Consider the Initial Value Problem:x₁x₂X₁=-i, №₁x₂ =(a) Find the eigenvalues and eigenvectors for the coefficient matrix.==9 cost + 7 sin t3x₁ + 3x₂- 6x₁ - 3x2¹-3-iand X2x₁(0)x₂ (0)=An ellipse with clockwise orientationpplane9.m in MATLAB to describe the trajectory.=(b) Solve the initial value problem. Give your solution in real form.x1 = 5 cost + 4 sin t= -i V259=−3+i61. Use the phase plotter

The given system of differential equation is: x1'=3x1+3x2x2'=-6x1-3x2 With x10=5 and x20=9.

Answered: Consider the Initial Value Problem: x₁…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter7: Real And Complex Numbers

Section7.2: Complex Numbers And Quaternions

Problem 45E

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Consider the Initial Value Problem: X1 = (a) Find the eigenvalues and eigenvectors for the coefficient matrix. 181 v1 x₁ x^2 = = - 3x₁ + 3x₂ 9 - 6x1 + 3x₂ " (b) Solve the initial value problem. Give your solution in real form. X1 = x2 = and A2 x₁ (0) x₂ (0) = " = = V2 = 2 7 [8]
Let A= (in the picture) (a) Find the eigenvalues and eigenvectors of A. (b) Rewrite A in the form A = P DP ^−1, where A, P and P −1 have their usual meanings and use this to find A^20. (c) Find a matrix B such that B^3 = A (Use A = PDP^−1).
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Find the matrix A of the quadratic form associated with the equation. 2x2 - 3xy - 2y2+ 11 = 0 A = Find the eigenvalues of A. (Enter your answers as a comma-separated list.) Find an orthogonal matrix P such that P'AP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ..], where each row is a comma-separated list.) P =

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