Find the equilibrium vector for the transition matrix. 0.65 0.10 0.25 0.10 0.80 0.10 0.10 0.40 0.50 The equilibrium vector is
Find the equilibrium vector for the transition matrix. 0.65 0.10 0.25 0.10 0.80 0.10 0.10 0.40 0.50 The equilibrium vector is
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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![**Problem: Finding the Equilibrium Vector for a Transition Matrix**
Consider the following transition matrix:
\[
\begin{bmatrix}
0.65 & 0.10 & 0.25 \\
0.10 & 0.80 & 0.10 \\
0.10 & 0.40 & 0.50 \\
\end{bmatrix}
\]
**Objective:**
Determine the equilibrium vector for this matrix by identifying the vector that remains unchanged when the matrix is applied to it.
The equilibrium vector is represented as:
\[
\begin{bmatrix}
\_ \\
\_ \\
\_ \\
\end{bmatrix}
\]
Each element of the vector should be expressed as an integer or a simplified fraction.
*Instructions:*
1. Solve for the equilibrium vector where the matrix times the vector equals the vector itself.
2. Ensure the vector components sum up to 1, reflecting the probabilities across states.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5403849-9f1b-47b1-a027-5bfd8ac96652%2Fa0ac605d-81ed-4935-bcff-6b0ead4a1bd0%2F7lj5y1_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Finding the Equilibrium Vector for a Transition Matrix**
Consider the following transition matrix:
\[
\begin{bmatrix}
0.65 & 0.10 & 0.25 \\
0.10 & 0.80 & 0.10 \\
0.10 & 0.40 & 0.50 \\
\end{bmatrix}
\]
**Objective:**
Determine the equilibrium vector for this matrix by identifying the vector that remains unchanged when the matrix is applied to it.
The equilibrium vector is represented as:
\[
\begin{bmatrix}
\_ \\
\_ \\
\_ \\
\end{bmatrix}
\]
Each element of the vector should be expressed as an integer or a simplified fraction.
*Instructions:*
1. Solve for the equilibrium vector where the matrix times the vector equals the vector itself.
2. Ensure the vector components sum up to 1, reflecting the probabilities across states.
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