Write a python code to implement the Power method and use it to derive the largest eigenvalue lambda $1$ and corresponding eigenvector x$1$ of A$1.$ Find $$x$1=$ x$1/\backslash |$ x$1\backslash |2.$ii$)$ Write a code in your chosen programming language to implement the

Power method and use it to derive the largest eigenvalue ${}_1$ and corre$-$

sponding eigenvector $x_1$ of $A_1.$ Find hat$(x{)}_1=\frac{x_1}{||x_1|{|}_2}.$ Compare the values

obtained in i$)$ with these values.

Deliverables: The handwritten code that implements the Power method,

the first $10$ iterates of eigenvalue generated by the algorithm and the

final $\backslash$lambda $1$ and $$x$1$ and a comment on the comparison.