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?
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.
Thank you! Thats how I orginally did it when it was homework last week ha. I saw someone do it another way online and then I got all confused. Thats what I was trying to replicate. I better get some sleep.
Originally Posted by Jose27