Question

Use the age transition matrix L and age distribution vector x1 to find the age distribution vectors x2 and X3. 0 34 1 0 0 20 20 L= X1 = 0 0 20 X2 = 11 X3 = Then find a stable age distribution vector, X =

Answer 1

Stob we have Obtain the age distribution rector I by finding the product Lx, 0 در 4 20 140 1 6 20 20 0 0 12 20 0 10 140 20 lo . obtain the age distribution vector is by finding the product Lan 132 D 3 4 140 100 1 0 20 140 o 0 0 10 lo 100 140 lo step To obtain the seable age distribution vector, find are eigenrection of I wore ponding wo wth positive eigenvame shown يامهم

find the legeso values of L IL-AI)=0 O- 3 4 0-1 0 - 0 0- O d) (-d² - 3 (-22 +4 (1)=0 -13 +34 +2=0 d -3 -2=0 fl-2)(0+1)=0 = 2,-1,-1 the positive eigenvalue of Lin d=2. find une eigenector you a=2. 0-2 3 4 1-2 3 4 0-2 ½ ½ -2 0 1 -2 o 0-2 0 O - -4 o U O Solfe the mattix equation -87 iwe have 0 10 - 0 -4 0 3 - 8z o. vs - 4z = a v = dz & 2 = 40

래 BV 8 8 4 vs 4 t v2 rez 413 V3 - Let Va=t, ter The eiginrector in 8 4 t v= - age distribution thes, the slable reclor i 8 4 2 = t 1