Note that even if you had a different basis from theirs, it doesn't imply that you made an error. There's an infinity of basis for . For example is also a basis for .
Given S = span{(0,-1,1), (2,0,3)} and T = span{(1,0,-1), (0,1,2),(1,2,3)}, find a basis for .
My answer: { (3/4, 1, 5/4) }.
Their answer: { ( 6, 5, 4) }.
Whose is right?
Ah, oops, made a silly mistake! Nevermind.