Question: 6.14 (a) (Computing the inverse of a block matrix.) Let A = (A, Am ( An A12 ). Assume that An and Azz are square

6.14 (a) (Computing the inverse of a block matrix.) Let A = (A, Am ( An A12 ). Assume that An and Azz are square and that An and A2 - An An Alz are nonsingular. Let B = (0 In ( On Be ) be the inverse of A. Then show that B2 = (An - AmAnAn)". Bu= - An AnBiz, By = -BazAnAn, and Bu = App - BizAn An Exercises on Chapter 6 173 (b) How many flops are needed to compute A" using the results of (a) if An and An are, respectively, m x m and p x p? (c) Use your result of (a) to compute A", where 4+ 4 A = 4 0 A

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