Exercise 3.1. Find f'(x), Vf(x) and V?f(x) for the following functions of n variables.(a) f(x) = }a"Hx, where H is an n x n constant matrix (not necessarily symmetric).(b) f(x) = b"Ar – a"A™Ax, where A is an m x n constant matrix and b is a constantm-vector.(c) f(x) = }E", F:(x)², where F is a vector-valued function F : R" → R" with twice-differentiable components {F;(x)}.%3D

Given, fx=12xTHx, where H is an n×nconstant matrix.…

Exercise 3.1. Find f'(x), Vf(x) and V²f(x) for the following functions (a) f(x) = }r"Hx, where H is an n x n constant matrix (not necessaril (b) f(x) = b"Ar – žr™A™Ax, where A is an m x n constant matrix ar m-vector.

Exercise 3.1. Find f'(x), Vf(x) and V²f(x) for the following functions (a) f(x) = }r"Hx, where H is an n x n constant matrix (not necessaril (b) f(x) = b"Ar – žr™A™Ax, where A is an m x n constant matrix ar m-vector.

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

Exercise 3.1. Find f'(x), Vf(x) and V?f(x) for the following functions of n variables.
(a) f(x) = }a"Hx, where H is an n x n constant matrix (not necessarily symmetric).
(b) f(x) = b"Ar – a"A™Ax, where A is an m x n constant matrix and b is a constant
m-vector.
(c) f(x) = }E", F:(x)², where F is a vector-valued function F : R" → R" with twice-
differentiable components {F;(x)}.
%3D

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