Q26E 26: Based on your answers in Exe... [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 7: Q26E (page 336)

26: Based on your answers in Exercises 24 and 25, sketch a phase portrait of the dynamical system
_{$\overset{炉}{x} (t + 1) = [\begin{matrix} 0.5 & 0.25 \\ 0.5 & 0.75 \end{matrix}] \overset{炉}{x} (t)$}

Short Answer

Expert verified

Phase portrait of a dynamical system is: $A^{t} x_{0} = [\begin{matrix} 0 . 25^{t} 伪 + 0.25 尾 \\ - 0 . 25^{t} 伪 + 0.5 尾 \end{matrix}]$

Step by step solution

Transition Matrix

Transition matrix may refer to: The matrix associated with a change of basis for a vector space. Stochastic matrix, a square matrix used to describe the transitions of a Markov chain. State-transition matrix, a matrix whose product with the state vector at an initial time gives state vector at that time.

Sketching a phase portrait of the dynamical system:

As we clearly now that,

$v_{1} = [\begin{matrix} 1 \\ - 1 \end{matrix}] v_{2} = [\begin{matrix} 0.25 \\ 0.5 \end{matrix}]$

role="math" localid="1659584611493" $x_{0} = 伪 [\begin{matrix} 1 \\ - 1 \end{matrix}] + 尾 [\begin{matrix} 0.25 \\ 0.5 \end{matrix}] A^{t} x_{0} = 0 . 25^{t} 伪 [\begin{matrix} 1 \\ - 1 \end{matrix}] + 尾 [\begin{matrix} 0.25 \\ 0.5 \end{matrix}] = [\begin{matrix} 0 . 25^{t} 伪 + 0.25 尾 \\ - 0 . 25^{t} 伪 + 0.5 尾 \end{matrix}]$

Hence, the final answer is: $A^{t} x_{0} = [\begin{matrix} 0 . 25^{t} 伪 + 0.25 尾 \\ - 0 . 25^{t} 伪 + 0.5 尾 \end{matrix}]$

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91影视

26: Based on your answers in Exercises 24 and 25, sketch a phase portrait of the dynamical system
_{$\overset{炉}{x} (t + 1) = [\begin{matrix} 0.5 & 0.25 \\ 0.5 & 0.75 \end{matrix}] \overset{炉}{x} (t)$}

Short Answer

Step by step solution

Transition Matrix

Sketching a phase portrait of the dynamical system:

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91影视

26: Based on your answers in Exercises 24 and 25, sketch a phase portrait of the dynamical systemx炉(t+1)=[0.50.250.50.75]x炉(t)

Short Answer

Step by step solution

Transition Matrix

Sketching a phase portrait of the dynamical system:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Logic and Functions

Statistics

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

26: Based on your answers in Exercises 24 and 25, sketch a phase portrait of the dynamical system
_{$\overset{炉}{x} (t + 1) = [\begin{matrix} 0.5 & 0.25 \\ 0.5 & 0.75 \end{matrix}] \overset{炉}{x} (t)$}