Question

(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) =

Answer 1

solution: We are given that Repeated eigen values are: 1, = -3 and t = -3 and eigen vector / L] ext, the generalized eigen vector w= [ ] (A) eiges walue ) eigen vector foron:- ht XL) yets tice) я с че + C [ Wt vt +*+]es -3t e s1 X14 ylts =G, -3t e to, CJ-41) -26 -3t е. => act) y ct) 1 t2 -36 - е (het) er [1-6] ezt Matrix fory: w um (B) an fondan fundamental -36 е, (4+1) 83 xits yet) -36 c2 G-best (6) As two equations: -36 X(t) = c est to Chether -3 of c₂ -3t Cint) et YCE) = = -6