(2 points) If L and U are invertible, then (LU) -1 = U-1 1-1. Inverses of Upper and Lower triangular matrices are easier to calculate than inverses of general square matrices. Use this to Find A- from the given LU factorization: A=LU- 7 41-[1 81 13 -31 AT = 188 =(2 points) Find the LU factorization of 2 1 4 2 A = 10 9 15 9 2 9 4 5 That is, write A = LU where L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix. (2 points) If L and U are invertible, then (LUT1 = U'1L_1. Find A'1 from the given LU factorization: 8 32 16 1 0 0 8 32 16 A = LU = 16 58 50 = 2 1 0 0 6 18 72 282 157 9 1 1 0 0 5 This problem should really be in Week5, but again we are just using the fact that inverses of triangular matrices are easier to find. For example, just use the Gauss-Jordan method to find each of U'1 and L'l. We learned (actually "will learn") in class a partition matrix shortcut for quickly doing U '1 (upper triangular). 1 Good review: L'1 is the transpose of (LT) and LT is upper triangular