Question: Consider the linear system Ar = b where 2 5 10 8 32 1 8 13 A = 8. b = -16 (a) Compute

Consider the linear system Ar = b where 2 5 10 8

Consider the linear system Ar = b where 2 5 10 8 32 1 8 13 A = 8. b = -16 (a) Compute the PA = LU factorization of A. Use exact arithmetic. Show all intermediate calcu- lations, including Gauss transforms and permutation matrices. (b) Use the factorization computed in (a) to solve the system. (c) Why is Gaussian Elimination usually implemented as in this question (i.e., PA = LU is com- puted separately, and then the factorization is used to solve Ar = b)?

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