Problem 4: was poorly done, probably because they didn't fully understand the 
question; there were some comments 
about not knowing what {R}/0 meant. I usually gave 2/10 if there was some 
effort.


Problem 5: was done in a 'reversed' bad way.
They did the classic error of starting the proof wrong, which made it 
impossible to give part marks. This is what a lot of people did:
aT(x)+bT(y)=0 such that a=b=0
then they just went on
T(ax+by)=0
since
T(0)=0
ax+by=0 ... therefore since a=b=0 then x and y are linearly independent.