Consider the system of differential equations dy 6x - 2y, dt da dt The coefficient matrix [ eigenvalues are 10 and 5. Select the option that gives the general solution of this system. Select one: O O []=[(-2₂2] =a =A =α -2 6 = -] =a -2x +9y. 2] elot + B elot + ß + D---- = előt has eigenvectors [1] [2] est sin (10t) + B cos (10t) + B est est [1] H cos(5t) sin (5t) [4] and [] and the corresponding

Using eigenvalues, find the general solution to the following system of equations. x' = x + y y' = -2x - y

please solve it on paper

For a linear DDS with multiple equations, assume that A is the matrix of the system with eigenvalue c and eigenvector u. Which of the following is true? Check all that apply. X(n) = A"X(0) is the recursive equation for the DDS □X(n) = A"X(0) is the explicit solution for the DDS □X(n) = AX(n − 1) is the recursive equation for the DDS We can always compute X(n) as X(n) = c"X(0) using the eigenvalue c We can compute X(n) as X(n) = X(0) when X(0) is a multiple of