Polytopes: Understanding Linear vs Affine Spans

[arthurhenry]

The context is polytopes...reading some introductory material.

It talks about two points in R3, namely p=(1,0,0) and q=(0,1,0)
and tells me to notice that the linear span of of p and q and the affine span of p and q are not the same.

Could somebody tell me the difference? Thanks

 

[Stephen Tashi]

My guess is that the linear span is the set of all linear combinations of p and q and the affine span is the set of all affine linear combinations of p and q. (An affine linear combination requires that the sum of coefficients in the linear combination is 1 )

 

[micromass]

The linear span will be the plane <(0,0,0),(1,0,0),(0,1,0)>.
The affine span will be the line <(1,0,0),(0,1,0)>.

Do you see why??