Nullspace and Column Space Question

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Nullspace and Orthogonal Complement

Quick question: is the nullspace the orthogonal complement of the column space or the the row space?

Thanks, sorry I don't have my textbook nearby.
 
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Hey that was just in my linear algebra exam the other day. The theorem goes:
nullspace[W]=rowspace[V]

where W is the subspace and V is the orthogonal complement
 
I never memorize these things. Especially when they are quite easy to reproduce.
A vector x is in the nullspace of A iff Ax=0.
The components of Ax are the dot products of the row vectors of A with x. All the components must be zero, so x is in the nullspace of A iff it is orthogonal to all the rows of A.
Therefore the the nullspace of A the is orthogonal complement of the rowspace of A.
 

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