I'm really good at visualizing things and it's how linear algebra really makes sense to me, but I had the intuition that if you have a matrix A with a col space and a nullspace, if you take the transpose of A, you now essentially swapped your col space and null space (which I guess I'm implying that I think the null space is my row space). I'm pretty sure I'm going wrong somewhere and someone correct my misunderstanding?
I'm trying to think why
$(Col(A))^⊥ = Null(A^T)$