Q25E For the matrices A and the vecto... [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: Q25E (page 355)

For the matrices A and the vectors ${\overset{鈫�}{x}}_{0}$ in Exercises 25 through 29, find $\lim_{t 鈫� 鈭�} (A^{t} {\overset{鈫�}{x}}_{0})$ . Feel free to use Theorem 7.4.1.
role="math" localid="1659603230321" $A = [\begin{matrix} 0.3 & 1 \\ 0.7 & 0 \end{matrix}], \overset{鈫�}{x_{0}} = [\begin{matrix} 0.64 \\ 0.36 \end{matrix}]$

Short Answer

Expert verified

The value of $\lim_{t 鈫� 鈭�} A^{t} \overset{鈫�}{x_{0}} = [\begin{matrix} \frac{10}{17} \\ \frac{7}{17} \end{matrix}]$

Step by step solution

Substituting the given matrix in Ax = x

$A x = x [\begin{matrix} 0.3 & 1 \\ 0.7 & 0 \end{matrix}] [\begin{matrix} x_{1} \\ x_{2} \end{matrix}] = [\begin{matrix} x_{1} \\ x_{2} \end{matrix}] 0.3 x_{1} + x_{2} = x_{1}, 0.7 x_{1} = x_{2,} x_{1} + x_{2} = 1$

Finding the equilibrium distribution xequ of A

$x_{1} = \frac{10}{17} x_{2} = \frac{7}{17} x_{e q u} = [\begin{matrix} \frac{10}{17} & \frac{7}{17} \end{matrix}] \lim_{t 鈫� 鈭�} A^{t} [\begin{matrix} 0.64 \\ 0.36 \end{matrix}] = [\begin{matrix} \frac{10}{17} \\ \frac{7}{17} \end{matrix}]$

Therefore, the value of $\lim_{t 鈫� 鈭�} A^{t} \overset{鈫�}{x_{0}} = [\begin{matrix} \frac{10}{17} \\ \frac{7}{17} \end{matrix}]$ $\lim_{t 鈫� 鈭�} A^{t} \overset{鈫�}{x_{0}} = [\begin{matrix} \frac{10}{17} \\ \frac{7}{17} \end{matrix}]$

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91影视

Short Answer

Step by step solution

Substituting the given matrix in Ax = x

Finding the equilibrium distribution xequ of A

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91影视

For the matrices A and the vectors x鈫�0in Exercises 25 through 29, find limt鈫�鈭�(Atx鈫�0). Feel free to use Theorem 7.4.1.role="math" localid="1659603230321" A=[0.310.70],x0鈫�=[0.640.36]

Short Answer

Step by step solution

Substituting the given matrix in Ax = x

Finding the equilibrium distribution xequ of A

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Calculus

Probability and Statistics

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.