S5)Please answer in legible and clear handwriting.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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S5)Please answer in legible and clear handwriting.

5) Considering the Newton's iteration of the following system of equations:
f1(x, y) = x² – y – 1 = 0,
f2(x, y) = (x – 2)² + (y – 0.5)² – 1 = 0,
(a) extract the Jacobian matrix.
(b) apply Doolittle LU factorization on the Jacobian matrix.
(c) perform three iterations on the factorized system using (xo, Yo) = (2, 2).
Transcribed Image Text:5) Considering the Newton's iteration of the following system of equations: f1(x, y) = x² – y – 1 = 0, f2(x, y) = (x – 2)² + (y – 0.5)² – 1 = 0, (a) extract the Jacobian matrix. (b) apply Doolittle LU factorization on the Jacobian matrix. (c) perform three iterations on the factorized system using (xo, Yo) = (2, 2).
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