Problem 1: PA-LU factorization of square matrices For this problem, you will find by hand three square matrices P.L, U of the same size as a given matrix A, suck s P, L, u of the same size as a given matrix A, such that PA Lu You will then compare your results to their computational counterparts, found by the Matlab lu function. Find the PA Lu factorization of each of the matrices 01 (b) A22 4 2 -1 0 3 (a) A1 2 such that In your prob10, find P1, P2, Li, L2, ui, U2 given by the lu function and compare them to the ones you found by hand. Write your observations as comments in pro