- #1
Rijad Hadzic
- 321
- 20
Homework Statement
Homework Equations
The Attempt at a Solution
So for a subspace 2 criteria have to be met:
its closed under addition, and scalar multiplication.
Now I have the question
"Which of the following subsets of R3 are subspaces? The set of all vectors of the form (a,b,c) where a,b, and c are:
integers"
This subset is closed under addition, but if I multiply by a scalar, I get (ka,kb,kc), which seems like it is closed under scalar multiplication, but if that scalar is negative wouldn't I get: (-ka, -kb, -kc)? which means its actually not closed..
But then I have another question that says
"Consider the sets of vectors of the following form. Determine whether the sets are subspaces of R2 or R3. :"
(a,0)
Again passes addition, but I don't understand why it passes scalar multiplication as well?
if I multiply it by k, I get (ka,0)
which is of the same form as (a,0)
but if k is a negative scalar, wouldn't I get (-ka, 0), which means its not a subspace?
but my book is telling me that it is indeed a subspace.
Does anyone know what I'm missing here?