(MATLAB) Consider the square system Ax=b, with A tridiagonal such that A = 2*eye(3+3) - diag(diag(ones(3+2)),1) - diag(diag(ones(3+2)),-1)

b = [11*ones(3, 1); 3*ones(3,1)]

a) Show that the factorization A=LU with unitary lower triangular L and upper triangular U is unique. Then solve the original system by setting up the triangular systems Ly=b, Ux=y

b) Determine a factorization A=QR with the method of Householder reflections where Q is orthogonal and R is upper triangular. Show the computation of each Householder matrix Hk at each step. Solve the original system using this factorization.

Please be clear and include all steps.