Jacobi method

Question 3 1 pts Suppose we have the following setup using the Jacobi method What is the spectral radius of 12 0 2 Remember, the spectral radius of a matrix is the largest eigenvalue of the matrix in absolute value/magnitude. Question 4 1 pts Suppose we have the following setup using the Gauss-Seidel method and]= [8 2] [am]+ [3]. What is the spectral radius of 6 2 ? Remember, the spectral radius of a matrix is the largest eigenvalue of the matrix in absolute value/magnitude.Random events SS 2019./2020. 1st set of home exercises 1. Consider the Markov chain with three states S=(1,2,3), that has the following transition probability matrix: WINPIE P = N/H O O Draw the state transition diagram for this chain. Write the transition probability matrix for three steps. 2. Write Markov transition matrix for following state transition diagram: 4 Classify of states of the Markov chain. 3. Find eigenvalues and eigenvectors of the transition probability matrix for following system: 0.4 0.6 0.8 rain no rain 0.21. Consider a birth and death process with 4 attainable states: (0, 1, 2, 3). The steady state probabilities of these states are PO, PI, P2, and P3. The birth and death rates are summarized in the below table: State Birth Rate Death Rate 0 NNN 0 a) Construct the rate diagram for this birth and death process. b) Develop the balance equations c) Solve these equations to find PO, PI, P2, P3 (steady state probabilities). d) Calculate L.Consider the process of birth and death with three possible states (0, 1, and 2), whose respective probabilities steady state are P 0, P 1 and P 2. The birth and death rates are summarized in the following table: State birth rate death rate 0 4 0 1 2 4 2 0 6 a) Build the rate diagram of this birth and death process b) Develop the balance equations. c) Solve the equations to find P 0, P 1 and P 2 d) Use the general formulas of the birth and death process to calculate P 0, P 1 and P 2. Also calculate L and W.Problem 4. Consider a combined birth and death process with initial population size no = 10, birth rate A = 0.5, and death rate # = 0.25. Determine the probability of extinction at time t