Question

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Use the age transition matrix L and age distribution vector x1 to find the age distribution vectors X2 and X3. 0 3 4 1 0 0 L = X1 = 20 20 20 0 X2 L. It X3 = Then find a stable age distribution vector. x = t 11

Answer 1

ANSWER:
ejeven that & 3 L- -4 0 0 Ź 0 20 X,s 20 -20 Now, 3.4 112 2o X2=LX, 1 20 20 obz 0X20 + 3x20 +4420 1 X 20 + 0x20 + 0 x 20 0.320.+ 120 + 0 x 20 10 12 0+60+80 20to to 0 t loto T60780 5 20 10 140 s 20 LO

3 4 140 X 3 1 으 불 이 10 S ox140.73X20 + 4X10 1x140 + 0x 20 +0.NO 0x140 12 x 20 + 0x10 + 0 + 60+40 40+ oto 0+ to to T6otyo 12 140 10 Too 1140 10. To find stable age distree bution Vector, Firest we fond eggen' values: IL-AI | 50 -- 3 4 -> o 0 [ ->

3 -2x+3y tuzo y +20=0 x - 2.2 2 Then, = x= 4.2 9 +23 +2uso = 4+2142150 =) y s s8Z putting the value in equation o -2x + 3y + 4z Eo 9 -2442) +36-82) +42=0 = -8 2 + 2yZ tyZ =0 Oso Ч7 82 i 2- 5 1: X=YZ jy 1582 y Z SZ Z 4 ệ t=2 So, legen veetore ose to ។ eigen vectore of a

9 We find the eigen vectore for the eigen voue (A=-1) [141] =0 1 3 4 - o y $ 0.51 Z x + 3y + 4zso xty so 4+2=0 =) y = -22.9 x = 22 2 х - It is not possible صار 2 because negative Z age not possible 140 100 X 2 = Aze 20 140 10: 100 stable eage distreebution vectora st Ang -65
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