5. In each case, the eigenvalues of a transition matrix A are given, as well as...

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5. In each case, the eigenvalues of a transition matrix A are given, as well as a basis for each eigenspace. For the dynamical system xt+1 entries of the state vectors) will eventually stabilize, disappear, or grow without bound. Determine the eventual (approximate) ratio between the population numbers – for this analysis, you may as- sume the initial state vector is not an eigenvector of A. Axt, determine if the population numbers (corresponding to the {(} {(}• a) A1 = 1 with basis for E, and A2 = 0.6 with basis 3 for Ex 11 {} b) d1 = - with basis for E, and A2 = with basis for Ex2 2 for Ex, and A2 = 1 with basis A1 = 3 with basis for Ex2 5. In each case, the eigenvalues of a transition matrix A are given, as well as a basis for each eigenspace. For the dynamical system xt+1 entries of the state vectors) will eventually stabilize, disappear, or grow without bound. Determine the eventual (approximate) ratio between the population numbers – for this analysis, you may as- sume the initial state vector is not an eigenvector of A. Axt, determine if the population numbers (corresponding to the {(} {(}• a) A1 = 1 with basis for E, and A2 = 0.6 with basis 3 for Ex 11 {} b) d1 = - with basis for E, and A2 = with basis for Ex2 2 for Ex, and A2 = 1 with basis A1 = 3 with basis for Ex2