Create a function called largest eig$()$ and add it to your HW$2.$py file. This

function will determine the largest eigenvalue and its associated eigenvector with

the power method as discussed in class. The function should take the matrix

A$,$ an allowed error tolerance, and a maximum iteration number as input and

produce both the highest eigenvalue of A and its eigenvector along with the

final error and iteration number. In order to ensure standard output between

everyone$$s implementation, scale the eigenvector so that the largest absolute

value of the eigenvector is equal $1.$ The function should take the following

inputs in this order:

$$ numpy array A : the matrix that defines the linear system

$$ float epsilon: the error tolerance

$$ int max it: the maximum allowed number of iterations

And produce the following outputs in this order:

$$ float: eig: the largest eigenvalue

$$ numpy array x: the eigenvector corresponding to the largest eigenvalue

$$ int n it: the number of iterations taken to reach solution

$$ float error : the calculated error in the last iteration

The error for this case should be computed by calculating the relative error

between the eigenvalue of the current and precvious iteration:

error $=|(\backslash$lambda subi$+1\backslash$lambda subi$)\backslash \backslash$lambda subi$+1|$

where i is the iteration number. Please write in python