1) Find a basis for, and the dimension of, , where

I'm don't really know what means. But would you start of this question by:

1) Reducing into reduced row-echelon form.

2) Then looking at the leading columns (or pivot columns) and take those to the basis.

3) Dimension can then be determined

So the reduced row-echelon form is:

I just need someone to verify whether what I'm doing is correct here.