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![--18 2 6x,-18 X₂ = 0 x = 322 * 2 = 21 2x - 62 = x = 32 - [u] =X X2 :. The Eigen vector Com esponding to Eigen value Y for ano](http://img.homeworklib.com/questions/9b48e860-107b-11eb-8572-e362d6c5d9cd.png?x-oss-process=image/resize,w_560)
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Question 3: Find the general solution of the system given as: -18 X'=13 Question 4: Find...
[-/2 Points] DETAILS Find the general solution of the given system. 4 - 1 2 X'...
[-/2 Points] DETAILS Find the general solution of the given system. 4 - 1 2 X' = -1 4 0 X -1 04 X(t) = Submit Answer [-/2 Points] DETAILS Solve the given initial-value problem. (1 -4 -6 X' = 1 2-3 X, X(0) = 1 -2 - 2 X(t) [-/2 points) DETAILS Solve the given initial-value problem. X' = 8 -1 5 +6)x, x(0) = (-3) X(t)
2. (12 points) Write the ODEs as a 2 x 2 system and then find the general solution using the eige...
2. (12 points) Write the ODEs as a 2 x 2 system and then find the general solution using the eigenvalues and eigenvectors of the constant (0) 9. matrix that appears in your system. Find the solution if the initial values are x(0)(0)-y(0)0 and
2. (12 points) Write the ODEs as a 2 x 2 system and then find the general solution using the eigenvalues and eigenvectors of the constant (0) 9. matrix that appears in your system. Find the...
For each of the following systems: (i) Find the general solution by using eigenvalues and eigenvectors....
For each of the following systems:
(i) Find the general solution by using eigenvalues and
eigenvectors.
(ii) State whether the origin is stable, asymptotically stable,
or unstable.
(iii) State whether the origin is a node, saddle, center, or
spiral.
For each of the following systems: (i) Find the general solution by using eigenvalues and eigenvectors. (ii) State whether the origin is stable, asymptotically stable, or unstable. |(iii) State whether the origin is a node, saddle, center, or spiral. Problem 1:...
Chapter 3, Section 3.3, Question 02 Consider the given system of equation. 2 -4 X 6 -8 (a) Find the general solution of...
Chapter 3, Section 3.3, Question 02 Consider the given system of equation. 2 -4 X 6 -8 (a) Find the general solution of the given system of equation 1 +c2e2t VI The general solution is given by X (t) = ci where V2. |and 21 >A2 =| ; vi = and v2 (b) Draw a direction field and a phase portrait. Describe the behavior of the solutions as t - o. 1) If the initial condition is a multiple of...
Find the general solution of the given system.
Find the general solution of the given system. Solve the given initial-value problem.
Suppose a dynamical system is modeled with a difference equation x- Ax-1 k0.1.2.3.... where 4 2 8...
Linear Algebra Question
Suppose a dynamical system is modeled with a difference equation x- Ax-1 k0.1.2.3.... where 4 2 8 .2 1 1 7 Three linearly independent eigenvectors of A are The initial condition is x: In the manner discussed in class, express the initial condition as a linear combination of the eigenvectors of A. Then construct the general solution to the difference equation using the eigenvalues and eigenvectors of A. Finally determine the long term steady-state solution to the...
4) Given the system of equations {x-3x2 + 2x2 lxa a) Rewrite the system in the...
4) Given the system of equations {x-3x2 + 2x2 lxa a) Rewrite the system in the form of x' = Aš b) Solve for the general solution using eigenvalues and eigenvectors c) Sketch the eigenvectors and a few typical trajectories indicating direction of solutions. 8 6 2 -10 -8 6.4 -2 6 8 10 2 -4 -6 -10
Find the general solution to the system of linear differential equations X'=AX. The independent variable is...
Find the general solution to the system of linear differential equations X'=AX. The independent variable is t. The eigenvalues and the corresponding eigenvectors are provided for you. x1' = 12x1 - 8x2 x2 = -4X1 + 8x2 The eigenvalues are 11 = 16 and 12 = 4 . The corresponding eigenvectors are: K1 = K2= Step 1. Find the nonsingular matrix P that diagonalizes A, and find the diagonal matrix D: p = 11 Step 2. Find the general solution...
a. Find the most general real-valued solution to the linear system of differential equations x =...
a. Find the most general real-valued solution to the linear system of differential equations x = -[42]; xid) + c2 x?(༧) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these (1 point) Consider the linear system -6 7-11) -9 15 y. Find the eigenvalues and eigenvectors for the coefficient matrix. 21 = V1 = , and 12...
