I just received a message from the Linear Algebra lecturer
that there are a couple of typos on Linear Algebra Sheet 1.

In Question 4, you can assume that V is finite-dimensional.

Question 5 should read as follows:

Question 5.  Let V be a vector space over a field F and let E_1 
and E_2 be projections on V.

(i)  Show that E_1 + E_2 is a projection if and only 
if E_1E_2 + E_2E_1 = 0.

(ii)  Suppose that Char F  noteq 2.  Prove that E_1 + E_2 is a
projection if and only if E_1E_2 = E_2E_1 = 0.  [Hint: consider
E_1E_2E_1 in two different ways.]  Assuming this is the case, find the
kernel and image of E_1 + E_2 in terms of those of E_1 and E_2.

(iii)  What can be said if Char F = 2?