==============MATLAB QUESTION=============

Please answer in Matlab.

5.29. Newton's method can be used to compute an eigenvalue and corresponding eigenvector x of an n x n matrix A. If we define the function f: Rn+1 Rn+1 by Write a program to compute an eigenvalue- eigenvector pair of a given input matrix A us- ing this iteration scheme. A reasonable starting guess is to take xo to be an arbitrary normal- ized nonzero vector (i.e., x^xo 1) and take 25Axo (why?), Test your program on some random matrices and compare its accuracy and efficiency with those of conventional methods for computing a single eigenvalue-eigenvector pair, such as the power method. Note, however, that Newton's method does not necessarily converge to the dominant eigenvalue. then f(z,A-o precisely when is an eigenvalue and z is a corresponding normalized eigenvector Because 0 Newton's method for solving this equation has the Tk+1 8k +1 where [8k +]T 1s the solution to the linear sys- ten