Give a basis of a subspace

**Hi MHF,**

We have the following vectorial subspace $\displaystyle W$ pertaining to $\displaystyle \mathbb{R}^4$ such that $\displaystyle W=\{ (x,y,z,w) \in \mathbb{R}^4 : 2x-z+w=0, x-y-z=0 \}$.

1)Find a basis of W.

2)Find a basis of W orthogonal.

My __attempt__ :

1)I just wrote the 2 equations defining W as a matrix and chosen the 2 first column vectors of the matrix as being a basis of W.

Precisely I got that a basis of W is {(2,1),(0,-1)}. (0,-1) being the last column vector of the matrix I formed.

2)I'm **not** 100% sure about what I've done here. I chosen the basis {(2,1),(1,0)}.

__How can I check if I'm right on this?__ I guess I could form a matrix with the vectors in the basis I gave and try to get a null row or column when reducing it. But I'm not sure, and not sure how to form the matrix too.

Can you help me?