# I A nonempty subspace

1. Oct 6, 2016

### Mr Davis 97

I have a simple question. Say we have some subspace that is nonempty and closed under scalar multiplication and vector addition. How could we deduce that $0 \vec{u} = \vec{0}$?

2. Oct 6, 2016

### Krylov

It holds that $0\vec{u} = \vec{0}$ for every $\vec{u} \in V$, where $V$ is any vector space. This follows directly from the defining axioms and does not require the introduction of a subspace.

What did you try yourself to prove it?

3. Oct 6, 2016

### Math_QED

Every subspace is non empty, closed under scalar multiplication and vector addition so no need to say that.

You should show some effort.