(1 point) Consider the initial value problem 7=[8_5]: x0=(-3) Find the eigenvalue 1, an eigenvector vi,...
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 -2 j' = [ y, y(0) +3] 0 -2 a. Find the eigenvalue 1, an eigenvector 1, and a generalized eigenvector ū2 for the coefficient matrix of this linear system. = --1 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. g(t) = C1 + C2 c. Solve the original initial value problem. yı(t) = y2(t) ==
'= [_! :]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) 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)...
(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)...
the solution need to be in terms of sin and cos (1 point) Consider the linear system -3 -2 = r. 5 3 Find the eigenvalues and eigenvectors for the coefficient matrix. 1 11 = -I V1 = help (numbers) help (matrices) -(3-1)/2 and 1 12 = -. help (numbers) help (matrices) 1 V2 = -(3+i)/2 Find the real-valued solution to the initial value problem x1 = -321 – 2x2, x = 5x1 + 3x2, x1(0) = 2, x2(0) =...
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 the following eigenvalues and eigenvectors: 4 = 2 with vi = and |_ G 12 = -2 with v2 = Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: x(t) (50) = C1 + C2 e e B. In fundamental matrix form: (MCO) = I: C. As two equations: (write "c1" and "c2" for C1 and c2) x(t) = yt) =
The matrix has eigenvalues 11 = -7 and 12 = 2. Find eigenvectors corresponding to these eigenvalues. and v2 = help (matrices) Find the solution to the linear system of differential equations * = -25x - 18y y = 27x + 20y satisfying the initial conditions (0) = 4 and y0) = -5. help (formulas) help (formulas)