Question

Consider the following system. dx dt dy dt 5 x + 4y 2 3 =X - 3y 4 Find the eigenvalues of the coefficient matrix Alt). (Enter your answers as a comma-separated list.) Find an eigenvector for the corresponding eigenvalues. (Enter your answers from smallest eigenvalue to largest eigenvalue.) K K₂ = Find the general solution of the given system. (x(t), y(t)) =

Answer 1

dn dt =-{n+uy dy at - n-34 돌니 jo ASI -3 Now characteristic equation и - 2 - 4. ml -3-3 - ctb)(3+) -3=0. 3+ + > 을 2X+113 +9=0. = 0 or. (2%+90(%+1) = 30=-2,- Eigen valuus 2- -, -1 Auswu) find Eigen neem. zu x=-1. - + 4 13.) () = (8). V (8 :) (*2)=63). &i=8162 P کن ģdia 2012 10 ) 2,58. 22= 3 a Ky

fu.x=-2 / -{+ 4 2 ) (3)=(0) 3 -3 + 9 / Ri ÅR, 2 R₂ R₂ - 8/8R 0 0 2,7242=0, x=2, d₂=-1 (ó 2) (%) = (8) Kp = () k, M D 2,-1) Amum K₂= ) (8,3) thurgune <uky, 909) = {2,654 percet, ce se +36) please type a carefully