Problem 5. (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the...
Problem 5. (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. and iz = b. Find the real-valued solution to the initial value problem - -3y - 2y2 Syı + 3y2 yı(0) = -7, (0) = 10 Use I as the independent variable in your answers. Y() = Note: You can earn partial credit on this problem. Problem 6. (1 point) Find the most general real-valued solution to the linear system of differential...
[-/2 Points] DETAILS Find the general solution of the given system. 4 - 1 2 X' = -1 4 0 X -1 04 X(t) = Submit Answer [-/2 Points] DETAILS Solve the given initial-value problem. (1 -4 -6 X' = 1 2-3 X, X(0) = 1 -2 - 2 X(t) [-/2 points) DETAILS Solve the given initial-value problem. X' = 8 -1 5 +6)x, x(0) = (-3) X(t)
2. (12 points) Write the ODEs as a 2 x 2 system and then find the general solution using the eigenvalues and eigenvectors of the constant (0) 9. matrix that appears in your system. Find the solution if the initial values are x(0)(0)-y(0)0 and
2. (12 points) Write the ODEs as a 2 x 2 system and then find the general solution using the eigenvalues and eigenvectors of the constant (0) 9. matrix that appears in your system. Find the...
For each of the following systems:
(i) Find the general solution by using eigenvalues and
eigenvectors.
(ii) State whether the origin is stable, asymptotically stable,
or unstable.
(iii) State whether the origin is a node, saddle, center, or
spiral.
For each of the following systems: (i) Find the general solution by using eigenvalues and eigenvectors. (ii) State whether the origin is stable, asymptotically stable, or unstable. |(iii) State whether the origin is a node, saddle, center, or spiral. Problem 1:...
Chapter 3, Section 3.3, Question 02 Consider the given system of equation. 2 -4 X 6 -8 (a) Find the general solution of the given system of equation 1 +c2e2t VI The general solution is given by X (t) = ci where V2. |and 21 >A2 =| ; vi = and v2 (b) Draw a direction field and a phase portrait. Describe the behavior of the solutions as t - o. 1) If the initial condition is a multiple of...
Linear Algebra Question
Suppose a dynamical system is modeled with a difference equation x- Ax-1 k0.1.2.3.... where 4 2 8 .2 1 1 7 Three linearly independent eigenvectors of A are The initial condition is x: In the manner discussed in class, express the initial condition as a linear combination of the eigenvectors of A. Then construct the general solution to the difference equation using the eigenvalues and eigenvectors of A. Finally determine the long term steady-state solution to the...
4) Given the system of equations {x-3x2 + 2x2 lxa a) Rewrite the system in the form of x' = Aš b) Solve for the general solution using eigenvalues and eigenvectors c) Sketch the eigenvectors and a few typical trajectories indicating direction of solutions. 8 6 2 -10 -8 6.4 -2 6 8 10 2 -4 -6 -10
Find the general solution to the system of linear differential equations X'=AX. The independent variable is t. The eigenvalues and the corresponding eigenvectors are provided for you. x1' = 12x1 - 8x2 x2 = -4X1 + 8x2 The eigenvalues are 11 = 16 and 12 = 4 . The corresponding eigenvectors are: K1 = K2= Step 1. Find the nonsingular matrix P that diagonalizes A, and find the diagonal matrix D: p = 11 Step 2. Find the general solution...
a. Find the most general real-valued solution to the linear system of differential equations x = -[42]; xid) + c2 x?(༧) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these (1 point) Consider the linear system -6 7-11) -9 15 y. Find the eigenvalues and eigenvectors for the coefficient matrix. 21 = V1 = , and 12...
Problem 5. (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. and iz = b. Find the real-valued solution to the initial value problem - -3y - 2y2 Syı + 3y2 yı(0) = -7, (0) = 10 Use I as the independent variable in your answers. Y() = Note: You can earn partial credit on this problem. Problem 6. (1 point) Find the most general real-valued solution to the linear system of differential...
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