Linear Algebra - dimension of orthogonal complement

[GuiltySparks]

I've attached a copy of the problem and my attempt at a solution.

This seems like a relatively straightforward question to me, but my answer seems to be the exact opposite of what the answer key says.

I reach the conclusion that the answer is C, but the answer is apparently D.

I'm beginning to think that the answer key is wrong. Can anybody verify my solution?

 

[Dick]

I think your answer key is wrong.