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8. 20 pts.] Suppose that a 2 x2 matrix A has the following eigenvalues and eigenvectors:...
I'm completely stumped on these. I don't know how to proceed once I get to the...
I'm completely stumped on these. I don't know how to proceed
once I get to the eigenvalue since my typical method for solving
would be to set Ax=x
, then solve. However, this would give me
-5x1=-5x1 and -5x2=-5x2
which makes A trivial. I just realized that means the eigenvectors
will be <1,0> and <0,1>, but I'm still stumped on parts
b and c.
Consider the following system. (A computer algebra system is recommended.) dx = -5 0x dt *...
(i) Find the general solution by using eigenvalues and eigenvectors (ii) State whether the origin is...
(i) Find the general solution by using eigenvalues and eigenvectors (ii) State whether the origin is stable, asymptotically stable, or unstable spiral (iii) State whether the origin is a node, saddle, center, or -1 2 2 -1
(i) Find the general solution by using eigenvalues and eigenvectors (ii) State whether the origin is stable, asymptotically stable, or unstable spiral (iii) State whether the origin is a node, saddle, center, or
-1 2 2 -1
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:...
Question 2 please MATH308: Differential Equattons Problems for Chapter 7.6 (Complex-Valued Eigenvalues) 1. The following ODE...
Question 2 please
MATH308: Differential Equattons Problems for Chapter 7.6 (Complex-Valued Eigenvalues) 1. The following ODE systems have complex eigenvalues. Find the general solution and sketch the phase plane diagrams 3 -2 1 -A x=( x, 5 -1 1 -1*.(49) mu+ku 0 (50) where u(t) is the displacement at time t of the mass from its equilibrium position (a) Let -und show that the resulting system is 1) (51) b) Find the eigenvalues of the matrix in part (a). (c)...
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...
3 - 36 a. Find the most general real-valued solution to the linear system of differential...
3 - 36 a. Find the most general real-valued solution to the linear system of differential equations = 2. 1 -3 x1(t) = C1 + C2 x2(t) 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) Given that ū = and are eigenvectors of the matrix -12 24 determine the...
(1 point) Given that ū = and are eigenvectors of the matrix -12 24 determine the corresponding eigenvalues. 21 = -1 12 = 1 (1 point) Solve the system -6 1 dx dt х -6 -1 with the initial value 0 x(0) = -2 x(t) = (1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the roots of the polynomial which defines the eigenvalues. You also may want to...
Consider the following differential equation system: x' = 16x + 8y y = -24x – 12y...
Consider the following differential equation system: x' = 16x + 8y y = -24x – 12y (a) Find the general solution. (b) Without a computer, sketch a phase diagram that shows four linear solution trajectories and that shows one solution trajectory in each of the four regions between the separatrices. (c) Determine the solution that satisfies x(0) = 1 and y(0) = 0. x(t) = yt) = (d) The point (0,0) is a ... Osaddle point stable node unstable node...
8 -12 a. Find the most general real-valued solution to the linear system of differential equations...
8 -12 a. Find the most general real-valued solution to the linear system of differential equations zē' = [; . 9-13 x1(t) = = C1 + C2 X2(t) - b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle O center point / ellipses spiral source Ospiral sink none of these
-5 2 1 a. Find the most general real-valued solution to the linear system of differential...
-5 2 1 a. Find the most general real-valued solution to the linear system of differential equations z' do o 0 xi(t) = C1 + C2 x2(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle O center point / ellipses spiral source spiral sink none of these
I'm completely stumped on these. I don't know how to proceed
once I get to the eigenvalue since my typical method for solving
would be to set Ax=x
, then solve. However, this would give me
-5x1=-5x1 and -5x2=-5x2
which makes A trivial. I just realized that means the eigenvectors
will be <1,0> and <0,1>, but I'm still stumped on parts
b and c.
Consider the following system. (A computer algebra system is recommended.) dx = -5 0x dt *...
(i) Find the general solution by using eigenvalues and eigenvectors (ii) State whether the origin is stable, asymptotically stable, or unstable spiral (iii) State whether the origin is a node, saddle, center, or -1 2 2 -1
(i) Find the general solution by using eigenvalues and eigenvectors (ii) State whether the origin is stable, asymptotically stable, or unstable spiral (iii) State whether the origin is a node, saddle, center, or
-1 2 2 -1
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:...
Question 2 please
MATH308: Differential Equattons Problems for Chapter 7.6 (Complex-Valued Eigenvalues) 1. The following ODE systems have complex eigenvalues. Find the general solution and sketch the phase plane diagrams 3 -2 1 -A x=( x, 5 -1 1 -1*.(49) mu+ku 0 (50) where u(t) is the displacement at time t of the mass from its equilibrium position (a) Let -und show that the resulting system is 1) (51) b) Find the eigenvalues of the matrix in part (a). (c)...
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...
3 - 36 a. Find the most general real-valued solution to the linear system of differential equations = 2. 1 -3 x1(t) = C1 + C2 x2(t) 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) Given that ū = and are eigenvectors of the matrix -12 24 determine the corresponding eigenvalues. 21 = -1 12 = 1 (1 point) Solve the system -6 1 dx dt х -6 -1 with the initial value 0 x(0) = -2 x(t) = (1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the roots of the polynomial which defines the eigenvalues. You also may want to...
Consider the following differential equation system: x' = 16x + 8y y = -24x – 12y (a) Find the general solution. (b) Without a computer, sketch a phase diagram that shows four linear solution trajectories and that shows one solution trajectory in each of the four regions between the separatrices. (c) Determine the solution that satisfies x(0) = 1 and y(0) = 0. x(t) = yt) = (d) The point (0,0) is a ... Osaddle point stable node unstable node...
8 -12 a. Find the most general real-valued solution to the linear system of differential equations zē' = [; . 9-13 x1(t) = = C1 + C2 X2(t) - b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle O center point / ellipses spiral source Ospiral sink none of these
-5 2 1 a. Find the most general real-valued solution to the linear system of differential equations z' do o 0 xi(t) = C1 + C2 x2(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle O center point / ellipses spiral source spiral sink none of these
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