Ok so I know the the four fundamental subspaces are Ker(A), Ker(A*), Range(A) and Range(A*), where * denotes the conjugate transposed matrix. So after calculating for example Ker(A), which has (1,1,-2)^T as a basis, how does one proceed to find the matrix of orthogonal projection?

I also know that after I've found the matrix of orthogonal projection of Ker(A) that I need everyhting that is orthogonal to this space to find Ran{A*), since Ker(A)= Ran(A*) _|_, where _|_ denotes that it's orthogonal.

I just need help with the actual calculations..