[Sherman-Morrison formula, 4+4pt] Sometimes, one has to solve linear systems that are rank-1 modifications of other linear systems, for which a factorization is already available. Let us derive a solution algorithm for the modified system. Let A ∈ R n×n be invertible and u, v ∈ R n be column vectors. A + uvT is invertible with inverse (A + uvT ) −1 = A −1 − 1 1 + v TA−1u A −1uvTA −1 . if and only if v TA−1u 6= −1. (a) Let v TA−1u 6= −1 and assume given the LU decomposition of A. Specify an efficient algorithms based on the Sherman-Morrison formula to solve the rank-1 modified system (A + uvT )x = b for a given right hand side b