Why isn't removing zero rows an elementary operation? My prof taught us that during Gaussian Elimination, we can perform three elementary operations to transform the matrix:
1) Multiple both sides of a row by a non-zero constant
2) Add or subtract rows
3) Interchanging rows
In addition to those, why isn't removing zero rows an elementary operation? It doesn't affect the system in any way. Define zero rows to be a row with no leading variables.
For example isn't $\begin{bmatrix}a & b & k\\c & d & m\end{bmatrix} \rightarrow 
\begin{bmatrix}a & b & k\\c & d & m\\0 & 0 & 0\end{bmatrix}$

Because we want the dimensions of the matrix to remain fixed.  I can think of two reasons for this.


*

*So that performing an elementary row operation will correspond to multiplication on the left by an elementary matrix.

*Changing the dimensions of the matrix by adding or removing zero rows does not help us solve the system, so why allow it?  The (other) row operations do not change the size of the matrix, so let's keep things simple and fix it once and for all.
