Hi all,

Got asked the following question in lecture:

Let $\displaystyle \bf v$ $\displaystyle \in R^n$. Prove that $\displaystyle P = \{\bf u \in R^n: \bf v * \bf u = 0\}$ is a subspace of $\displaystyle R^n$.

I understand that I must show that:

1. P is not empty.

2. P is closed under addition

3. P is closed under scalar multiplication

Just not sure, how I would show the 2nd and 3rd property. Thanks