What is ?
To show that W is closed under addition and scalar multiplication take and where and . Now and since is closed under addition we get that where and so on. In the same manner and is closed under multiplication...and the rest you can do.
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?