Here's what I would have submitted:

Question 1:

Multiplication by N takes accomplishes the change of basis from B to the 
standard basis, so the change of basis from the standard basis to B is 
N^-1,

[10 -3 0]
[-3  1 0]
[-9  3 1]


Question 2:

We have N*([e1]_B)=e1, so [e1]_B=N^-1*e1 =

[10]
[-3]
[-9]


Question 3:

H is known to have three pivots and two free variables.
Thus Col A has dimension 3, and Nul A has dimnesion 2.