dy- 13Consider the linear system=AY with A =dt2620Find the corresponding straight-line solutions Y₁ (t) = (21())coordinates of Y₁ (0) and Y₂ (0) equal to 1.x₁(t) =y₁ (t):x₂ (t)y₂(t) =19=Let A₁ A₂ be the eigenvalues of A.and Y2 (4) = (22(6)with the y-

Introduction: In linear algebra, eigenvalues are related to eigenvectors. In the analysis of linear…

Answered: Consider the linear system dt = AY with…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CR: Review Exercises

Problem 15CR: For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of...

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For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of multiplicity 2. b A has 1 and 2 as eigenvalues. c A has real eigenvalues.
Find all values of the angle for which the matrix A=[cossinsincos] has real eigenvalues. Interpret your answer geometrically.
Xn Let vn be the solution to the discrete dynamical system: Yn 6xn – 13yn Oxn – 7yn Xn+1 Yn+1 [:] -3 If vo find vn- -1 Put the eigenvalues in ascending order when you enter xn, Yn below. Xn = Yn = )"+ )" ||
x1(t) Let x(t) = be the solution to the discrete dynamical system: x2(t) x1(t + 1) = −8x1(t) + 1x2(t) x2(t+1) = −2x1(t) — 5x2(t) -4 If x(0) = find x(t). -2 Put the eigenvalues in ascending order when you enter x1(t), x2(t) below. x1(t) = x2(t) = )+ )*+ )t )t
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
Consider the following system. dx dt Find the eigenvalues and eigenvectors. Number of eigenvectors: Two r1 -1 §(¹) = 12 2 (3³) (²) - ( 8 ) Classify the critical point (0,0) as to type and determine whether it is stable, asymptotically stable, or unstable. The critical point (0,0) is Choose one 5 - (₁ -¹8 ) x 1 =
= y2, Consider a system of two linear first-order ordinary differential equations: y₁ a) The corresponding eigenvalues are A₁ = 3, 1₂ = −3 b) The corresponding eigenvectors of this linear ODE system are I and IV II and III where I:u₂ = II:u₂ III:u₁ IV:u₁ (3₁) (-3₁) (3) = (³1) 3i 3i = = λ₁ = 3i, λ₂ = -3i c) The phase portrait for this system of ODEs is Unstable focus with spiral out I and III Stable focus with spiral in y2 = -9y₁. ₁9, λ₂ = -9 I and III Stable node Centre
Consider the linear system X1 = and Find the eigenvalues and eigenvectors for the coefficient matrix. A₂ = 0 JI ← A, V₁ 9 V2 = 81 = = -3 6 - - 4 x. help (numbers) help (matrices) help (numbers) help (matrices) For each eigenpair in the previous part, form a solution of a' = Ax. Use t as the independent variable in your answers.
eigenvalues 4 -1 - 2 To To 1 -2 - 1 8 3 CỤ OTC 19 0 2 3 -2 -3 1-11 5 -2 0 4 -2 421O 1 -2 4 0
please solve it on paper
Consider the initial value problem Find the eigenvalue X, an eigenvector ₁, and a generalized eigenvector 72 for the coefficient matrix of this linear system. λ = x₁(t): = x₂(t) = x₂ (t) = help (numbers) help (matrices) Find the most general real-valued solution to the linear system of differential equations. Use c₁ and c₂ to denote arbitrary constants, and enter them as "c1" and "c2". Solve the original initial value problem. x₁(t) = , V₁ = V1 = = , V₂ = help (formulas) help (formulas) help (formulas) x₁ x₂ help (formulas) = = 3x2, x₁ (0) = 2, -3x1 +6x2, x₂(0) = 6.
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Consider the linear system dt = AY with A = Find the corresponding straight-line solutions Y₁ (t) = coordinates of Y₁ (0) and Y₂ (0) equal to 1. x₁(t) = y₁ (t) = = x₂(t) = 26 20 21(t) y₁ (t) Let A₁ A₂ be the eigenvalues of A. 1 Y2₂(t) = (#₂(t)) with the y- and