This is probably a very dumb question, but I just can't wrap my head around what I'm supposed to be doing.
The question is:
"Determine whether the set is a subspace of R3:
All vectors of the form (a,b,c) where a = 2b + 3c"
u + v is an element of R3
ku is an element of R3
The Attempt at a Solution
My question is.. is R3 just the set of all vectors with 3 terms..(a,b,c), (d,e,f)...etc? OR does it mean that the vector I get after multiplying by the scalar has to be of the same form as u, such that a = 2b + 3c
I think I'm phrasing this wrong so I will give an example.
Let's say I am checking vector addition.
So u = (2b + 3c, b, c) and v = (2e + 3f, e, f)
When I add them I get (2b+3c+2e+2f, b+e, c+f)
Is that in R3 since it has 3 terms which in fact would make it a vector space? Or do I need to check if the first term (2b + 3c + 2e + 2f) = 2(b+e) + 3(c+f) ?