Question

Use an appropriate method to solve the given system e *-=( ")x+ te'

please show work and steps thank you

Answer 1

Given that, x' 8 xt (e e-t tet Let A= 18 I -1 The characteristic equation is, A-NI co 1-X o 8 -1- : (t-> )(-1-))-8=0 72-9=0 -3) (2+3)=0 :Jis £ 3 Eigenvector corresponding to 1-3 CA-I 2 = -2 8 2 af 20-44co OC = 44 ... Required eigen vectoe is, ( 4 1

-det+ b[tet tet = [ 24+ (!)] ett [bAt(o)tet Comparing the coefficients we get a At b = la Aten Let as coun) bellen Now fa 8 + az az -1 EG ay 8 -1 هه t - t au A2 raut802 a -au = ait802+) - Q2 = ax-a2 .: 01 =0, A2=-YO = a ( a a) (8)

(E)(3)(..)+10 ( ( but $b2 ) + (0) bi-bz p = b 1-351 b = bi-b2+1 8.62= bi+1=0 bit b=0 (bs) o xp = et elis) + tet (o) ) + tet 8 Genos solution is X(t)=X&typ 78 X(t)= ge Gesta 3t tzea (a + C2 (-2) tello) +tet