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

See similar textbooks

Related questions

Q: 3. Let A € Mn,n and let λ be an eigenvalue of A. Suppose A satisfies the equation 2A²+5A-10In Show…

Q: (11) Find the eigen values, their algebraic and geometric multiplicities, and the eigen vectors of 2…

Q: Assume that a 3 x 3 matrix A has eigenvalues 21 = 1, 22=0.8, 23=0.6 With corresponding eigenvectors…

Q: rify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. а13 -11, х, 3 (1, 2,…

Q: Find a basis for the eigenspace corresponding to the eigenvalue. 9 -1 2 A = 3 5 6 ,^ = 8 - 3 3 2 ...…

Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. -4 -2 = -11, x, =…

Q: (b) Find a complete orthonormal set of eigenvectors {v1, v2, V3}, where v; is an vector for A;.…

Q: What is the eigenvalue of the operator T, given by T(x) = 3x + 2, for the vector x = [1, 2]?

A: Eigenvalue: A number is said to be an eigenvalue of a linear transformation if there exists a…

Q: 3 41 0 -1 3 2. Without computing, list the Lo o o 21 eigenvalues of A giving reason(s) for your…

A: Given matrix is an upper triangular matrix

Q: Verify that λ, is an eigenvalue of A and that x, is a corresponding eigenvector. A₁ = 13, x₁ = (1,…

Q: b) 3 -2 Given matrix A = -2 6 2. Suppose the eigenvalues of A and the bases for the 4 2…

A: A matrix A is said to be Orthogonally diagonalizable if there exist a orthogonal matrix Q and a…

Q: (d) Let T be a matrix with only two eigenvalues, 1 and 2. Let u and w be two non-zero eigenvectors…

A: dIt is given that the transformation T be a matrix with only two eigen values1 and 2. Let u and v be…

Q: 2.- a) find eigenvalue/eigenvalues and the corresponding eigenvector/eigenvectors of A. b) consider…

A: Given system of differential equationx′=−x+5yy′=−yWhich can be written as in matrix…

Q: Find an eigenbasis (a basis of eigenvectors) and diagonalize. -1 -2 7 A = | -13 6 11 - 11 -2 17…

Q: Suppose that a matrix A has the following eigenvalues and eigenvectors: T • λ=−1haseigenvectorx=[1,…

A: Given: The eigenvalues and eigenvectors of the matrix are as follows, • λ=−1 The eigen vector…

Q: One eigenvalue of the matrix A 1 12 167 -3 14 12 is A₁ = 5. -10 30 45. Find enough vectors to form a…

Q: Consider the difference equation with initial condition Xo = That is, write xo = c1v1 + c2V2 In…

A: Here we have given a matrix M of order 2 with its eigenvalue and eigenfunctions.

Q: 6. (BH) Let A € R"×n be diagonal. Show that the eigenvectors of A are the standard basis vectors…

Q: 5. If X any Y are sets, then X-Y= {r€ X: 1¢Y} If X is open set and Y is closed set. Prove that (a)…

Q: Let A = = 1 Let di-[-2] = and 2 = H -2 -3 A) Create two plots (just sketch by hand). In one plot,…

Q: 1. Without actually setting up any equations, write down the eigenvalues of the following matrix: 1…

Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. 2, = 5, x, = (1, 2,…

Q: ) Siya Kolisi found this matrix M =2 1 p0 1 q0 2 0.(a) Find p, q if122 is an eigenvector of…

A: Step 1: Step 2: Step 3: Step 4:

Q: Let M be a 2 x 2 matrix with eigenvalues ₁ = -0.8, 2 = 1 with corresponding eigenvectors Consider…

Q: Let vn = be the solution to the discrete dynamical system: Yn 6xn – 13yn Yn+1 = 0xn – 7yn Xn+1 -3 If…

A: Using diagonalisation of the coefficients matrix.

Q: Find the eigenvalues of the complex valued matriX A given by 1+i 4i Let A= where i = V-1. 1+i -3 2…

Q: The following matrix is invertible when t + 2/13. 10 t A = 0 2 3 5 t 1 (i) Verify this result by…

Q: Problem 21. Let T(x, y) = (x – y, 3x). Then find all eigenvalues and eigen- vectors of T.

A: The given transformation is:T(x, y)=x-y, 3x

Q: 2 2 is: 1 3, One of the eigenvectors of the matrix A

A: Let A = aijn×n be any n-rowed square matrix and λ is a scalar. The equation AX = λX is called the…

Q: Compute the other eigenvector. And draw each of the eigenvectors and the transformed vectors (with…

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

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Matrix Eigenvalues and Eigenvectors$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

(3) Let matrix A have eigenvectors . . associated with eigenvalues Xo = 4, A₁ = 2, A₂ = 0), respectively. Suppose some vector 7 is: 7 = №n +27₁ +30¹₂ Compute Ar. Give your result as a linear combination of eigenvectors ₁.
Find the eigenvectors of the matrix A= 1 1 -1 0 5 0 0 1 -1
A H the eigenvalues X₁ = 2 and A₂ = -1, respectively. What is A(v₁ + V₂)? Suppose A is a 3 x 3 matrix with eigenvectors V₁ A 3 2 B Ⓡ = 0 and V₂ = 2 -2 corresponding to D H
Provide a coherent answer for items C and D.
b) Consider the matrix TM UTM UTM UTM -1 21 A = OTM UTM 7TMUTM UTM 4 i. Compute the dominant eigenvalue, di and the corresponding eigen- -4 20 UT vector x1 for the matrix A using power method starting with x0) = (1, 1, 1)" and stop the iterations when |mg+1 – mel < 0.05. AUTM %3D ii. Determine the smallest eigenvalue, Az for matrix A by using shifted power method based on the results in (i). Start the iteration with initial vector x) = (1,0,0)" and stop the iterations when ||x*+1) – x*)|| < 0.05. TM UTM UTM (k) %3D
Let M be a 2 x 2 matrix with eigenvalues A₁ = 0.3, A2 = -0.25 with corresponding eigenvectors = [2²] ²2² = [9] · V2 Consider the difference equation with initial condition xo That is, write xo = C1V1 + C₂V2 H Write the initial condition as a linear combination of the eigenvectors of M. In general, X = Specifically, X4 V1 = For large k, xk Xk+1 = V₁+ )k v₁+ Mxk A V2 7)k V₂
9. Determine which of the following vectors 1 -1 is an eigenvector of the matrix 1 1 1 1 -1 1 -1 W = -1 -1 1 -1 -1 1 and find the corresponding eigenvalue.
In each case, determine whether the vector v is an eigenvector of the 3 by 3 matrix A. No A = No A = No A = 9 -5 18 -8 6 -18 -4 5 -13 -7 -2 3 17 2 -13 -12 -2 8 -1 -4 -8 10 3 -2 -5 -4 -4 1. V = 2. " 3. υ: || 3 7 1 -1 1 -1 7 B 4 1
What is the vector where it is orthogonal to the eigenvectors