Hi. I have the 3*3 matrix C=(1,-1,1; 2,0,1+i; 0,1+i,-1) and I must find an orthonormal basis for it's nullspace.(Headbang)

So first I have reduced the matric to row echelon form and I have this matrix

(1,-1,1; 0,1,-0.5+0.5i; 0,0,0)

How do I read off from this the nullspace of this matrix? What is a basis for this nullspace?

My plan once I have that is to use gram schmitt to create an orthonormal basis.

Any help much appreciated!