3) Write a general solution in the form Y(o)-kke to a linear system Y'-AY such that...
if someone could calculate a few of these that would be great so I can understand Solution by eigenvalı 8.2 e general solution in vector form. 4. a) Solve by eigenvalues/eigenvectors and write th b) Write the general solution in z(t), v(t) form. -2x +y di-2y 6) -V +2y Solution by eigenvalı 8.2 e general solution in vector form. 4. a) Solve by eigenvalues/eigenvectors and write th b) Write the general solution in z(t), v(t) form. -2x +y di-2y 6)...
(1 point) Consider the linear system "(-1: 1) y. a. Find the eigenvalues and eigenvectors for the coefficient matrix. 1 v1 = and 2 V2 b. For each eigenpair in the previous part, form a solution of y' = Ay. Use t as the independent variable in your answers. (t) = and yz(t) c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions? Choose
Problem 6 (3 points) The general solution of the system of the linear system * = AY, Y)= ((0),y(t)), is given below. (1) Sketch the strait- line solutions and the phase portrait. DO NOT forget to use ARROWS. Make sure that your sketch shows ABSOLUTELY CLEAR slopes of Tangent line as t oot -oo. (2) Is the solution stable? Y(t) = kV1 + kye" V2; V. =(2,-1), V, = (1,3)
(1 point) The general solution of the linear system y = - Ay is 0 Wt) = [ [E] O et/6 Determine the constant coefficient matrix A. A =
Consider the linear system y⃗ ′=[6−124−8]y⃗ . Problem 1. (10 points) Consider the linear system 4 ' = [-12 -8 a. Find the eigenvalues and eigenvectors for the coefficient matrix. te and 12 = v2 = b. For each eigenpair in the previous part, form a solution of y' = Ay. Use t as the independent variable in your answers. gi(t) = and yz(t) = c. Does the set of solutions you found form a fundamental set (i.e., linearly independent...
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...
(1 point) a. Find the most general real-valued solution to the linear system of differential equations x -8 -10 x. xi(t) = C1 + C2 x2(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these ОООООО (1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the...
a. Find the most general real-valued solution to the linear system of differential equations x = -[42]; xid) + c2 x?(༧) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these (1 point) Consider the linear system -6 7-11) -9 15 y. Find the eigenvalues and eigenvectors for the coefficient matrix. 21 = V1 = , and 12...
In this exercise we consider the second order linear equation y" therefore has a power series solution in the form 4y = 0. This equation has an ordinary point at x = 0 and We learned how to easily solve problems like this in several different ways but here we want to consider the power series method (1) Insert the formal power series into the differential equation and derive the recurrence relation Cn-2 for n - 2, 3, NOTE co...
Write each statement as True or False (a) If an (nx n) matrix A is not invertible then the linear system Ax-O hns infinitely many b) If the number of equations in a linear system exceeds the number of unknowns then the system 10p solutions must be inconsistent ) If each equation in a consistent system is multiplied through by a constant c then all solutions to the new system can be obtained by multiplying the solutions to the original...