1
$\begingroup$

$$\begin{bmatrix}1&0&2&0 \\ 0&1&1&0 \\ 0&0&0&1\end{bmatrix}$$

I see that the leading ones are in order by row (ie. the leading one in a row below is to the right of the above).

I also see that the leading 1's are the only non-zero entry in the column.

Issue:

One condition for RREF is:

All rows containing a non zero entry are above rows which only contain 0's.

This is clearly false for this example, then how is this a RREF?

  • 0
    There aren't any rows which only contain zeroes in the identity, so none of its rows meet that condition , would you say that it is not rref either? – 2017-01-16
  • 0
    @Nij, then what is the criteria? – 2017-01-16

2 Answers 2

3

The example doesn't fail that criterion!

To fail it, there would have to be a row of zeros above a nonzero row.

I'm the current situation, you can say it is vacuously true since now zero is exists to meet the criterion, but if you append a row of zeros to the bottom, it would be non vacuously satisfied. If you prepended a row of zeros at the top, he criterion would fail.

1

The condition you note as "clearly false" is in fact irrelevant, since the matrix you give does not have any rows which contain only zeroes.