The subspace of R^3 consisting of vectors whose second entry is zero.

So I made the kernel L={[a,0,b]^T }

I then let x = [1,0,1]^T be in L.

Now, I know I need to find a matrix A such that Ax=0. I'm not sure how to go about this...

I just wrote some stuff down:

0 1 0

0 1 0

0 1 0

Which does indeed make Ax=0 true, but it just doesn't seem right to me for reasons I can't explain..

What am I doing wrong?