Ok, I made many mistakes. I know the answer now.
I end up with a reduced row echelon:
1 0 1
0 1 -2
0 0 0
(Numbers to the right of "x" represent sub-numbers)
x3=t (all real)
Then, the basis is:
I have more questions. How do I know that I'm being asked to find a basis in this form rather than one for the row or column space?
Thank you for your patience.