Question: Diagonalize the quadratic forms in Exercises 1-3 by finding an orthogonal matrix Q such that the change of variable x = Qy transforms the given

Diagonalize the quadratic forms in Exercises 1-3 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.
1.

2. x2 + 8xy + y2
3.

2x + 5x - 4x,x,

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