Suppose $A_n^{(a)}$ is the symmetric $nn$ tridiagonal matrix with the constant value $a$ on its main diagonal and $-1$ on the sub$-$ and super$-$diagonals and let $b=Ae,$ where $e$ is a vector of ones. Produce a jupyter notebook which plots a graph that shows the following three things:

The number of iterations it takes the conjugate gradient method to solve the system $A_n^{(a)}x=$ b with an error tolerance of ${10}^{-5}$ for a given value of $n$ as a varies from $2$ to $10.$

The number of iterations it takes the SOR method with $=1\mathrm{.}2$ to solve the system $A_n^{(a)}x=b$ with an error tolerance of ${10}^{-5}$ for a given value of $n$ as a varies from $2\mathrm{.}5$ to $10.$

The number of iterations it takes the SOR method with $=1\mathrm{.}5$ to solve the system $A_n^{(a)}x=b$ with an error tolerance of ${10}^{-5}$ for a given value of $n$ as a varies from $2\mathrm{.}5$ to $10.$

Plot these graphs for $n=10,n=100$ and $n=500.$