form** if:
1. All nonzero rows are above any rows of all zeros.
2. The leading entry (first nonzero entry from the left, also called the **pivot**) of each nonzero row is in a column to the right of the leading entry of the row above it.
3. All entries in a column below a leading entry are zeros.
**Example (in echelon form):**
$$\begin{pmatrix} \boxed{2} & 3 & 1 \\ 0 & \boxed{4} & 5 \\ 0 & 0 & \boxed{6} \end{pmatrix}$$
**Note:** Some definitions additionally require the leading entry to be 1, but this is not universal. When leading entries are all 1 and are the only nonzero entries in their column, the matrix is in **reduced row echelon form**.