My question asks me to consider a matrix A

Then find a basis for the nullspace of A, and hence then dimension of the nullspace;

which I find to be .

Since there are two basis vectors the dimension is 2, right?

My problem then is "Using the rank-nullity theorem or otherwise, determine the dimension of the subspace of R^{4} spanned by the four columns of A".

R-N states that dimension null = #cols - rank...

So dimension null =2 , #cols = 4, so I'm guessing rank = 2...

I'm confused by the mention of the "dimension of the subspace of R^{4}" though.

Is the answer they're looking for simply 2? And how ought I to phrase this to explain my answer, rather than merely subtracting one number from another?

Thanks in advance