LU factorization
Use the recursive LU factorization algorithm. Algorithm 2.1 provided in the lecture notes factorizes the matrix A = LU, where L ∈ L(R?) and U ∈ U(R?). In other words, find its LU factorization. If we drop the requirement that L is normalized, the LU factorization is no longer unique. Prove this for the matrix A above by finding a second LU factorization where L is normalized. Hint: Try inserting the product of two appropriate matrices (say, for example, S and 8-) between L and U.