Question

Please help me solve this, thanks!

Find the general solution to the system x' = Ax where A is the given matrix. | -2 -2 -6 A= 0 0 6 | 0 -2 -8 b) X(t)=( X(t)= Ce

Answer 1

$ 01 AUGUST : SATURDAY AUGUST. SATURDAY 19 20 222 75 1) Here X = AX net A= 1-2-2-6 Lor2-8 Post of " we that find eigen values and eigen vector matrix 12 Consider IA-d7120 1-2nd 2-6 o 2-8-11 (-2-4) [ + (8 +d) + 1 2] + 2 [0]-600] =0 (-2-d) [ +² +84 +12] =0 02 SUNDAY (1+2) [(4+2)(4+0)]=0 . d, = -2, dy=-2 Az = -6 Tofintigen vector correspond to 4,= -2 . Corgider CA-DI] [XJ = 0 042 2020 2020-4-27 00:09

MONDAY. AUGUST MONDAY • AUGUST 03 OC o -2-6 22 O-2- C1710 - fah ZR & R Pz - BRT R2 R₂ + R & R ₂ - R &R o-2-6 Toy 22 Looola lol • system has infinite solh. system has one egh ( no. of unknowns put x = p 8 x z=q. 222 +683 20 x2 = -3*3. x2 = -39 - K3 P -34 L1 Iptoq I op- 39 lopta 2020 2020-4-27 00:09

AUGUST TUESDAY Ola eigen vector corresponding to eigen value put d =-2 9=2 8-2 care Tol 2 To vector corresponding to find eigen Az =-6. Consider [A11] [x] = ro] T-2+6 - 2w6 Tu X2 o-2 -8+6/123 (2 o 66 Lo-2- 2 x3] RB R3t / 3 R2 2020 2020-4-27 00:09

S M T WT 31 JULYO FRIDAY JULY FRIDAY 29 30 21-1930 4- 2 - 6T 06 6 Oo o 23 system has infinite solh take ( =/ x2 = -1 4, -2726*3-0 gep 23 a. solh is - 2t Ice Lo - 27 & cate f I T- 6 X Lt) = ce tc-6try + ca e- Aug: None of these. 2020 2020-4-27 00:09

FRIDAY. AUGUST WK 32) 220-146 1-2016-1 Coulder | Adl=0 - 10 O- 1 1-20 16 -1-d - [(2+) -16] - (20) -[d?td-16 ]-20 d3d²+ 16d-20=0 di=2, dq=2 3 = 5 for d =de=2 we have to Coneider find eigen vectors Tadf] Ex 7 =0 1 - 2 1 1-20 16-3 2020 3 T 2020-4-27 00:10

S M T W T F 08 S AUGUST SATURDAY R3 R3TIORI P R + 8 R2 system has infinite son put x =P 2,= ply SUNDAY 22 2020 2020-4-27 00:10

MONDAY O RUCUST 10 MONDAY • AUGUST eigen vector for di-5 | A-da [x]=ro] 1-20 16 4 02 223 R2 Z R3t4RI az To 204 Rqg R3-4R2 0 5 1 ooo X2 x3 put xz=P X2=-1/6P 24 = old P p- 25 gel - put ez 25 re 3 2020 2020-4-27 00:10

M T W T F S AUGUST TUESDAY ME un roots are repeated to Xl 5H col T-5 I 25 2020 2020-4-27 00:10