eigenvalue 1 is 4 eigenvalue 2 is 0 eigenvector 1 is {1,0} eigenvector 2 is {0,1} where do i draw the straight line solution in the xy phase portrait?
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eigenvalue 1 is 4 eigenvalue 2 is 0 eigenvector 1 is {1,0} eigenvector 2 is {0,1} where do i draw the straight line solution in the xy phase portrait?
Problem 1. Each of the following linear systems has one eigenvalue and one line of eigenvectors....
Problem 1. Each of the following linear systems has one eigenvalue and one line of eigenvectors. For each system, (a) find the eigenvalue; (b) find an eigenvector; (c) sketch the direction field; (d) sketch the phase portrait, including the solution curve with initial condition Yo = (1,0); and (e) find the general solution;
Here is the phase portrait of a homogeneous linear system of differential tions. 4. equa- (a) Cla...
Here is the phase portrait of a homogeneous linear system of differential tions. 4. equa- (a) Classify the equilibrium (b) If λί is the eigenvalue with corresponding eigenvector (1,1) and A2 is the eigenvalue with corresponding eigenvector (-1,3), place the three numbers 0, λ, and λ2 in order frorn least to greatest. (c) If ((t), y(t) is the solution satisfying the initial condition (x(0),y(0)- (-2,2). Find i. lim r(t) i. lim rlt) ii. lim y(t) iv. lim y(t)
Here is...
6 |and 5 2i 1 + has complex eigenvalue, eigenvector pairs (5 + 2i, (j) A...
6 |and 5 2i 1 + has complex eigenvalue, eigenvector pairs (5 + 2i, (j) A 5 - 4 Draw the phase portrait of the linear system X' = AX. Make sure to label relevant features and to include arrows to indicate directions of trajectories.
6 |and 5 2i 1 + has complex eigenvalue, eigenvector pairs (5 + 2i, (j) A 5 - 4 Draw the phase portrait of the linear system X' = AX. Make sure to label relevant...
6 -1 1 and 5 2i 1 (j) A 5 has complex eigenvalue, eigenvector pairs (5...
6 -1 1 and 5 2i 1 (j) A 5 has complex eigenvalue, eigenvector pairs (5 + 2i 4 - 1 - 2i 1+2i Draw the phase portrait of the linear system X' = AX. Make sure to label relevant features and to include arrows to indicate directions of trajectories
6 -1 1 and 5 2i 1 (j) A 5 has complex eigenvalue, eigenvector pairs (5 + 2i 4 - 1 - 2i 1+2i Draw the phase portrait of the...
1. (20 marks) This question is about the system of differential equations Y. dt=(k 1 (a) Consider the case k = 0. i...
1. (20 marks) This question is about the system of differential equations Y. dt=(k 1 (a) Consider the case k = 0. i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). ii. Write down the general solution. iii. Sketch a phase portrait for the system. (b) Now consider the case k3 In this case, the matrix has an eigenvalue 2+V/2 with eigenvector i. -1+iv2 and an eigenvalue 2 iv2 with eigenvector . Determine the type of equilibrium...
(3 points) Given the system 1. -2 0 2i and for the eigenvalue λ-2, the vector V-(1) is an eigenvector. we know that...
(3 points) Given the system 1. -2 0 2i and for the eigenvalue λ-2, the vector V-(1) is an eigenvector. we know that λ- (a) find the general solution; (b) determine if the origin is a spiral sink, a spiral source, or a center; (e) determine the direction of the oscillation in the phase plane (do the solutions go clockwise or countercdlocdkwise around the origin?); or counterclockwise
(3 points) Given the system 1. -2 0 2i and for the eigenvalue...
1. (20 marks) This question is about the system of differential equations dY (3 1 (a) Consider the case k 0 i. Dete...
1. (20 marks) This question is about the system of differential equations dY (3 1 (a) Consider the case k 0 i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). i. Write down the general solution. ili Sketch a phase portrait for the system. (b) Now consider the case k -3. (-1+iv ) i. In this case, the matrix has an eigenvalue 2+i/2 with eigenvector and an eigenvalue 2-W2 with eigenvector Determine the type of equilibrium at...
1) Find the general solution of di = Ay where Then sketch the phase portrait in...
1) Find the general solution of di = Ay where Then sketch the phase portrait in the x-y plane, where Finally, classify the equilibrium solution at the origin as a source, spiral sink, etc. 2) Repeat for the matrix | 3 -31 -2 -2] 3) Repeat for the matrix 4 — 4) Repeat for the matrix [95 -9 15 but you don't need to sketch the phase portrait.
Given the matrix A467 333 0 2 0 0 The eigenvector associated with the largest eigenvalue...
Given the matrix A467 333 0 2 0 0 The eigenvector associated with the largest eigenvalue ofA is [7-3 1]T (a) Determine the eigenvalue associated with this eigenvector (b) For b-[1 1 1]T, find the approximate solution to b in the system x-Ab due to this eigenvector and compare it the exact solution.
