1. ## conflicting solution (basis) - Nevermind

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 $\displaystyle S\cap T$.

My answer: { (3/4, 1, 5/4) }.

Their answer: { ( 6, 5, 4) }.

Whose is right?

Ah, oops, made a silly mistake! Nevermind.

2. 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 $\displaystyle S\cap T$. For example $\displaystyle \{ ( 12, 10, 8) \}$ is also a basis for $\displaystyle S\cap T$.

3. Yes, but mine wasn't a scalar multiple of theirs . I understand what you're saying though.