Answer Exercise 7.5.12 for the inner product based on

Exercise 7.5.12
Consider the weighted inner product (v, w) = v1w1 + 1/2v2w2 + 1/3v3w3 on R3.
(a) What are the conditions on the entries of a 3 × 3 matrix A in order that it be self-adjoint?
(b) Write down an example of a non-diagonal self-adjoint matrix.

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