-2 Compute the matrix exponential e4 for the matrix A =
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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![### Matrix Exponential Calculation
#### Problem Statement:
Compute the matrix exponential \( e^A \) for the matrix \( A = \begin{bmatrix} -2 & 0 \\ 0 & 1 \end{bmatrix} \).
#### Solution:
The matrix exponential \( e^A \) is given by:
\[
e^A = \begin{bmatrix} -2e^2 & 0 \\ 0 & e^2 \end{bmatrix}
\]
#### Explanation:
- The matrix \( A \) is a 2x2 diagonal matrix with values \(-2\) and \(1\) on the diagonal.
- The matrix exponential of a diagonal matrix is computed by taking the exponential of each of the diagonal elements and forming a new diagonal matrix.
For more information and help with matrices, refer to the [help page on matrices](#).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F411fdfa3-98d6-4c96-a283-c3e756a59776%2F232ada9c-b7b9-4ffb-9fb6-1b6442121b7d%2F01q5gp_processed.png&w=3840&q=75)
Transcribed Image Text:### Matrix Exponential Calculation
#### Problem Statement:
Compute the matrix exponential \( e^A \) for the matrix \( A = \begin{bmatrix} -2 & 0 \\ 0 & 1 \end{bmatrix} \).
#### Solution:
The matrix exponential \( e^A \) is given by:
\[
e^A = \begin{bmatrix} -2e^2 & 0 \\ 0 & e^2 \end{bmatrix}
\]
#### Explanation:
- The matrix \( A \) is a 2x2 diagonal matrix with values \(-2\) and \(1\) on the diagonal.
- The matrix exponential of a diagonal matrix is computed by taking the exponential of each of the diagonal elements and forming a new diagonal matrix.
For more information and help with matrices, refer to the [help page on matrices](#).
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