Find the general solution to the system of linear differential equations X'=AX. The independent variable is t. The eigenvalues and the corresponding eigenvectors are provided for you. x1' = 12x1 - 8x2 x2 = -4X1 + 8x2 The eigenvalues are 11 = 16 and 12 = 4 . The corresponding eigenvectors are: K1 = K2= Step 1. Find the nonsingular matrix P that diagonalizes A, and find the diagonal matrix D: p = 11 Step 2. Find the general solution...
Problem 1. x(1) 67 (1 point) Given X = AX with X(t) = , A = and x(0) = Vt)] -20 91 (a) Write the eigenvalues and eigenvectors of A (b) Write the solution of the initial-value problem in terms of xt), y(t) x(t) = yt) =
Problem 5. (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. 1 = . and 12 = V2 = b. Find the real-valued solution to the initial value problem = -3y - 2y, 5y + 3y2 (0) = -11, y (0) = 15. Usef as the independent variable in your answers. y (t) = (1) =
(1 point) For the linear system [12 61- У -3 31 Find the eigenvalues and eigenvectors for the coefficient matrix. and λ
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...
(1 point) Consider the linear system 3 a. Find the eigenvalues and eigenvectors for the coefficient matrix 0 and A b. Find the real valued solution to the initial value problem -392 5y + 3y (0) 9, y(0) - -10. Use t as the independent variable in your answers, (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
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) =...
(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)
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t > 0, and A has the eigenvalues and eigenvectors below. 4 2 11 = -2, V1 = 2 0 3 12 = -3, V2= 13 = -3, V3 = 1 7 2 i) Identify three solutions to the system, xi(t), xz(t), and x3(t). ii) Use a determinant to identify values of t, if any, where X1, X2, and x3 form a fundamental set of...