1. (a) Let f: R" → R be a differentiable function such f(tx) = tm f(x) for all t € R, ï ¤ R" and somefixed me N. Show that:i=1Xiafəxi=mf(x)Hint: Consider the function g(t) = f(tx) and g'(1)(b) Let f: R → R be a non-linear function such that f(tx) = tf(x) for all t ≤ R, x ER". Show thatf is not differentiable at 0.

Answered: Image /qna-images/answer/78daabe2-fa61-4bc8-9309-2e7ba22db261.jpg

(a) Let f: R → R be a differentiable function such f(tx) = tf(x) for all t ≤ R, x € Rª and some fixed me N. Show that: n [ i=1 af Xi ¹Jxi = mf(x) = Hint: Consider the function g(t) = f(tx) and g'(1) (b) Let f: Rn → R be a non-linear function such that f(tx) = tf(x) for all t = R, x ER". Show that f is not differentiable at 0.

(a) Let f: R → R be a differentiable function such f(tx) = tf(x) for all t ≤ R, x € Rª and some fixed me N. Show that: n [ i=1 af Xi ¹Jxi = mf(x) = Hint: Consider the function g(t) = f(tx) and g'(1) (b) Let f: Rn → R be a non-linear function such that f(tx) = tf(x) for all t = R, x ER". Show that f is not differentiable at 0.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 30EQ

See similar textbooks