Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

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

share|cite|improve this question
This is a good question. Many people talk about row reduced echelon form, but it is not clear when exactly we can consider a matrix in RREF for all cases. – nbro Jun 2 '15 at 11:01
There's here also a good explanation: – nbro Jun 2 '15 at 11:08

Yes, that matrix is indeed in row echelon form. There are three conditions for row echelon form

  1. All zero rows are at the bottom of the matrix.
  2. All rows begin with a leading $1$.
  3. The leading entry of a row is strictly to the right to any leading entries from above rows.

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.

Many matrices, especially if they are not square, will not have all the leading ones along the main diagonal, and that's perfectly O.K. As long as they satisfy the definition give above, they will be in row echelon form.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.