PROBLEM $3$: $(10$ points$)$ Consider the N $\backslash$times N tridiagonal matrix

A$=1/$h$^2([2\backslash$epsi $+$h$^2-\backslash$epsi $0...000$; $-\backslash$epsi $2\backslash$epsi $+$h$^2-\backslash$epsi $...000$; $.....................$; $............-\backslash$epsi $2\backslash$epsi $+$h$^2-\backslash$epsi ; $............0-\backslash$epsi $2\backslash$epsi $+$h$^2])$

$1$ and the vector f$=($f$\_1,...,$ f$\_$N$)^$T$,$ where f$\_$i$=2$ i h$+1,$ h$=2^-$n$,$ N$=2^$n$-1,$ n$=1,2,...,8.$ Take $\backslash$epsi $=10^-3$ and solve the system A u$=$f using L U factorization for tridiagonal matrix as discussed in the notes. In your code do not create the matrix A$.$ For each value of n$=1,2,...,8,$ plot the points $($x$\_$i$,$ u$\_$i$),$ i$=1,...,$ N$,$ where u is the solution of the system and x$\_$i$=$i h$.$