Question

QUESTION 4 One solution of x' = The general solution is 1 2 e3t ОА. + C3 e3t Int x+b(e) is x(e) = [7] 0 [8]+ole [l] to (o) ( OB + Ci Int] et + e3t OD ci Int OC e3t Ci + C2 + C3 Int

Answer 1

Given, x":[? 2 x + b(t), where X(L) - - Link ent voca This is in the foom of, X'=AXT A= - [2 arrollocano 2 want to find Eigen value and vectoos. So, characteristic equation 1A-XII 2-X guls coon 2-> x-4x+3=0 - (x-3) (x-1)=0 x=3 and x=1 Thus eigen values are (X.) = 1,3. Now want to find eigen vectors

i) x=1, [2-7 1 2-X perform dow operations, R2 - R₂-RI sitiostos bo DN: Now solve matrix equation, =) V, +V2 = 0 If we take, then Vat vist V2=-t SO VE t. - Eigen vector.

1) 1-3. (2-) 2-X [1] JE perform now operations, 100W R2 R2 + Ri tacco Emol - notuba loon R RI O solve matrix equation, L (*):C: If we take, uzat then v=t and 2-t V= - [ + ] - [i]t - Eiger vector

The general solution is, 1)t се A (3) + се е + int 3t e t + 3t + ent option cliş correct. Result? t 36 general solution =c f) it + 3t Int nologia