Here's what I would have submitted:


Question 1:
A, B, D, and M have pivots in every row, so they're onto.
B and E have pivots in every column, so they're one-to-one.



Question 2:
T takes e1 to e2, then to e1, then to e1.  
T takes e2 to -e1, then to -e2, then to 0.
So the matrix is [T(e1) T(e2)]=[e1 0], or 
[1 0]
[0 0].



Question 3:
L(e1+e3)=L(1/2((e1+e2+e3)+(e1-e2+e3)))
=1/2(L((e1+e2+e3)+(e1-e2+e3))=1/2(L(e1+e2+e3)+L(e1-e2+e3))
=1/2(5+1)
=3.