Question

DETAILS LARLINALG8 7.4.003. Use the age transition matrix L and age distribution vector x, to find the age distribution vectors x, and xz. 0 341 1 0 0 L = x1 = 16 1 16 X2 11 II хз Then find a stable age distribution vector. x=t 11

Answer 1

14 Page Josh 0 3 4 Date 0 O 16 L a O X, 16 20 X2 = LXI - 0 3 4 16 112 1 16 16 0 0 8 X3 = LX 2 = 0 3 4 112 20 1 O 17 112 VO ४ 8 vector stable Age distribution find Eigenvalue :- IL-I = 0 3 4 0 20 -3+32+2=0 (941) (4-2)=0 3 7 = -1,-1, 2 TUOLO Vector Eigen for a=2 24 X- IL-281 X=0 है 7 71 0 --2 3 4 0 1 zu 0 o (1) ½ - 21+34 +42=0 2-24 = 0 - 4 - 22=0 G = 42) X-9 (47) = 0 =) (2 82 x-2y = 6

Rutting Eq_(1). -2x + values in 34 + 4730 -21871+ 3 (42) +42=0 -167 +12.7 +47 = 0 0 0 x = 82 8 Z. 2 9 y = = 42 -- X- So Eign vector is ; +=2 2/ Eigen 8 vector ia for 2=-1 X 3 4 0 IL+I) X=0 O 4 0 % z X+ 34+42=0 a tyo ty & y=-dz ス3 +2=0 yo 3 x=22 21 x = -2 rue it Anot possible valus not possible] zi

112 X 80 %3D X33 16 8 stable nge distribution vector X- 1/8 ५