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# How to perform multiple row operations on a matrix simultaneously?

Posted 10 years ago
 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!
 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 )