0
$\begingroup$

Take $A = [1, -2, 0, 4]$ and $B=[1, 0, 0, 0]$ for example. I know the conditions to be in row echelon form are:

  • The first nonzero element in the row is a $1$ if the row does not consist entirely of zeros (a leading $1$).
  • All rows where the elements are zero are grouped to the bottom of the matrix.
  • In any two successive rows (say $\text{r}_1$, $\text{r}_2$), the "leading $1$" occurs farther to the right in $\text{r}_2$ than in $\text{r}_1$.
  • Each column that has a "leading $1$" has zeros everywhere else in that column.

Based on these conditions, is it safe to say that $A$ and $B$ are in row echelon form or reduced row echelon form?

$\endgroup$
3
$\begingroup$

Any $1\times n$ matrix is automatically in echelon form. However, if the leading entry is not a $1$, it will not be in reduced echelon form, so you'll have to divide through and fix that.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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