Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

Answers without the blur.

Just sign up for free and you're in.

Short Answer

TRUE OR FALSE?

For every transition matrix A there exists a nonzero vector $\vec{x}$ such that $A \vec{x} = \vec{x}$ .

The statement is false.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Consider the parameters.

Consider the system.

$A x = x$

Step 2: Consider the condition.

The system is $\begin{array}{l} A x = x \end{array}$ implies,

$\begin{array}{l} A x = x \\ \Rightarrow A x - x = 0 \\ \Rightarrow (A - l) x = 0 \end{array}$

Let any matrix $B = A - l$ then it is written as,

$\Rightarrow B x = 0$

This implies, $B x = 0 \equiv A x = x$ .

Thus, the system will have infinitely many solutions.

Hence, the statement is false.

Find Study Materials for

Create Study Materials

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

TRUE OR FALSE?

For every transition matrix A there exists a nonzero vector $\vec{x}$ such that $A \vec{x} = \vec{x}$ .

Step by Step Solution

Step 1: Consider the parameters.

Step 2: Consider the condition.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

TRUE OR FALSE? For every transition matrix A there exists a nonzero vector x→ such that Ax→=x→.

Step by Step Solution

Step 1: Consider the parameters.

Step 2: Consider the condition.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

TRUE OR FALSE?

For every transition matrix A there exists a nonzero vector $\vec{x}$ such that $A \vec{x} = \vec{x}$ .