Some vector spaces

The GAP code

vecs:=[[1,0,0],[1,1,1],[0,1,1]];
V:=VectorSpace(Rationals,vecs);
GeneratorsOfVectorSpace(V);
B:=Basis(V);
dim:=Length(B);

constructs the vector space over $\mathbb{Q}$ spanned by the vectors $(1,0,0),(1,1,1),(0,1,1)$, finds a basis, and computes its dimension.

Exercise 3.11.1   Construct the vector space over $\mathbb{Q}$ spanned by the vectors $(1,0,0),(1,1,1),(0,-1,1)$, find a basis, and compute its dimension. Do the same, but with $\mathbb{Q}$ replaced by $GF(3)$.