[0.4 0.2 0.5 ] -5 Consider the matrix A = 0.2 0.4 0.25 and the vector v2 = 5 Compute Av2 and 0.4 0.4 0.25 compare it to V2. This demonstrates that is an eigenvalue of A. (Answer with a decimal representation, not a fraction.)
[0.4 0.2 0.5 ] -5 Consider the matrix A = 0.2 0.4 0.25 and the vector v2 = 5 Compute Av2 and 0.4 0.4 0.25 compare it to V2. This demonstrates that is an eigenvalue of A. (Answer with a decimal representation, not a fraction.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![### Analyzing Eigenvalues in Matrices
Consider the matrix **A**:
\[
\begin{bmatrix}
0.4 & 0.2 & 0.5 \\
0.2 & 0.4 & 0.25 \\
0.4 & 0.4 & 0.25
\end{bmatrix}
\]
and the vector **v₂**:
\[
\begin{bmatrix}
-5 \\
5 \\
0
\end{bmatrix}
\]
#### Instructions:
1. **Compute A**v₂:**
- Multiply the matrix **A** by the vector **v₂**.
2. **Compare the result to v₂.**
- Determine if the resulting vector is a scalar multiple of **v₂**.
3. **Eigenvalue Determination:**
- If **A**v₂ is a scalar multiple of **v₂**, this scalar is an eigenvalue of **A**.
- Note the scalar in decimal form (not a fraction).
#### Task:
Record the eigenvalue on a sheet of paper for your reference. This exercise demonstrates the concept of eigenvalues and how they relate to transformations represented by matrices.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4aa50f7-4a9b-4570-bf30-bca8a26e60c3%2F1122aa65-1549-4c29-b906-16852878c98c%2Frscej3d_processed.png&w=3840&q=75)
Transcribed Image Text:### Analyzing Eigenvalues in Matrices
Consider the matrix **A**:
\[
\begin{bmatrix}
0.4 & 0.2 & 0.5 \\
0.2 & 0.4 & 0.25 \\
0.4 & 0.4 & 0.25
\end{bmatrix}
\]
and the vector **v₂**:
\[
\begin{bmatrix}
-5 \\
5 \\
0
\end{bmatrix}
\]
#### Instructions:
1. **Compute A**v₂:**
- Multiply the matrix **A** by the vector **v₂**.
2. **Compare the result to v₂.**
- Determine if the resulting vector is a scalar multiple of **v₂**.
3. **Eigenvalue Determination:**
- If **A**v₂ is a scalar multiple of **v₂**, this scalar is an eigenvalue of **A**.
- Note the scalar in decimal form (not a fraction).
#### Task:
Record the eigenvalue on a sheet of paper for your reference. This exercise demonstrates the concept of eigenvalues and how they relate to transformations represented by matrices.
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