39E Sketch rough phase portraits for... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 9: 39E (page 427)

Sketch rough phase portraits for the dynamical systems given in Exercise 32 through 39.
$\overset{鈫�}{x} (t + 1) = [\begin{matrix} 0.8 & - 0.4 \\ 0.3 & 1.6 \end{matrix}] \overset{鈫�}{x} (t)$

Short Answer

Expert verified

Thus, the rough sketch of the system in the explanation.

Step by step solution

Given in the question.

The given systems are:

$\overset{鈫�}{x} (t + 1) = [\begin{matrix} 0.8 & - 0.4 \\ 0.3 & 1.6 \end{matrix}] \overset{鈫�}{x} (t)$

Solve the given system.

Solve the given system as follows:

$[\begin{matrix} t_{1} + 1 \\ t_{2} + 1 \end{matrix}] = [\begin{matrix} 0.8 & - 0.4 \\ 0.3 & 1.6 \end{matrix}] [\begin{matrix} t_{1} \\ t_{2} \end{matrix}] [\begin{matrix} t_{1} + 1 \\ t_{2} + 1 \end{matrix}] = [\begin{matrix} 0.8 t_{1} - 0.4 t_{2} \\ 0.3 t_{1} + 1.6 t_{2} \end{matrix}]$

Now, equating both sides gives:

$\{t_{1} + 1 = 0.8 t_{1} - 0.4 t_{2} t_{2} + 1 = 0.3 t_{1} + 1.6 t_{2} \{1 = - 0.2 t_{1} - 0.4 t_{2} 1 = 0.3 t_{1} + 0.6 t_{2}$

Thus the solutions is the span of $[\begin{matrix} 2 \\ - 1 \end{matrix}] [\begin{matrix} 2 \\ - 3 \end{matrix}]$

Determine the graph of the given system.

The graph is plotted below:

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91影视

Sketch rough phase portraits for the dynamical systems given in Exercise 32 through 39.
$\overset{鈫�}{x} (t + 1) = [\begin{matrix} 0.8 & - 0.4 \\ 0.3 & 1.6 \end{matrix}] \overset{鈫�}{x} (t)$

Short Answer

Step by step solution

Given in the question.

Solve the given system.

Determine the graph of the given system.

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91影视

Sketch rough phase portraits for the dynamical systems given in Exercise 32 through 39.x鈫�(t+1)=[0.8-0.40.31.6]x鈫�(t)

Short Answer

Step by step solution

Given in the question.

Solve the given system.

Determine the graph of the given system.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Sketch rough phase portraits for the dynamical systems given in Exercise 32 through 39.
$\overset{鈫�}{x} (t + 1) = [\begin{matrix} 0.8 & - 0.4 \\ 0.3 & 1.6 \end{matrix}] \overset{鈫�}{x} (t)$