00 Find the transition matrix from B to B'. B = {(4, 2), (3, -1)}, B' = {(1, 0), (0, 1)} %3D %3D STEP 1: Begin by forming the following matrix. [B':B] = STEP 2: Determine the transition matrix. P-1 %3D
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![Find the transition matrix from B to B'.
B = {(4, 2), (3, -1)}, B' = {(1, 0), (0, 1)}
STEP 1: Begin by forming the following matrix.
88
[B':B] =
%3D
1 1
STEP 2: Determine the transition matrix.
P-1 =
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a70e2d2-d641-435a-b212-d4266cff05fc%2Fd5bfb6de-1792-4e3b-a5f3-5486a4b7b16f%2Fedz4cjl_processed.jpeg&w=3840&q=75)
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- Find transition matrix from B to B’ B={(1,1,-1),(1,1,0),(1,-1,0)} B’={(1,-1,2),(2,2,-1),(2,2,2)(a) Find the transition matrix from B, to B2 (b) Find the transition matrix from B, to B.Find the transition matrix from B to B′ for the bases for R3 below.B = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} and B′ = {(1, 0, 1), (0, −1, 2), (2, 3, −5)}
- Approximate the stationary matrix S for the transition matrix P by computing powers of the transition matrix P.For the transition matrix P, solve the equation SP = S to find the stationary matrix S and the limiting matrix P.In at tropical forest, the populations of falcons and mice are related toeach other. The mice eat everything they can while the falcons eat the mice. The population sizes of falcons and mice evolve according to the rule. * At the beginning of 2023, there were 10 falcons and 40 mice. a) Approximately how many falcons and mice will there be at the beginning of 2068? b) c) Find a diagonalization, A = BDB-1, of the transition matrix A from part (b), where D is a 2x2 diagonal matrix, and B is an invertible2x2 matrix. d) Use your answer to (c) to estimate the (approximate) numbersof falcons and mice there will be at the beginning of 2058. e)
- In at tropical forest, the populations of falcons and mice are related toeach other. The mice eat everything they can while the falcons eat the mice. The population sizes of falcons and mice evolve according to the rule. * At the beginning of 2023, there were 10 falcons and 40 mice. a) Approximately how many falcons and mice will there be at the beginning of 2068? b) c) Find a diagonalization, A = BDB-1, of the transition matrix A from part (b), where D is a 2x2 diagonal matrix, and B is an invertible2x2 matrix. d) Use your answer to (c) to estimate the (approximate) numbersof falcons and mice there will be at the beginning of 2058. e) what restrictions on the initial population sizes ensures the long time survival of both species in the forestAt any given time, a subatomic particle can be in one of two states, and it moves randomly from one state to another when it is excited. If it is in state 1 on one observation, then it is 3 times as likely to be in state 1 as state 2 on the next observation. Likewise, if it is in the state 2 on one observation, then it is 3 times as likely to be in state 2 as state 1 on the next observation. 1. Find the transition matrix for this Markov chain. 2. Researchers estimate that the particle is currently 4 times as like to be in state 1 as state 2. Find the probability vector representing this estimation. 3. Based on the estimation, what is the probability that the particle will be in state 2 two weeks from now? 4. What is the probability that the particle will be in state 1 three weeks from now?
