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

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

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,41 = Ax,. Choose the correct answer below.
0.2
O A. X=
0.5 + (0.7)k -3 + (0.1)k
0.3
1
2
- 1
0.2
O B. X =
-3 +0.2(0.7)k
0 +0.3(0.1)k 0.5
1
0.3
0.2
-1
Oc. X = 0.5 +0.2(0.7)k -3
+0.3(0.1)k
0.3
Describe what happens to x, as k0o. Choose the correct answer below.
O A
As k becomes sufficiently large, Xg 0.2(0.7)*
- 3
+0.3(0.1)k
- 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

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