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.