Confused about col/rows of matrices

[PragmaOnce]

Can someone tell me (when RREFing a matrix) when do we put the vectors of a subspace in columns of a matrix and when in rows?

Example from my notes:
Here, my prof put the vectors in columns:

and here, he put the vectors in rows:

Thanks!

 

[mathwonk]

an mxn matrix represents a linear map from k^n to k^m. the rows represent linear components functions of the map, i.e. linear maps from k^n to k, and there are m of them. the columns represent vectors in the target space k^m, and there are n of them. they are the values of the map on the n standard basis vectors of the source space.