Question: Diagonalize the quadratic by finding an orthogonal matrix Q such that the change of variable x = Qy transforms the given form into one with

Diagonalize the quadratic by finding an orthogonal matrix Q such that the change of variable x = Qy transforms the given form into one with no cross-product terms. Give Q and the new quadratic form.

x² + z² - 2xy + 2yz

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