Okay yes, I should have been able to figure that out myself. But then suppose you have row reduced matrix like the one on the attached picture. As a basis for the range you choose the vectors equal to columns with pivot points -i.e. column 1,2,3. However - wouldn't it be just as good to choose 1,2 and 4? Since that'd also make a 3 pivot points.
And lastly: Would it then also work to choose any other combination of 3 vectors out of the 4?