1. Consider the linear systemwhere2[³]* = Ax₂_x(0) = [xA=[-3 2-4 1a. Find the complex eigenvalues and eigenvectors of Ab. Sketch the phase portrait and classify the critical point at the originas a spiral point or center and determine its stabilityc. Solve the system.

Given linear system is, x'=Ax where A=-32-41 and x(0)=2-3 The objective is to , a. Find the complex…

Answered: where der the system x = Ax, x(0) = [ A…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.7: The Inverse Of A Matrix

Problem 32E

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Let vn = be the solution to the discrete dynamical system: Yn 6xn – 13yn Yn+1 = 0xn – 7yn Xn+1 -3 If vo find vn. -1 Put the eigenvalues in ascending order when you enter xn, Yn below. Xn = )"+ Yn = )"+
please be handwritten
O A₁ = 2, V₁ = OA₁2, V₁ = O A₁ = 2, V₁ = The phase portrait shown above is for a linear system associated eigenvectors: O X₁ = -2, V₁ 5 [3] M [³] 5 3 = 0 A₁ = -2, V₁ = = [3] 5 fre frame [3] 5 4 and X₂ = 3, V₂ = = and A₂-3, V₂= = and A₂3, V₂ = and A₂3, V₂ = dy dt and A₂-3, V₂ = 0 H H H = = 0 7 -N 7 1 1 1 3 x AY where the matrix A has eigenvalues and
Suppose that i = Ax. Draw the phase portrait where the 2 x 2 matrix A has complex eigenvalue A = +5i with i 0.
Please solve all part
please solve it on paper
please solve it on paper
Match each linear system with one of the phase plane direction fields. (The blue lines are the arrow shafts, and the black dots are the arrow tips.) ? ✓ | 1. z ' = || a' ? 2. ': = ? 3.' = 4. a: = 11 8] -10 3 1 5 -2 1 -5 -13 10] -10 x2 A x2 с x1 (x2 B 2x2/ D Note: To solve this problem, you only need to compute eigenvalues. In fact, it is enough to just compute whether the eigenvalues are real or complex and positive or negative.
Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. (-3+i) A₁ = 1 , vi b. Find the real-valued solution to the initial value problem [{ and A₂ = -3y1 - 2/2, 591 +33/2, Use t as the independent variable in your answers. vi(t) =(5-5/2i)e^(-it)(-3/5-1/5)+(5+5/2i)e^(it)(-3/5+i/5) 32(t)= (5-5/2)^(-it)+(5+5/2)^(it) 4 vo = 3/1 (0) = 6, 3/2 (0) = -5. (-3-1)/
Show that the eigenvalues of the Sturm-Liouville system dy + Ay = 0 dx² %3D y(0) = 0, y(L) = 0 %3D gre all positive.
3. Consider the linear system (-2 Y dY dt (a) Determine the type of the equilibrium point at the origin. (b) Find the eigenvalues and eigenvectors and sketch the phase plane.
Consider the linear system a. Find the eigenvalues and eigenvectors for the coeffhcient matrix. and A2 = For each eigenpair in the previous part, form a solution of y'= Aỹ. Use t as the independent variable in your answers. (t) = and y2(t) = Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions? Choose

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where der the system x = Ax, x(0) = [ A = -3 2 2 -3 a. Find the complex eigenvalues and eigenvectors of A b. Sketch the phase portrait and classify the critical point at the origin as a spiral point or center and determine its stability c. Solve the system