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)

x1=- x3

x2=2 x3

x3=t (all real)

Then, the basis is:

-1

2

1.

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.