**Objective:**Find the steady-state vector associated with the given transition matrix. (Give exact answers. Do not round.)**Transition Matrix:**\[\begin{bmatrix}0.3 & 0.7 \\0.4 & 0.6\end{bmatrix}\]**Explanation:**The matrix provided is a 2x2 transition matrix, which represents the probabilities of moving from one state to another in a Markov chain. The goal is to find the steady-state vector, which is the vector that remains unchanged when the transition matrix is applied.**Diagram Description:**Below the matrix, there are two empty boxes arranged horizontally, which are meant to hold the steady-state vector's values. Arrows pointing left and down suggest that the values are to be filled in and checked for balance.**Instructions:**1. Set up the system of equations based on the transition matrix.2. Solve for the steady-state vector, ensuring that the sum of the vector's entries is equal to 1.3. Input the exact values into the provided spaces.

The given transition matrix is 0.30.70.40.6. Let the steady state vector associated with the given transition matrix be xy.Then we have, xy0.30.70.40.6=xy0.3x+0.4y0.7x+0.6y=xyThat implies,0.3x+0.4y=x ……(1)0.7x+0.6y=y ……(2) From equation (1), (1)⇒0.3x-x+0.4y=0 ⇒-0.7x+0.4y=0 ……(3) Since xy is a steady state vector, we have x+y=1. Then, x=1-y Substitute x=1-y in -0.7x+0.4y=0 and solve for y as follows. -0.7x+0.4y=0-0.7(1-y)+0.4y=0-0.7+0.7y+0.4y=0-0.7+1.1yy=0.71.1 =711Now find x as shown below. x=1-y=1-711=411 Therefore, the steady state vector associated with the transition matrix 0.30.70.40.6 is 411711.

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Math

Advanced Math

Find the steady-state vector associated with the given transition matrix. (Give exact answers. Do not round.) ´ 0.3 0.7 0.4 0.6

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**Objective:**

Find the steady-state vector associated with the given transition matrix. (Give exact answers. Do not round.)

**Transition Matrix:**

\[
\begin{bmatrix}
0.3 & 0.7 \\
0.4 & 0.6
\end{bmatrix}
\]

**Explanation:**

The matrix provided is a 2x2 transition matrix, which represents the probabilities of moving from one state to another in a Markov chain. The goal is to find the steady-state vector, which is the vector that remains unchanged when the transition matrix is applied.

**Diagram Description:**

Below the matrix, there are two empty boxes arranged horizontally, which are meant to hold the steady-state vector's values. Arrows pointing left and down suggest that the values are to be filled in and checked for balance.

**Instructions:**

1. Set up the system of equations based on the transition matrix.
2. Solve for the steady-state vector, ensuring that the sum of the vector's entries is equal to 1.
3. Input the exact values into the provided spaces.

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