This set of solutions gives two variants for problems 17-19. 
The first solutions marked `ad hoc' pretend to know nothing about 
row transformations. They represent a naive approach knowing 
merely that the row space is the span of the rows, so from 
the rows we may need to kick out redundant ones (if any) to get a 
set that is linearly independent. These solutions are here to illustrate 
the definitions. They are not the way you'd usually solve these problems 
and are not how it is done in the book. 

The second set of solutions is in the style how one uses row 
transformations to find bases of row space and column space 
effectively. You'll wnat to use this method in practice. 

The answers in both solution variants differ, and legitimately so:
The questions ask to find *a* basis of the row / column space. 
So there are many correct solutions, and different solutins can be 
retrieved by different approaches.