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.