If V={(x_1, x_2) ∈ R2|x_1≤0, x_2≤0} Is V a linear subspace of R2?
Sol: I wrote, it's not a subspace since the vector -v= [-1,-1] belongs to the set but v does not belong to it. Am I right? Help!
Yes, you are.
Fernando Revilla
Just to elaborate a bit:
is not an -subspace of because it is not closed under scalar multiplication by elements from the field (which is basically what your example is saying).
That is, dealing with vector spaces over some field , one of the conditions for to actually be a subspace of is that, for any , we must have .
This is not the case in your example. As you pointed out, and , but .