Question

Find the general solution 1 o 9X OT O -

Answer 1

1 0 x х 4 o L o X' АХ = 0 L I A = 0 Y 1 V -- o A-II = 0 I I 0 - T 1 V I V- اح 0-) I 0-1 ſ y Determinant -13 +31 +2 = 0 (1-2) (141) 11+1) = Eigen values 1 = 2 2 - A=-1

for t= -1 IDE have to finor ejenveelor - 1 A-XI 1 R₂ R₃ - Ry R3 R3 - RJ 1 o o 0 10 o x + x2 + x2 = 0 X, - X2 - X3 X2 * 3 --X2 X₂ x = X2 t3 } 0 X2 + X₂ 1 0 X3 = 0 far X₂ = 1 V = out & X₂ = 0 Yg=1 V2 = Os

80 for x=2 -2 1 A-11 - 2 I 1 -2 & R,-) Í R, R2 - Rz -R, -1/2 -3/2 3/ - 2 I -1/2 1 R3 R₃-RI R₂ → - Re/t36) 1-1/2 -]12 O 1 - 0 312 3/2 Rgt R3 3 2 R2 RI RI ) R2 21 o 1 - 1 0 0 X2 1 1:48) X3 0 o X, - X3 =0 X2 - X3 = 0 1 So for X 1 Us

So the general solutn بد - 2 t +63 XLE) 1 * chceme +C₂ e C, e = د 0 1 1 t -t 27 - C₂ e t C e -t 2t cie + C₃ e -t Get tapet 27 et (circa) t +C₂ C . alt t coot + C₂ 0 ²t Gettholt Am