 The set {(1, 0, 0), (0, 1, 0), (1, 1, 0)} is not a spanning set of R3; instead its span is the space of all vectors in R3 whose last component is zero.That space (the space of all vectors in R3 whose last component is zero) is also spanned by the set {(1, 0, 0), (0, 1, 0)}, as (1, 1, 0) is a linear combination of (1, 0, 0) and (0, 1, 0).It does, however, span R2.