-1 1 13. x' = 1 -4 1 -3
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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I need help please with 13 and 16
![### 5.5 Problems
**Instructions:**
Find general solutions of the systems in Problems 1 through 22. In Problems 1 through 6, use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system.
**Explanation:**
This section involves solving differential systems. For Problems 1 to 6, you will use computational tools to visualize the direction field and analyze typical solution curves. These visual aids help in understanding the behavior of differential equations within the given systems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03106fa3-330c-422f-ad56-a6718a5c3a13%2F085ac93b-78bb-4d41-83d5-e766d45daedc%2Flwfj999_processed.png&w=3840&q=75)
Transcribed Image Text:### 5.5 Problems
**Instructions:**
Find general solutions of the systems in Problems 1 through 22. In Problems 1 through 6, use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system.
**Explanation:**
This section involves solving differential systems. For Problems 1 to 6, you will use computational tools to visualize the direction field and analyze typical solution curves. These visual aids help in understanding the behavior of differential equations within the given systems.
![The text appears to be a series of matrix equations representing linear transformations. Each equation consists of a matrix multiplying a vector \( x \).
13. \( \mathbf{x'} =
\begin{bmatrix}
-1 & 0 & 1 \\
0 & 1 & -4 \\
0 & 1 & -3 \\
\end{bmatrix} \mathbf{x} \)
14. \( \mathbf{x'} =
\begin{bmatrix}
0 & 0 & 1 \\
-5 & -1 & -5 \\
4 & 1 & -2 \\
\end{bmatrix} \mathbf{x} \)
15. \( \mathbf{x'} =
\begin{bmatrix}
-2 & -9 & 0 \\
1 & 4 & 0 \\
1 & 3 & 1 \\
\end{bmatrix} \mathbf{x} \)
16. \( \mathbf{x'} =
\begin{bmatrix}
1 & 0 & 0 \\
-2 & -2 & -3 \\
2 & 3 & 4 \\
\end{bmatrix} \mathbf{x} \)
17. \( \mathbf{x'} =
\begin{bmatrix}
1 & 0 & 0 \\
18 & 7 & 4 \\
-27 & -9 & -5 \\
\end{bmatrix} \mathbf{x} \)
18. \( \mathbf{x'} =
\begin{bmatrix}
1 & 0 & 0 \\
1 & 3 & 1 \\
-2 & -4 & -1 \\
\end{bmatrix} \mathbf{x} \)
19. \( \mathbf{x'} =
\begin{bmatrix}
1 & -4 & 0 & -2 \\
0 & 1 & 0 & 0 \\
6 & -12 & -1 & -6 \\
0 & -4 & 0 & -1 \\
\end{bmatrix} \mathbf{x} \)
20. \( \mathbf{x'} =
\begin{bmatrix}
2 & 1 & 0 & 1 \\
0 & 2 & 1 & 0 \\
0 & 0 & 2 & 1 \\
0 & 0 & 0 & 2 \\
\end{bmatrix](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03106fa3-330c-422f-ad56-a6718a5c3a13%2F085ac93b-78bb-4d41-83d5-e766d45daedc%2F6fmvr6e_processed.png&w=3840&q=75)
Transcribed Image Text:The text appears to be a series of matrix equations representing linear transformations. Each equation consists of a matrix multiplying a vector \( x \).
13. \( \mathbf{x'} =
\begin{bmatrix}
-1 & 0 & 1 \\
0 & 1 & -4 \\
0 & 1 & -3 \\
\end{bmatrix} \mathbf{x} \)
14. \( \mathbf{x'} =
\begin{bmatrix}
0 & 0 & 1 \\
-5 & -1 & -5 \\
4 & 1 & -2 \\
\end{bmatrix} \mathbf{x} \)
15. \( \mathbf{x'} =
\begin{bmatrix}
-2 & -9 & 0 \\
1 & 4 & 0 \\
1 & 3 & 1 \\
\end{bmatrix} \mathbf{x} \)
16. \( \mathbf{x'} =
\begin{bmatrix}
1 & 0 & 0 \\
-2 & -2 & -3 \\
2 & 3 & 4 \\
\end{bmatrix} \mathbf{x} \)
17. \( \mathbf{x'} =
\begin{bmatrix}
1 & 0 & 0 \\
18 & 7 & 4 \\
-27 & -9 & -5 \\
\end{bmatrix} \mathbf{x} \)
18. \( \mathbf{x'} =
\begin{bmatrix}
1 & 0 & 0 \\
1 & 3 & 1 \\
-2 & -4 & -1 \\
\end{bmatrix} \mathbf{x} \)
19. \( \mathbf{x'} =
\begin{bmatrix}
1 & -4 & 0 & -2 \\
0 & 1 & 0 & 0 \\
6 & -12 & -1 & -6 \\
0 & -4 & 0 & -1 \\
\end{bmatrix} \mathbf{x} \)
20. \( \mathbf{x'} =
\begin{bmatrix}
2 & 1 & 0 & 1 \\
0 & 2 & 1 & 0 \\
0 & 0 & 2 & 1 \\
0 & 0 & 0 & 2 \\
\end{bmatrix
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