Question

a) Solve the system using Operator (D) elimination. Write the answer in both scalar and vector form =x+2v dt dy = 4x+3y dt b) Solve the above system using Eigenvalues and Eigenvectors. Write the answer vector and scalar form

the answers should be the same but I'm not getting it. please help.

Answer 1

dt dy = 4x+3Y =* + 2 (4x +3y) + 8X + 6 Y +8x +3 ( -x) = 4 d +g. -4 Auxiliay equation: m- 4m - S =D0 (m+1)(m - S) = D '.x=dēt +Best. che - u (-Aēt+SBES+) - Aē-Bēst = - 2Aē + 4BeSt + 2Be St (b) 2. (A - aI|=0 =) (I- a) (3-2)-8=o =) 4 a=-) (A - a1) x =0 ( :)C)() (x,y) E (x, - n) = x (1, - 1) ',1, -) is on eign vector comesponting 4x +49 - o to a = -I (A - aI) x =o L. (x,y) = (×, 2x) =x (1, 2) .'. Cl,2)is an eign vector Corresponding to a =5. +Be2t Aēt +Be?t 2B24 (:), 2v = () -: 4(+) = A ēE +Be2t + 21Be4