Answered: [4 2 2 4. Let A = 2 6 2 2 2 5 a) Show…

[4 2 2 4. Let A = 2 6 2 2 2 5 a) Show that A is a positive definite matrix. b) Find a Cholesky factorization of A. c) Use this Cholesky factorization to solve the system Ax = [4 6 -1]

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

[4 2 2
4. Let A = |2 6 2
2 2 5
a) Show that A is a positive definite matrix.
b) Find a Cholesky factorization of A.
c) Use this Cholesky factorization to solve the system Ax = [4 6 -1]

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