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6) Solve the following System of FODEs with a repeated, real eigenvalue. Write the general solution....
(1 point) Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: X= -4 with eigenvector v = and generalized eigenvector ū= [] (-1) Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: t t [CO] = C1 + C2 + I g(t). e . - 1 B. In fundamental matrix form: [CO] C. As two equations: (write "c1" and "c2" for 1 and 2) X(t)...
Solve each of the following systems by the eigenvalue method. If ICs are given, find the particular solution to the system. If no ICs are given, find the general solution. Write all solutions in vector form. x'1 = 3x1 - x2, x'2 = 7x1 - 5x2
(1 point) Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: i = -3 with eigenvector v = and generalized eigenvector w= = [-] = [4] Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: 1 (O) = - 18.05.8:8)... y(t) B. In fundamental matrix form: (O)- x(1) y(t) [:] C. As two equations: (write "c1" and "c2" for c and c2) X(t) = yt)...
alue problem yn value) +13y=0, y(0)=3.y (0)-Owe use the To solve an initial v eigenvalue method. (Complex eigenvalue 1. I) Convert the equation into a first order linear system 2) Write the system in the matrix form: 3) Find the eigenvalues: 4) Find associated eigenvector(s): 5) Write the general solution of the system figure out the c and c2 To find the particular soluion 6) 2 7) Find the particular solution of the system 8) Write the particular solution of...
In this problem, we will investigate the strategy to deal with repeated eigenvalues in two wavs. Consider A-I 7-2-6 1. Find the only eigenvalue λο of A. Calculate (A-λ01)2 and (A-λ01)3. Does | 0 | satisfy (A-λ01YP P 0 or not? 2. Let M (PIAPIAP). Compute M-1AM. 3. Let Y -M-1X. From the system of equation for Y, deduce the differential equation of order n containing only уз (it should not contain yl or y2) and solve it 4. Obtain...
Please clear hand write ,thank you ???? 5. a) (7 pnts) Determine the general solution to the system x' = Ax for the given matrix A = [2 81 b) (6 pnts) Write one unique solution, by assuming some values for the arbitrary coefficients. c) (7 pnts) Ast → 00, what could you say about the limit of the solutions of this system? 4. a) (7 pnts) Write the following system of linear equations in x' = Ax form. x...
Please clear hand write ,thank you ???? 5. a) (7 pnts) Determine the general solution to the system x' = Ax for the given matrix A = [2 81 b) (6 pnts) Write one unique solution, by assuming some values for the arbitrary coefficients. c) (7 pnts) Ast → 00, what could you say about the limit of the solutions of this system? 4. a) (7 pnts) Write the following system of linear equations in x' = Ax form. x...
Please note that all the steps are meant to help solve the problem. Question A1: We have yet to discover what happens when the matrix that defines our system has a repeated real eigenvalue. Let's start with the case of a system defined by a diagonal matrix, which has the twice repeated real eigenvalue A 3. Follow the steps below to analyze the shape of the trajectories and draw the phase plane portrait: 1. Write down the explicit solution to...
In each of the following problems, find the general (real) solution of the given system of equations. -3 0 2 b) x = (1 -1 0x -2 -1 0
The following system of differential equations has a repeated eigenvalue 2 da dt 2x3y dy 2y dt Suppose we choose its corresponding eigenvector to be (-1, 0). The initial conditions are x(0) = 5.77 and y(0)= 1.99 Find the value of x(0.31), giving your answer to 3 decimal places