5.4 Equilibrium Solutions and Phase Portraits 1. 2 3 3 2 . (a) Draw direction field....
5.4 Equilibrium Solutions and Phase Portraits 1. 2 3 3 2 . (a) Draw direction field. Use the points: (0,0), (+1,0), (0, +1), (+1, +1). (b) Draw the phase portrait. (c) Classify the equilibrium solution with its stability. 11 and 2. Suppose 2 x 2 matrix A has eigenvalues – 3 and -1 with eigenvectors respectively. (a) Find the general solution of 7' = A. (b) Draw the phase portrait. (C) Classify the equilibrium solution with its stability. 3. Suppose...
Problem 1. Each of the following linear systems has one eigenvalue and one line of eigenvectors. For each system, (a) find the eigenvalue; (b) find an eigenvector; (c) sketch the direction field; (d) sketch the phase portrait, including the solution curve with initial condition Yo = (1,0); and (e) find the general solution;
Here is the phase portrait of a homogeneous linear system of differential tions. 4. equa- (a) Classify the equilibrium (b) If λί is the eigenvalue with corresponding eigenvector (1,1) and A2 is the eigenvalue with corresponding eigenvector (-1,3), place the three numbers 0, λ, and λ2 in order frorn least to greatest. (c) If ((t), y(t) is the solution satisfying the initial condition (x(0),y(0)- (-2,2). Find i. lim r(t) i. lim rlt) ii. lim y(t) iv. lim y(t)
Here is...
6 |and 5 2i 1 + has complex eigenvalue, eigenvector pairs (5 + 2i, (j) A 5 - 4 Draw the phase portrait of the linear system X' = AX. Make sure to label relevant features and to include arrows to indicate directions of trajectories.
6 |and 5 2i 1 + has complex eigenvalue, eigenvector pairs (5 + 2i, (j) A 5 - 4 Draw the phase portrait of the linear system X' = AX. Make sure to label relevant...
6 -1 1 and 5 2i 1 (j) A 5 has complex eigenvalue, eigenvector pairs (5 + 2i 4 - 1 - 2i 1+2i Draw the phase portrait of the linear system X' = AX. Make sure to label relevant features and to include arrows to indicate directions of trajectories
6 -1 1 and 5 2i 1 (j) A 5 has complex eigenvalue, eigenvector pairs (5 + 2i 4 - 1 - 2i 1+2i Draw the phase portrait of the...
1. (20 marks) This question is about the system of differential equations Y. dt=(k 1 (a) Consider the case k = 0. i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). ii. Write down the general solution. iii. Sketch a phase portrait for the system. (b) Now consider the case k3 In this case, the matrix has an eigenvalue 2+V/2 with eigenvector i. -1+iv2 and an eigenvalue 2 iv2 with eigenvector . Determine the type of equilibrium...
(3 points) Given the system 1. -2 0 2i and for the eigenvalue λ-2, the vector V-(1) is an eigenvector. we know that λ- (a) find the general solution; (b) determine if the origin is a spiral sink, a spiral source, or a center; (e) determine the direction of the oscillation in the phase plane (do the solutions go clockwise or countercdlocdkwise around the origin?); or counterclockwise
(3 points) Given the system 1. -2 0 2i and for the eigenvalue...
1. (20 marks) This question is about the system of differential equations dY (3 1 (a) Consider the case k 0 i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). i. Write down the general solution. ili Sketch a phase portrait for the system. (b) Now consider the case k -3. (-1+iv ) i. In this case, the matrix has an eigenvalue 2+i/2 with eigenvector and an eigenvalue 2-W2 with eigenvector Determine the type of equilibrium at...
1) Find the general solution of di = Ay where Then sketch the phase portrait in the x-y plane, where Finally, classify the equilibrium solution at the origin as a source, spiral sink, etc. 2) Repeat for the matrix | 3 -31 -2 -2] 3) Repeat for the matrix 4 — 4) Repeat for the matrix [95 -9 15 but you don't need to sketch the phase portrait.
Given the matrix A467 333 0 2 0 0 The eigenvector associated with the largest eigenvalue ofA is [7-3 1]T (a) Determine the eigenvalue associated with this eigenvector (b) For b-[1 1 1]T, find the approximate solution to b in the system x-Ab due to this eigenvector and compare it the exact solution.
5.4 Equilibrium Solutions and Phase Portraits 1. 2 3 3 2 . (a) Draw direction field. Use the points: (0,0), (+1,0), (0, +1), (+1, +1). (b) Draw the phase portrait. (c) Classify the equilibrium solution with its stability. 11 and 2. Suppose 2 x 2 matrix A has eigenvalues – 3 and -1 with eigenvectors respectively. (a) Find the general solution of 7' = A. (b) Draw the phase portrait. (C) Classify the equilibrium solution with its stability. 3. Suppose...
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