Some vector spaces

The MAGMA code

V := VectorSpace(Rationals(),3);
W:=sub<V|[1,0,0],[1,1,1],[0,1,1]>;
W;
Basis(W);
Dimension(W);

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 3.15.1   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 $GF(3)$.