2. Let B Rnxn be s.p.d. and C = Rnxn such that A = R2nx2n defined...

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2. Let B Rnxn be s.p.d. and C = Rnxn such that A = R2nx2n defined as B A = = [8 B+CB-CT] [C is s.p.d. B 0 (a) (2p) Find a block elimination matrix E satisfying EAET = Compute E-1. (b) (2p) Let LB = Rn be the Cholesky factor of B. Compute the Cholesky factorization of A. (c) (2p) Let 6 R2. How is the Cholesky factorization of A used to solve Ax = b? 2. Let B Rnxn be s.p.d. and C = Rnxn such that A = R2nx2n defined as B A = = [8 B+CB-CT] [C is s.p.d. B 0 (a) (2p) Find a block elimination matrix E satisfying EAET = Compute E-1. (b) (2p) Let LB = Rn be the Cholesky factor of B. Compute the Cholesky factorization of A. (c) (2p) Let 6 R2. How is the Cholesky factorization of A used to solve Ax = b?