Q22E For the matrices A in Exercises ... [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: Q22E (page 355)

For the matrices A in Exercises 20 through 24 find $\lim_{t 鈫� 鈭�} A^{t}$ . Feel free to use Theorem 7.4.1
$A = [\begin{matrix} 0.8 & 0.6 \\ 0.2 & 0.4 \end{matrix}]$

Short Answer

Expert verified

The required solution is,

$\lim_{t 鈫� 鈭�} A^{t} = [\begin{matrix} \frac{3}{4} & \frac{1}{4} \\ \frac{3}{4} & \frac{3}{4} \end{matrix}]$

Step by step solution

definition of matrices

A function is defined as a relationship between a set of inputs that each have one output.

$A = [\begin{matrix} 0.8 & 0.6 \\ 0.2 & 0, 4 \end{matrix}]$

To find the equilibrium distribution $x_{e q u} o f A$

$A x = x [\begin{matrix} 0.8 & 0.6 \\ 0.2 & 0.4 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \end{matrix}] = [\begin{matrix} x_{1} \\ x_{2} \end{matrix}] 0.8 x_{1} + 0.6 x_{2} = x_{1}, 0.2 x_{1} + 0.4 x_{2} = x_{2}, x_{1} + x_{2} = 1 x_{1} = \frac{3}{4} x_{2} = \frac{1}{4}$

divide the matrices

Then,

$x_{e q u} = [\begin{matrix} \frac{3}{4} \\ \frac{1}{4} \end{matrix}] \lim_{t 鈫� 鈭�} A^{t} = [\begin{matrix} \frac{3}{4} & \frac{1}{4} \\ \frac{3}{4} & \frac{3}{4} \end{matrix}]$

Hence,

$\lim_{t 鈫� 鈭�} A^{t} = [\begin{matrix} \frac{3}{4} & \frac{1}{4} \\ \frac{3}{4} & \frac{3}{4} \end{matrix}]$

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91影视

For the matrices A in Exercises 20 through 24 find $\lim_{t 鈫� 鈭�} A^{t}$ . Feel free to use Theorem 7.4.1
$A = [\begin{matrix} 0.8 & 0.6 \\ 0.2 & 0.4 \end{matrix}]$

Short Answer

Step by step solution

definition of matrices

divide the matrices

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91影视

For the matrices A in Exercises 20 through 24 findlimt鈫�鈭�At. Feel free to use Theorem 7.4.1A=[0.80.60.20.4]

Short Answer

Step by step solution

definition of matrices

divide the matrices

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Statistics

Mechanics Maths

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

For the matrices A in Exercises 20 through 24 find $\lim_{t 鈫� 鈭�} A^{t}$ . Feel free to use Theorem 7.4.1
$A = [\begin{matrix} 0.8 & 0.6 \\ 0.2 & 0.4 \end{matrix}]$