Suppose that the set $S$ in the hypothesis of Theorem GSP is not just linearly independent, but is also orthogonal. Prove that the set $T$ created by the Gram-Schmidt procedure is equal to $S$. (Note that we are getting a stronger conclusion than $\spn{T}=\spn{S}$ — the conclusion is that $T=S$.) In other words, it is pointless to apply the Gram-Schmidt procedure to a set that is already orthogonal.