how do i prove that every subspace is a spanning set for itself?
sorry im very weak at proofing.
let S be the subspace.
so we need to show that S = span(S)
we shall show that S⊂span S ( shown in previous post) and span S ⊂S
to show that spanS ⊂ S,
lets assume that S is in n dimension where xi∈ S where 1<i<n
span S =a1x1+...+anxn ⊂ S as S being a subspace obeys the laws of scalar multiplication and addition.
is this done like this?