Question

Find a general solution of the system x'(t) = Ax(t) for the given matrix A. 8 2 A=1 34 - 8 x(t)= (Use parentheses to clearly denote the argument of each function.)

Answer 1

х(t) - Рx(+) А- 3 (3 - ) Firstly A valec Find Ә) есем — о Ax=hx — 2 (A – ) X I-4 eden Vogue |Алт 1 = о 3-А – 2 о 퀘 2 3 ч - 3- А о (- 3 – 4) (Я - А) + 68 = (2+4) C#-А) +68 ~ — (6ч - A) 4 68 - о こり 2. и -) К-и- =) +4+K2. — h2 + 2

eisen Vecta fu ha zi (A-211 ) =) [722][3) = 20) R, 34 Ri R₂ - (8-20 ) R2 -2(34) 34 (8-21) 34(8-22) g -(8+2i) (8-20) 1/3)- 10) J/33-7) 34 (8-21) -68 34( 8-21) -68 R2 -> R2 RI 34 (8-21) -62 165)=[:)] C 34 C8-21) X -68 y (8-20x= 2 y Put x=1 => y = hi =1 Xe eil 4-i Fa h=-zi (A +211) X = o 8+2i =) 22] [5)-( 34 - 8+20 R2 (8+22) R₂-34R, 8720 "L 33] [5)-(3) (8+ 21 )2 = 2y Put x=1 y = 8+2 i -1 uti

Generd Solution is hit hat + C2 e Xlla Cie IX X2 zit Се -zit + C2 e - |--1] [More] As