Q:

Why is any subspace affine?

I am studying 'Convex Optimization' written by Stephen Boyd. I am confused by an assertion in the book(page 27). Any one can tell me why and give an explanation ? 

Any subspace is affine, and a convex cone (hence convex).
   --Convex Optimization

A:

If $u, v \in U$, then $c_1u+ c_2v \in U$ where $c_1,c_2 \in \Bbb R$ . This is by the closure of subspace. 
Thus if we replace them with familiar constants this is simply, $c_1u+ (1-c_1)v \in U$ where we have chosen $c_2 = 1 - c_2.$

