Problem 1 a) Let 3-1 1 A=11 30 Find a lower triangular matrix L, a unit upper triangular matrix U, and a permutation matrix P , such that LU PA. Use the algorithm given in class, incorporating the partial pivoting strategy. Do it by hand computation. b) Use Matlab's lu command (type help lu to learn about it) to find a unit lower triangular matrix L, an upper triangular matrix U, and a permutation matrix P such that PA LU. To enter the matrix A into Matlab, type the following (the semicolons separate the rows): A [1 1 3; 3 -1 1; 1 3 0]