Determining the dimension of V: is this correct?

Question

For clearance: am I doing it right?

So, I have the vector in REF, which gives me:

1 1 -1 2
0 1 -3 1
0 0 0 0 
0 0 0 0

So, we have a rank of 2, hence: we have two pivot columns. We have a nullity of two, because we have two columns without a pivot (= free variables = nullity), so the dimension should be:

Dimension = Rank (2) + nullity (2) = 4

Am I correct or not?