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Economics Dynamics Problems 232

# Economics Dynamics Problems 232 - 216 Economic Dynamics In...

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216 Economic Dynamics In this instance the output in both programmes is almost identical. Mathematica , however, qualifes the solution For z[t] by adding 15 If[t==0,1,0] .IF t is time, then this will not occur, and so this conditional statement can be ignored, in which case the two programmes give the same solution – which is also the one provided on p. 214. 5.4.2 Solving using the Jordan form In section 5.3 we Found the eigenvalues oF the matrix A and used these to fnd the matrix V Formed From the set oF linearly independent eigenvectors oF A . The diagonal matrix J = diag( λ 1 ,...,λ n ) (5.6) is the Jordan Form oF A and V is the transition matrix, such that V 1 AV = J (5.7) ±rom this result we have A t = VJ t V 1 and since the solution to the system u t = Au t 1 is u t = A t u 0 , then u t = VJ t V 1 u 0 where J t = λ t 1 0 ··· 0 0 λ t 2 0 . . . . . . . . . 00 λ t n (5.8)
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