We know that a subspace (of a vector space $V$) is a vector space that follows the same addition and multiplication rules as $V$, but is a vector space a subspace of itself?
Also, I'm getting confused doing the practice questions, on when we prove that something is a vector space by using the subspace test and when we prove V1 – V10, which are the ten axioms of vector spaces. So for example in $\Bbb R^2$, we have that $\vec{x} + \vec{y} = \vec{y} + \vec {x}$, etc..
Best Answer
Yes, every vector space is a vector subspace of itself, since it is a non-empty subset of itself which is closed with respect to addition and with respect to product by scalars.