We consider the linear equation Axb, where A = and b= 0 DAx Db where D = -3 a) Show that is a solution to Ax=b if and only if a solves the modified linear system 69 b) Can the modified system DAx = Db be solved via CG? If yes, apply the CG method with initial point x = 0 and compute the respective solution to the linear equation Ax = b. c) Consider a general linear system Ax = b with symmetric, positive definite matrix A Rnxn. Suppose b = R"{0} is an eigenvector of A and let us apply the conjugate gradient method to solve Ax = b with initial point = 0. Perform one step of the CG method - what can you say about the iterate ? We consider the linear equation Axb, where A = and b= 0 DAx Db where D = -3 a) Show that is a solution to Ax=b if and only if a solves the modified linear system 69 b) Can the modified system DAx = Db be solved via CG? If yes, apply the CG method with initial point x = 0 and compute the respective solution to the linear equation Ax = b. c) Consider a general linear system Ax = b with symmetric, positive definite matrix A Rnxn. Suppose b = R"{0} is an eigenvector of A and let us apply the conjugate gradient method to solve Ax = b with initial point x = 0. Perform one step of the CG method - what can you say about the iterate ?