How to perform multiple row operations on a matrix simultaneously?

Questions
,
1

There are some neat ways to perform row operations, according to this discussion: http://mathematica.stackexchange.com/questions/3069/elegant-operations-on-matrix-rows-and-columns

However, I would like to perform multiple row operations without having to change the matrix for each operation.
Say I have a matrix and want to perform all these operations:

[ {

{1, 8, 3},

{4, 4, 6}, - R2 - R3

{4, 8, 5} - R3 - R2

} ]

Doing these simultaneous operations make the row reduction process much simpler and neater especially for showing working out.
How can this be done on mathematica?

Thanks!

2

For correctness one should mention the iteration step in operations: after having subtracted R2(0) from R2(0) the new R2 is R2(1) = {0,0,0}.
Subtracting then R3(0) the new R2 is R2(2) = R2(1) - R3(0) = -R3(0). This counting considers row operations only and does not fit to the general case. But let’s say you mean

 [{
{1,8,3},
{4,4,6}, - R2(0) - R3(0)
{4,8,5}  - R3(0) - R2(0)
}]

i.e. all operations have to take place with the initial rows, then it means to exchange R2 with R3 and have both negative

In[80]:= Clear[mKnill]
mKnill={{1,8,3},{4,4,6},{4,8,5}};
In[83]:= {{1,0,0},{0,0,-1},{0,-1,0}}.mKnill // MatrixForm
Out[83]//MatrixForm= (1	8	3
-4	-8	-5
-4	-4	-6
)