Prove.

Where, if V is a subspace,

is perpendicular to

Now, I know the rank is number of linearly independent columns in a matrix. So the rank of would be the number of linearly independent rows of A.

I know that the nullspace is the solutions to

However, the "perpendicular compliment" is a term I am not familiar with. And the simple definition does not really help me. Can someone help me with this proof?