0.48 - 0.02 0.380.2Let A= 0.150.85 0.15The vector v0.5is an eigenvector for A, and two eigenvalues are 0.7 and 0.1. Construct the solution of the dynamical system x,1= Ax, that satisfies x, = (0.3, - 0.1,0.8). What happens to x, as k→o?0.370.17 0.470.3Find the solution of the equation x,41 = Ax,. Choose the correct answer below.0.2O A. X=0.5 + (0.7)k -3 + (0.1)k0.312- 10.2O B. X =-3 +0.2(0.7)k0 +0.3(0.1)k 0.510.30.2-1Oc. X = 0.5 +0.2(0.7)k -3+0.3(0.1)k0.3Describe what happens to x, as k0o. Choose the correct answer below.O AAs k becomes sufficiently large, Xg 0.2(0.7)*- 3+0.3(0.1)k- 1O B. As k becomes sufficiently large, x 0.3(0.1)*0.2OC. As k becomes sufficiently large, x0.50.3

To construct a solution of the dynamical system first we need to find remaining eigenvalue and…

0.48 - 0.02 0.38 0.2 Let A= 0.15 0.85 0.15 The vector v, = 0.5 is an eigenvector for A, and two eigenvalues are 0.7 and 0.1. Construct the solution of the dynamical system x,1= Ax, that satisfies x, = (0.3, - 0.1,0.8). What happens to x, as k+o? 0.37 0.17 0.47 0.3 Find the solution of the equation x +1 = Ax. Choose the correct answer below. 0.2 2 -1 O A. X = 0.5 + (0.7)k + (0.1)k -3 0.3 1 -1 0.2 O B. Xx= -3 +0.2(0.7)k 0 +0.3(0.1)k 0.5 0.3 0.2 2 Oc. X = 0.5 +0.2(0.7)k - 3 +0.3(0.1)k 0.3 1 Describe what happens to x, as ko. Choose the correct answer below. O A. As k becomes sufficiently large, x 0.2(0.7)* - 3 + 0.3(0.1)k 1 -1 O B. As k becomes sufficiently large, x, 0.3(0.1)* 0.2 Oc. As k becomes sufficiently large, x, 0.5 0.3

0.48 - 0.02 0.38 0.2 Let A= 0.15 0.85 0.15 The vector v, = 0.5 is an eigenvector for A, and two eigenvalues are 0.7 and 0.1. Construct the solution of the dynamical system x,1= Ax, that satisfies x, = (0.3, - 0.1,0.8). What happens to x, as k+o? 0.37 0.17 0.47 0.3 Find the solution of the equation x +1 = Ax. Choose the correct answer below. 0.2 2 -1 O A. X = 0.5 + (0.7)k + (0.1)k -3 0.3 1 -1 0.2 O B. Xx= -3 +0.2(0.7)k 0 +0.3(0.1)k 0.5 0.3 0.2 2 Oc. X = 0.5 +0.2(0.7)k - 3 +0.3(0.1)k 0.3 1 Describe what happens to x, as ko. Choose the correct answer below. O A. As k becomes sufficiently large, x 0.2(0.7)* - 3 + 0.3(0.1)k 1 -1 O B. As k becomes sufficiently large, x, 0.3(0.1)* 0.2 Oc. As k becomes sufficiently large, x, 0.5 0.3

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 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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