Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 7: Q30E (page 324)

consider the dynamical system
$\overset{鈫�}{x} (t + 1) = [\begin{matrix} 1.1 & 0 \\ 0 & 位 \end{matrix}] \overset{鈫�}{x} (t)$ .
Sketch a phase portrait of this system for the given values of $位$ :
$位 = 1.2$

Short Answer

Expert verified

The sketch a phase portrait of this system for the given values of $位$ is shown as below:

localid="1659583100415" $A^{t} x_{0} = [\begin{matrix} 1 . 1^{t} & x_{1} \\ 1 . 2^{t} & x_{2} \end{matrix}]$

Step by step solution

Definition of matrix

A diagonal matrix is a matrix in which the entries outside the main diagonal are all zero.

Sketch the phase portrait

Consider the given matrix

$A = [\begin{matrix} 1.1 & 0 \\ 0 & 1.2 \end{matrix}]$

Clearly, Ais diagonal, so for any

localid="1659583058249" $x_{0} = [\begin{matrix} x_{1} \\ x_{2} \end{matrix}]$

, we have

localid="1659583050285" $A^{t} x_{0} = [\begin{matrix} 1.1 & 0 \\ 1.2 & 1.2 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \end{matrix}] = [\begin{matrix} 1 . 1^{t} x_{1} \\ 1 . 2^{t} x_{2} \end{matrix}]$

So, the required sketch is shown as below using the technology.

$[\begin{matrix} 1 . 1^{t} x_{1} \\ 1 . 2^{t} x_{2} \end{matrix}]$

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91影视

consider the dynamical system
$\overset{鈫�}{x} (t + 1) = [\begin{matrix} 1.1 & 0 \\ 0 & 位 \end{matrix}] \overset{鈫�}{x} (t)$ .
Sketch a phase portrait of this system for the given values of $位$ :
$位 = 1.2$

Short Answer

Step by step solution

Definition of matrix

Sketch the phase portrait

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91影视

consider the dynamical systemx鈫�(t+1)=[1.100位]x鈫�(t).Sketch a phase portrait of this system for the given values of位:位=1.2

Short Answer

Step by step solution

Definition of matrix

Sketch the phase portrait

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

consider the dynamical system
$\overset{鈫�}{x} (t + 1) = [\begin{matrix} 1.1 & 0 \\ 0 & 位 \end{matrix}] \overset{鈫�}{x} (t)$ .
Sketch a phase portrait of this system for the given values of $位$ :
$位 = 1.2$