I am trying to show that

, is a basis for

Linear independence is alright.

where the first equation implies .

I can't figure out how to show it spans

Let

Find s.t.

so we get the system of equations

I can kind of see how r,s could exist. But I don't know how to express them explicitly.

Thank you for your help.

OR EDIT:

Since they are linearly independent, and dim C^2 = 2, it forms a basis.