Hello,

the task is following. Let's assume that is orthogonal vector set of subspace and . Also . It's defined that:

So, the problem is to show that is orthogonal to all vectors of .

When the sum is opened, we get:

It seems like formula from Gram-Schmidt process, so in my opinion it must be , because G-S process orthogonalizes vectors. I think I need a little bit more evidence to show the proposition, but I don't know how to continue. Any help is welcome. Thanks!