I am trying to find the null space and the column space for this matrix.

$\pmatrix{1&1&1&1\\1&2&0&3\\0&1&-1&2}$

The process I usually follow is to first convert to REF, which gives:

$\pmatrix{1&0&2&-1\\0&1&-1&2\\0&0&0&0}$

Which, reading from REF, seems to give a basis of the form $\pmatrix{-2\\1\\1\\0}\pmatrix{1\\-2\\0\\1}$ for the null space. It looks a little odd, but I suppose it makes sense that a matrix with $n=4$ would have vectors of $4$ entries.

Where I am really confused is how to find a basis for col(A). I would usually just take the two pivot columns and call that a basis, but clearly those vectors would not be the same size as the ones in null(A). How else would I find col(A) then?