I have this problem, I think I've solved the first part, anyway, I'd like you to see it, because I'm not sure if I've proceeded right.

The problem says: Let . Find if:

a) , where

b) A linearly independent set

So, basically what I did in a) was stating:

Then

Therefore

And then .

Is this right in the first place?

And for b) I've stated , here x and y are vectors in X.

I know there's no another possible linearly independent vector in X, so there are no others orthogonal complements I think. But I don't know how to proceed from here.

Bye, and thank you for your help, which is always useful.