**Hi MHF,**
We have the following vectorial subspace

pertaining to

such that

.

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?