(1 point) Consider the initial value problem -2 j' = [ y, y(0) +3] 0 -2...
1 point) Consider the initial value problem 0 -2 a. Find the eigenvalue λ, an eigenvector UI, and a generalized eigenvector v2 for the coefficient matrix of this linear system. v2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. c. Solve the original initial value problem. n(t)- 2(t)
(1 point) Consider the initial value problem -51เซี. -4 มี(0) 0 -5 a Find the eigenvalue λ, an eigenvector ul and a generalized eigenvector u2 for the coefficient matrix of this linear system -5 u2 = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers c2 c. Solve the original initial value problem m(t) = 2(t)- (1 point) Consider the initial value problem -51เซี. -4 มี(0)...
(1 point) Consider the initial value problem 7=[8_5]: x0=(-3) Find the eigenvalue 1, an eigenvector vi, and a generalized eigenvector v2 for the coefficient matrix of this linear system. a = vi = help (numbers) help (matrices) Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. F(t) = 61 IHO + C2 help (formulas) help (matrices) Solve the original initial value problem. xu(t) = help (formulas) x2...
'= [_! :]ā, co= (23) a. Find the eigenvalue ), an eigenvector v , and a generalized eigenvector ū2 for the coefficient matrix of this linear system. l= , Vj = b. Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in you answers. y(t) = 41 c. Solve the original initial value problem. yı(t) = yz(t) =
(1 point) Consider the linear system 3 2 ' = y. -5 -3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. 2 = 15 and 2 V2 b. Find the real-valued solution to the initial value problem Syi ly 3y1 + 2y2, -541 – 3y2, yı(0) = 0, y2(0) = -5. Use t as the independent variable in your answers. yı(t) y2(t)
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...
(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)...
Previous Problem Problem List Next Problem (1 point) Consider the linear system -3 -2 >= -3) y. 5 3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. di = on = and 12 = · U2 b. Find the real-valued solution to the initial value problem { vi = -3yı – 2y2, 5yı + 3y2, yı(0) = 11, y2(0) = -15. y۔ = Use t as the independent variable in your answers. yı(t) = y2(t) =
(1 point) Consider the linear system 3 y y 5 3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. 2 0 and A2 = -1 02 -3- -3+1 b. Find the real-valued solution to the initial value problem Svi C = -3y - 2y2, 591 +372 y.(0) = 6, 32(0) = -15. Use t as the independent variable in your answers. yı() y2(t) = 0
Problem 5. (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. and iz = b. Find the real-valued solution to the initial value problem - -3y - 2y2 Syı + 3y2 yı(0) = -7, (0) = 10 Use I as the independent variable in your answers. Y() = Note: You can earn partial credit on this problem. Problem 6. (1 point) Find the most general real-valued solution to the linear system of differential...