So, I think the basis of the row space of matrix M are rows in the reduced form of matrix M.
The question is what is the basis of the column space of matrix M. Are they columns in the reduced form of matrix M?
The question is what is the basis of the column space of matrix M. Are they columns in the reduced form of matrix M?
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NO , use the columns of the original that correspond to the lead 1's in the reduced form