### Matching a Linear SystemTo match the linear system with one of the phase plane direction fields below, consider the following system:\[ \mathbf{x'} = \begin{bmatrix} -2 & -1 \\ 5 & 0 \end{bmatrix} \mathbf{x} \]#### Phase Plane Direction FieldsBelow are four phase plane direction fields labeled A, B, C, and D, each representing different behaviors of the system. The axes are labeled as $ x_1 $ and $ x_2 $.**Field A:** - Arrows suggest motion along a particular trajectory.- Possible focus/spiral pattern.**Field B:** - Arrows indicate radial patterns.- May suggest node or saddle behavior.**Field C:** - Arrows show movement smoothly converging or diverging.- Possible stable or unstable node.**Field D:** - Circular or spiral patterns, suggesting a focus.#### Explanation of the Graphs- The plots use blue lines to represent arrow shafts, indicating direction of movement, while black dots highlight arrow tips.#### NoteTo solve the problem of matching the system to a field, it is crucial to compute eigenvalues. Knowing whether these eigenvalues are real or complex, and positive or negative, can guide the matching. Utilizing the Trace-Determinant plane can provide further insight. When doing so, a brief explanation about eigenvalues would be beneficial. Eigenvalues help determine the stability and type of fixed points in the system, which is pivotal in matching the system to the correct phase plane direction field.

Answered: Image /qna-images/answer/8ed59f26-df5f-4ca3-9be6-d000c34bcb44.jpg

Match a linear system -2 with one of the phase plane direction fields below: A B C D (The blue lines are the arrow shafts, and the black dots are the arrow tips.) Note: To solve this problem, you only need to compute eigenvalues. In fact, it is enough to just compute whether the eigenvalues are real or complex and positive or negative. If you se Trace-Determinant plane, give a brief explanation about eigenvalues. CS Scanned with CamScanner

Match a linear system -2 with one of the phase plane direction fields below: A B C D (The blue lines are the arrow shafts, and the black dots are the arrow tips.) Note: To solve this problem, you only need to compute eigenvalues. In fact, it is enough to just compute whether the eigenvalues are real or complex and positive or negative. If you se Trace-Determinant plane, give a brief explanation about eigenvalues. CS Scanned with CamScanner

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Find eigenvalue, and eizenvectors of the matrix - 14 12 1 - 20 17

A: The given matrix is -1412-2017 We have to find the eigenvalues and corresponding eigenvectors of…

Q: Consider the linear system 2 A₁ = Find the eigenvalues and eigenvectors for the coefficient matrix.…

Q: refer to image below.

Q: For the matrix B = find each eigenvalue, and a basis for each corresponding eigenspace. For this…

A: Given matrix is B=32−4−1. We have to find the eigenvalues of B and a basis for each corresponding…

Q: Match each linear system with one of the phase plane direction fields. (The blue lines are the arrow…

A: The phase plane is the graphical representation of all the solution curves of a system of…

Q: The trace (sum of entries on the main diagonal) of a matrix is equal to the sum of the eigenvalues…

A: Given: Trace of 2×2 matrix (trA)=14 determinant of 2×2 detA=45 Now, Let λ1 and λ2 be eigen values of…

Q: Part 1: For the given matrix and eigenvalue, find an eigenvector corresponding to the eigenvalue.…

Q: 36. Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has…

A: To find the condition on a, b, c, d .

Q: 4 V2 A =|1 4 B = 1 where each x represents an unknown number. Find the Givens rotation matrix G that…

A: Given that, The rotation matrix G is We have to find rotation matrix G which transforms A to B.…

Q: Show that the matrix is not diagonalizable. 2 −4 2 0 2 3 0 0 3 STEP 1: Use the fact that the…

Q: A 2x2 matrix is known to have the eigenvalues -3 and 4. What are the eigenvalues of the following…

A: We will find out the required value.

Q: x2 = x₁-2x₂ solution in matrix form?

Q: A linear system x = Ax with state variables x₁(t) and a₂(t) is defined by the equations: *1 = 3x1…

Q: Show that the matrix is not diagonalizable. 3-4 1 3 1 04 0 0 STEP 1: Use the fact that the matrix is…

Q: Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. 14 1 4…

Q: (1 point) Consider the linear system -3 -2 y. 3 a. Find the eigenvalues and eigenvectors for the…

Q: Apply the eigenvalue method to find a general solution of the given system. Use a computer system or…

Question

### Matching a Linear System

To match the linear system with one of the phase plane direction fields below, consider the following system:

\[
\mathbf{x'} = \begin{bmatrix} -2 & -1 \\ 5 & 0 \end{bmatrix} \mathbf{x}
\]

#### Phase Plane Direction Fields

Below are four phase plane direction fields labeled A, B, C, and D, each representing different behaviors of the system. The axes are labeled as $ x_1 $ and $ x_2 $.

**Field A:**
- Arrows suggest motion along a particular trajectory.
- Possible focus/spiral pattern.

**Field B:**
- Arrows indicate radial patterns.
- May suggest node or saddle behavior.

**Field C:**
- Arrows show movement smoothly converging or diverging.
- Possible stable or unstable node.

**Field D:**
- Circular or spiral patterns, suggesting a focus.

#### Explanation of the Graphs

- The plots use blue lines to represent arrow shafts, indicating direction of movement, while black dots highlight arrow tips.

#### Note

To solve the problem of matching the system to a field, it is crucial to compute eigenvalues. Knowing whether these eigenvalues are real or complex, and positive or negative, can guide the matching. Utilizing the Trace-Determinant plane can provide further insight. When doing so, a brief explanation about eigenvalues would be beneficial. Eigenvalues help determine the stability and type of fixed points in the system, which is pivotal in matching the system to the correct phase plane direction field.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Matrix Eigenvalues and Eigenvectors$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

If matrix A is square of size n x n with a rank equal to 2 and n > 2. The rank of a matrix is equal to the number of non-zero eigenvalues. Can you write A as the product of two matrices B E Rnxq and C E RPX" where we require that p < n and q < n? You may assume that A is diagonalizable. Show how to construct a matrix B and C such that A = BC.
For an electrical circuit containing an inductor, a resistor, and a capacitor, the charge Q(t) on the capacitor satisfies the ODE 8²³Q +2 dt² dQ dt +2 +2Q=0, (in suitably scaled variables). Write the equation as a system of first-order ODEs and find the general solution using the eigenvector method.
Kindly solve this question on matrix, refer to the screenshot;
solve B please
Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. -2 9 -5 -6 11 -3 λ = 2,4,5 -6 6 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 200 For P=D=0 40 005 (Simplify your answer.) OB. The matrix cannot be diagonalized.
Please help with questions 2 and 3.