This should be easy, I'm not sure what I'm missing!! Any help would be great...

Let W be a finite dim subspace of an inner product space V. Show

a projection,

on

along

such that the nullspace of T,

.

Then show

**What I know:**
So far, I know that by a theorem, there are unique vectors

such that

I know by definition

is a projection on W along

if for

with

, we have

Finally, I know if x and y are orthogonal vectors, that

It seems like it should fall into place so easily... I just don't know how to define my T function so it works for each case and still lands me in the complement of W. Please help!!