Q31E There exists a regular transitio... [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 2: Q31E (page 108)

There exists a regular transition matrix A of size 3 脳 3 such that $A^{2} = A$ .

Short Answer

Expert verified

The answer is true.

Step by step solution

Explaining

Let A be:

$A = [\begin{matrix} \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \end{matrix}]$

Then A is a regular transition matrix since all entries are positive and each column sums to 1.

Result

Now,

$A^{2} = [\begin{matrix} \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \end{matrix}] x [\begin{matrix} \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \end{matrix}] = [\begin{matrix} \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \end{matrix}] = A$

Thus, the answer is true.

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91影视

There exists a regular transition matrix A of size 3 脳 3 such that $A^{2} = A$ .

Short Answer

Step by step solution

Explaining

Result

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91影视

There exists a regular transition matrix A of size 3 脳 3 such that A2=A.

Short Answer

Step by step solution

Explaining

Result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Pure Maths

Calculus

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

There exists a regular transition matrix A of size 3 脳 3 such that $A^{2} = A$ .