PROBLEM 3: (10 points) Consider the NN tridiagonal matrix A=h212+h22+h20000002+h2002+h2 1 and the vector f=(f1,,fN)T, where fi=2ih+1,h=2n,N=2n1,n=1,2,,8. Take =103 and solve the system Au=f using LU 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 (xi,ui),i=1,,N, where u is the solution of the system and xi=ih