Hey there,

I have been studying all day for an exam I have tomorrow and now I find myself stuck on something I really ought to know...

Here is the problem: Let , , and be vectors in a vector space . Show that the set of all linear combinations of , ,

is a subspace of .

A: Well, this is clearly the of and therefore is a subspace of V. Even so, the teacher wants me to show W is nonempty, closed under addition, and closed under scalar multiplication.

So, would I just choose some and and then show W is closed under addition and scalar multiplication by showing ?

Do the constants in have to be primed or am I just concerned with distinguishing between my vectors?

Thanks