Question: help with this question thank you Let U E Rnxn, and suppose Vr E R, | Ux)| = ||x||. Prove that U is orthog- onal.

help with this question thank you

Let U E Rnxn, and suppose Vr E R", | Ux)| = ||x||. Prove that U is orthog- onal. Hint: Use the fact that v . w = (Iv + w/12 - |/v - w| |2), with v = Ux and w = Uy. Then use the fact that v . w = vTw and deduce that UTU = In. Finally, finish the problem with a theorem from class

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