Suppose H is a symmetric n x n matrix. We consider the problem of computing an eigenpair of H. (a) Show that if v is an eigenvector of H with unit norm, and u is its corresponding eigenvalue, then (v, ) is a stationary point of the Lagrangian function for the problem XT Hx minimize XERO subject to XI x = - 1. (b) Describe how you would use the method of Lagrange to find an eigenvalue and eigenvector of a symmetric matrix H. Be sure to write down the iteration; namely, clearly specify the linear system need to be solved and how the update would be computed each iteration. Suppose H is a symmetric n x n matrix. We consider the problem of computing an eigenpair of H. (a) Show that if v is an eigenvector of H with unit norm, and u is its corresponding eigenvalue, then (v, ) is a stationary point of the Lagrangian function for the problem XT Hx minimize XERO subject to XI x = - 1. (b) Describe how you would use the method of Lagrange to find an eigenvalue and eigenvector of a symmetric matrix H. Be sure to write down the iteration; namely, clearly specify the linear system need to be solved and how the update would be computed each iteration