Consider a three-dimensional vector space spanned by an orthonormal basis |1>,|2>,|3>. Kets |> and |> and are

Consider a three-dimensional vector space spanned by an orthonormal basis |1>,|2>,|3>. Kets |α> and |β> and are given by

(a) Construct <α |and <β |(in terms of the dual basis <1|,<2|,<3|).
(b) Find <α|β> and <β|α>, and confirm that <β|α> = <α|β>.
(c) Find all nine matrix elements of the operator in this basis, and construct the matrix A. Is it hermitian?

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la) i 1) - 2 12) - i|3), B) = i| 1) +2|3).