If u and v are two elements of a vector space V show that Sp

If u and v are two elements of a vector space V show that Span(u, v) is a subspace of V.

---- We need to prove that Span(u, v) is closed under addition and scalar multiplication .

If u, v are two elements in Span(S) then we can write:

u = c1v1 + c2v2 ....... cn*vn ; v = d1v1 +d2v2 +d3v3..... dnvn

So, u +v = (c1+d1)v1 + (c2 +d2)v2 + (c3+d3)v3.......

and for a scalar : cu = (cc1)u1 + (cc2)u2 + (cc3)u3.....

So, both u+v and cu are in span(S) because linear combination of elements in S

Hence Span(u,v) is closed under addition and scalar multiplication, so a subspace of V