= Consider the set of orthogonal polynomials with following recurrence relations fo(x) = 1, (n+1) fn+1(x) = (2n+ 1)xn(x) nfn-1(x). The polynomials are orthogonal with respect to the inner product 1 fn(x) fm (x) dx 2n18nm. Restrict the polynomials to n=0,2,4 and construct the 33 matrix for the operator A = xd/dx - xd/dx in this basis of fo, f2, f4. Consider the following matrix - ( A = 0 ak 0 ak 0 ik 0-ik 0 (5) Find the two values of a for which the matrix A is Hermitian. Find the eigenvalues and eigenvectors of this matrix for both these values.