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.

Letx,yS

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.