Economics Dynamics Problems 229

Economics Dynamics Problems 229 - Discrete systems of...

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Discrete systems of equations 213 Then A λ I = 1 λ 21 11 λ 0 3 6 1 λ Within Mathematica carry out the following instructions, where we have replaced λ by a m = {{1-a,2,1}, {-1,1-a,0}, {3,-6,-1-a}} sols = Solve[ Det[m]==0, a] or in Maple m:=matrix( [ [1-a,2,1], [-1,1-a,0], [3,-6,-1-a] ] ); sols:=solve(det(m)=0,a); which gives the three eigenvalues 4 q = 0 , r =− 1 and s = 2. The next task is to obtain the associated eigenvectors. For q = 0, then ( A 0 I ) v r = 121 11 0 3 6 1 v q 1 v q 2 v q 3 = 0 0 0 which leads to the equations v q 1 + 2 v q 2 + v q 3 = 0 v q 1 + v q 2 = 0 3 v q 1 6 v q 2 v q 3 = 0 We can solve this system within Mathematica with the instruction Solve[ {x+2y+z==0, -x+y==0, 3x-6y-z==0}, {x,y,z}] or in Maple with the instruction solve( {x+2*y+z=0, -x+y=0, 3*x-6*y-z=0}, {x,y,z});
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