How to find a subspace in $\mathbb{R}^3$ I am having trouble finding if there is a subspace in $\mathbb{R}^3$ for the following question:
$$\{(x,1,0) \, | \, x \, \text{arbitrary numbers}\}$$
What are the steps to solve such a question?
Thanks!
EDIT: 
I am having trouble understanding why this question is being closed. Can someone please explain the reason?

The way to test if a subset of a vector space is a subspace is to test:


*

*Is it closed under vector addition?

*Is it closed under scalar multiplication?

*Is it nonempty?


To be a subspace it must pass both tests, for all vectors and scalars.  This particular subset  fails both tests catastrophically, i.e. finding an example is very easy because anything you try will be an example.  Here are two, one for each (although only one is sufficient).
$(1,1,0)$ and $(2,1,0)$ are both in your set, but their sum $(3,2,0)$ is not.
$(2,1,0)$ is in your set, and $3$ is a real number, but the product $3(2,1,0)=(6,3,0)$ is not in your set.
