Finding a Basis for Subspace V Spanned by (1 1 2) etc.

[Dell]

if i am asked to fin a basis for the subspace V, which is spanned by ( 1 1 2) ( 2 -1 1) (1 -2 -1)...

i put them into a matrix system
1 1 2
2 -1 1
1 -2 -1
now after performing elementart operations i get
1 1 2
0 -3 -3
0 -3 -3
so since R3 and R2 are the same, dimV=2, my question is if i am asked to give a basis, should i give ( 1 1 2) (0 -3 -3) or should i return to the original vectors given and answer (1 1 2 ) (2 -1 1) or perhaps something else,, is ther a more correct answer if i am asked to give a basis

 

[Defennder]

There are an infinite number of possible bases for every vector space. They are all equally valid. Selecting one over another does not matter.