Deven Singh, Assignment 6, 09/27/2021

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#Question 1

#n[0](t) = 0.1*n[0](t - 1) + 1.2*n[1](t - 1) + 0.9*n[2](t - 1) + 0.1*n[3](t - 1))

#n[1](t) = 0.95*n[0](t - 1)

#n[2](t) = 0.97*n[1](t - 1)

#n[3](t) = 0.9*n[2](t - 1)

#n[1](t - 1) = 0.95*n[0](t - 2)

#n[2](t - 1) = 0.97*n[1](t - 2)

#n[3](t - 1) = 0.9*n[2](t - 2)

# n[0](t) = 0.1*n[0](t - 1) + 1.2*0.95*n[0](t - 2) + 0.95*0.9*0.97*n[0](t - 3) + (0.97*0.1*0.9)*0.95*n[0](t - 4)

GrowthCe := proc(REC) local x, i; evalf([solve(1 - add(REC[i]/x^i, i = 1 .. nops(REC)))])[1]; end proc;

GrowthCe([0.1, 1.2*0.95, 0.95*0.9*0.97, (0.97*0.1*0.9)*0.95]);

1.39



#Question 2

with(LinearAlgebra);

A := Matrix([[0.1, 1.2, 0.9, 0.1], [0.95, 0, 0, 0], [0, 0.97, 0, 0], [0, 0, 0.9, 0]]);

evalf(Eigenvalues(A));

#The largest eigenvalue is 1.39



#Question 3

P := Matrix([[0.5, 1/6, 1/6, 1/6], [3/15, 0.4, 3/15, 3/15], [7/30, 7/30, 0.3, 7/30], [4/15, 4/15, 4/15, 0.2]]);

evalm(P &^ 1000);

# 31.5% of surfers stay on S[1], 26.3% of surfers stay on S[2], 22.5% of surfers stay on S[3], 19.7% of surfers stay on S[4]

# Page Rank (from most popular to least popular) = S[1], S[2], S[3], S[4]