Question: Show that the standard basis vectors e1, e2, e3 form an orthogonal basis with respect to the weighted inner product (v, w) = v1 w1

Show that the standard basis vectors e1, e2, e3 form an orthogonal basis with respect to the weighted inner product (v, w) = v1 w1 + 2 u2 w2 + 3 v3 w3 on R3. Find an orthonormal basis for this inner product space.

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