Find the largest $($absolute value$)$ eigenvalue and the corresponding eigenvector for the matrix:

$[$

$2810$

$845$

$1057$

$]$

a$)$ using the power method $($hand$-$calculation$)$ with the initial guess $[111]$ and the tolerance $1\%,$

b$)$ using the Python code to check your solution $($write down the output$).$