Consider a three-dimensional vector space spanned by an orthonormal basis  Kets  and  are...

Consider a three-dimensional vector space spanned by an orthonormal basis  Kets  and  are given by

(a) Construct  and  (in terms of the dual basis ).

(b) Find  and , and conform that .

(c) Find all nine matrix elements of the operator , in this basis, and construct the matrix A. Is it hermitian?