Exercise 2.2. Given a vector r of appropriate dimension, find the Jacobian F'(x) for each of the following functions. (a) F(x)= Ax – b, where A is an m x n matrix and b is an m-vector. (b) F(x) = (e"" (4xí + 2x3 + 4x1x2+ 6x2 + 8x1 + e#1 (4x2 + 4x1 + 2) (2x1e#3 – 2ž sin æị 2x2 aže"3 + 2x3 coS 21 (c) F(x) = (a) F(2) = ( "). ((A – x„I)¤ Tī – 1 where r e R", ẽ is the vector of first n – 1 components of x, A is an (n – 1) x (n – 1) matrix, I is the (n – 1) × (n – 1) identity matrix and r, is the last component of æ.

Exercise 2.2. Given a vector r of appropriate dimension, find the Jacobian F'(x) for each of the following functions. (a) F(x)= Ax – b, where A is an m x n matrix and b is an m-vector. (b) F(x) = (e"" (4xí + 2x3 + 4x1x2+ 6x2 + 8x1 + e#1 (4x2 + 4x1 + 2) (2x1e#3 – 2ž sin æị 2x2 aže"3 + 2x3 coS 21 (c) F(x) = (a) F(2) = ( "). ((A – x„I)¤ Tī – 1 where r e R", ẽ is the vector of first n – 1 components of x, A is an (n – 1) x (n – 1) matrix, I is the (n – 1) × (n – 1) identity matrix and r, is the last component of æ.

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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