(Only need help with parts b and c)
Consider the transition matrix
If the initial state is x(0) = [0.1,0.25,0.65] find the nth state of x(n). Find the limn→∞x(n)
(Only need help with parts b and c) Consider the transition matrix If the initial state is x(0) =...
0.5 0 0 5. Let P 0.5 0.6 0.3represent the probability transition matrix of a Markov chain with three 0 0.4 0.7 states (a) Show that the characteristic polynomial of P is given by P-ÀI -X-1.8λ2 +0.95λ-0.15) (b) Verify that λι 1, λ2 = 0.5 and λ3 = 0.3 satisfy the characteristic equation P-λ1-0 (and hence they are the eigenvalues of P) c) Show thatu3u2and u3are three eigenvectors corresponding to the eigenvalues λι, λ2 and λ3, respectively 1/3 (d) Let...
Use the matrix of transition probabilities P and initial state matrix X_0 to find the state matrices X_1, X_2, and X_3. P = [0.6 0.2 0.1 0.3 0.7 0.1 0.1 0.1 0.8], X_0 = [0.1 0.2 0.7] X_1 = [] X_2 = [] X_1 = []
Use the matrix of transition probabilities P and initial state matrix Xo to find the state matrices X1, X2, and X3. 0.6 0.1 0.1 0.1 Р- Хо 0.3 0.7 0.1 0.2 = 0.1 0.2 0.8 0.7 X1 я X2 Хз
0 -2 - The matrix A -11 2 2 -1 has eigenvalues 5 X = 3, A2 = 2, 13 = 1 Find a basis B = {V1, V2, v3} for R3 consisting of eigenvectors of A. Give the corresponding eigenvalue for each eigenvector vi.
4. (15 pts Consider the following direction fields IV VI (5 pts)Which of the direction fields corresponds to the system x -Ax, where A is a 2x2 matrix with eigenvalues λ,--1 and λ2-2 and corresponding eigenvectors vand v- 1? a. is a 2x2 matrix with repeated eigenvalue λ = 0 with defect 1 (has only one linearly independent eigenvector, not two.) and corresponding eigenvector vi- 13 (5 pts) Which of the direction fields corresponds to the system x -Cx, where...
Find the next TWO state matrices, X1 and X2, from the given initial-state and transition matrix. X = 0.1 0.6 0.3 T = 0.2 0 0.8 0.3 0.4 0.3 0.1 0.7 0.2
Let Xn be a Markov chain with state space {0, 1, 2}, and transition probability matrix and initial distribution π = (0.2, 0.5, 0.3). Calculate P(X1 = 2) and P(X3 = 2|X0 = 0) 0.3 0.1 0.6 p0.4 0.4 0.2 0.1 0.7 0.2
Problem 4. (Discrete time dynamical system ). Consider the following discrete time dynamical system: Assume xo is given and 0.5 0.5 0.2 0.8 (a) Find eigenvalues of matrix A (b) For each eigenvalue find one eigenvector. (c) Let P be the matrix that has the eigenvectors as its columns. Find P-1 (d) Find P- AP (e) Use the answer from part (d) to find A" and xn-A"xo. (Your answers wl be in terms of n (f) Find xn and limn→ooXn...
Consider a 2x2 transition matrix P consisting of column vectors [a c] and [b d]. The matrix P has two eigenvalues: 1 and k. Find the value of k in terms of the elements of the matrix P and place constraints of the values of k. Calculate eigenvectors for each eigenvalue and hence write down the matrix S whose columns are the eigenvalues of P.
Consider the following Transition Matrix, T: From A B C A B C 0.2 0.5 0.3 0.3 0.3 0.4 0.5 0.1 0.4 Find the following probabilities: a.) moving from state A to state C b.) moving from state B to state A c.) remaining in state C