In the real vector space R^4, find a basis for the subspace Span(S), where S is

the sequence

(1, 0, 2, 0), (2, 2,−2, 4), (1, 1,−1, 2), (0, 2,−6, 4), (2, 0, 4, 0).

The solution which i downloaded from my uni's web is (1,0,2,0)

(0 ,1 ,-3 ,2).

this method i can see they wrote the vectors in rows and do suitable row operations.

But i used the method which taught in the lecture ,and i got the basis is (1,0,2,0),(1,1,-2,2),(0,2,-6,4).

(i wrote the vectors in columns and did row operations)

which one is right? can the subspace Span(S) have different basis??? Thank you very much!!