I am looking to describe geometrically (as a line, plane,...) all linear combinations of the following vectors-
$(1, 0, 0)$
$(0, 1, 1)$
so if to get all linear combinations I take c(1,0,0) + d(0,1,1) = (c, d, d)
This looks to me like it 'hits' every point in $R^3$ but only in the form of (c,d,d). So a point (5,9,7) isnt the set of combinations. So what is the geometric description for the set of all linear combinations?