Exercise II.2. let F(.) : R² → R³ and G(): R² → R² be given by(fi(x))f2(x)f3(x))y =9/₁F(x) =where f1(), f2), f3(-) are as in Exercise II.1(a). The notation is x =(a) x =and G(y) =(2y1 + 3y2y² + y²21I₂Use the Chain Rule to calculate (FG)'(x) for the various choices of x:- (₁²) (b) x = - (-³₁) (c) x =- (4) (d) x =For reference F1,F2, F3Exercise II.1. Consider the case n = 2.(a) Find the gradients of the following functions from R2 to R:(i) f₁ (22) := x² + x² − 2= 4x² +(iii) f3(ii) f₂:== 9(x₁ − 1)² + (²+¹)² — 2 (iv) fax1X2(=-¹).I1Inx1X₂and−1== ((x₁ + 1)² + (x₂ −2)²

Answered: Image /qna-images/answer/6620affb-1532-4dbd-971b-3d0c2c4a2687.jpg

xercise II.2. let F(): R² R³ and G(): R² R² be given by (fi(x)) f2(x) f3(x)) F(x) = (iii) f3 and ere fi(), f2), f3(-) are as in Exercise II.1(a). The notation is x = (2₂) (1₂). Use the Chain Rule to calculate (FoG)'(x) for the various choices of x: = (-₁²) (b) x = (3) (c) x = (a) x = () (d) x = = (-¹). 21 X₂ (2y1+342) y² + y² and_G(y) = (² For reference F1,F2, F3 Exercise II.1. Consider the case n = 2. (a) Find the gradients of the following functions from R² to R: x1 (i) fi := x² + x² - 2 (ii) f₂ | := 4x+1 X₂ := 9(x₁ - 1)² + (2+1)²-2 (iv) f₁ 21 X₂ I1 I₂. := √(x₁ + 1)² + (x₂ - 2)²

xercise II.2. let F(): R² R³ and G(): R² R² be given by (fi(x)) f2(x) f3(x)) F(x) = (iii) f3 and ere fi(), f2), f3(-) are as in Exercise II.1(a). The notation is x = (2₂) (1₂). Use the Chain Rule to calculate (FoG)'(x) for the various choices of x: = (-₁²) (b) x = (3) (c) x = (a) x = () (d) x = = (-¹). 21 X₂ (2y1+342) y² + y² and_G(y) = (² For reference F1,F2, F3 Exercise II.1. Consider the case n = 2. (a) Find the gradients of the following functions from R² to R: x1 (i) fi := x² + x² - 2 (ii) f₂ | := 4x+1 X₂ := 9(x₁ - 1)² + (2+1)²-2 (iv) f₁ 21 X₂ I1 I₂. := √(x₁ + 1)² + (x₂ - 2)²

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

Problem 70EQ

See similar textbooks