Find the general solution of the following inhomogeneous systems. Use either eigenvector decomposi- tion or undetermined coefficients method. These problems can be solved by hand, but you can also use technology to assist you at any stage. When using technology always report on what function you use. -48HR SIGHE + = (a) # X2 12 -2 5 5 -2 3e -2t -e-2t

Q: A 2 X 2 constant matrix A has an eigenvalue -3+4i. Determine if each of the following could be a…

A:

Q: Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. A₁ =…

A: The given problem is to find the eigen values and eigen vectors for the coefficient matrix and also…

Q: Consider the following initial-value problem. -1 -2 X'= ×·- (-² -² ) x + ( ³ ) × (0) - ( -5 ) X 3 4…

A: Given  system of differential equation is              x'=-1-234x+55  ,   x0=-67  compare this with…

Q: λ1 = -2, λ2=5  V1 = (1, -2)  V2 = (4, -1) Using the above eigenvalues and/or eigenvectors, find…

A: I have used eigenvalue and eigenvector method to solve the given system of ODE.

Q: X (0) = X. dx dt = 3 1 X

A:

Q: dr - 2x – 3y dt dy 3x + 8y dt

A:

Q: Apply the eigenvalue method of this section to find a general solution of the given system. If…

A: According to the given information it is required to determine the solution of given system by…

Q: Please answer this linear algebra question and show all steps.

A: The final answer given below:Explanation:

Q: -11 5]SX1 -8

A: This is a problem of stability analysis.

Q: The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the…

A:

Q: You may use a calculator to perform basic calculations on these problems: (just label when using…

A: Given,       x'=-103020-30-1x

Q: Q5) Given A = 0 – 2    4 determine if x = (1,1,0) is an eigenvector, why or why not?…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: (b) d dt x1 x2 ]-[ = 2 3 -1 -2 [2] + cos 3t 4

A:

Q: X1(t) Let x(t) be the solution to the discrete dynamical system: x2(t) X1(1 + 1) = 11x1(t) – 18x2(t)…

A:

Q: Consider the linear system 3 *' = Find the eigenvalues and eigenvectors for the coefficient matrix.…

A: The complete solutions are given below

Q: Problem 1: Solve the heat equation ut 5urz for a rod of length T with both ends insu- lated for all…

A:

Q: 1. Find the general solution of the system of equations. x² = ( 3 3 ) = x'

A: To Find: the general solution of the system of equations. x'=7-55-3x

Q: Find a 3 x 3 matrix A that has eigenvalues λ = 0, 12, -12, with corresponding eigenvectors DOO…

A: A  has eigenvalues , with the corresponding eigenvectorsThe aim is to find the matrix  that has the…

Q: A linear system x = Ax with state variables x₁(t) and a₂(t) is defined by the equations: *1 = 3x1…

A:

Q: Please solve the following by hand, have good detail and explain each part of the question step by…

A: image was blurr but i have tried my best to solve.

Q: (b) Find the fundamental matrix Þ(t) for the system x' = Ax which satisfies (0) = I. (c) Use Þ(t) to…

A:

Q: 2. Use the solution to the previous problem to solve the following initial value problem. Describe…

A:

Q: The eigenvalues are λ₁ < λ2 < A3 < №4, where A₁ = has an eigenvector eigenvector A = -37 15 0 0 -70…

A:

Q: The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the…

A: We have to find the general solution of the given system of differential equations.

Q: Problem #3: Consider the following matrix A (whose 2nd and 3rd rows are not given), and vector x. A…

A:

Q: λ1 = -2, λ2=5  V1 = (1, -2)  V2 = (4, -1) Using the above eigenvalues and/or eigenvectors, find…

A:

Q: 5. Use the matrix exponential (as done in class. Do not use generalized eigenvectors) to solve the…

A:

Q: [1 2 -31 are 1, 2, The eigenvalues for the matrix A = |o Lo -2 Find the corresponding eigenvectors.…

A:

Q: xi = 2x1 – 5x2 x2 = 4x1 – 2x2 X1 (0) %3D 2, х2(0) — 3 2х1

A: