The question:
Show that the set
for some
is a subspace of
My attempt:
Using Subspace Theorem:
S clearly contains the zero vector in since the set is all solutions to the parametric form of a line through the origin.
Let x,y S
x + y =
=
Since and , , so
=
(I'm unsure of that reasoning)
Therefore closed under vector addition.
Let
=
= Since and , so
=
Therefore closed under scalar multiplication.
Is this proof sound? Thanks.