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Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 2: Q61E (page 109)

TRUE OR FALSE?
There is a transition matrix A such that $\underset{m 鈫� 鈭�}{l i m} A^{m}$ fails to exist.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Consider the parameters

Consider the matrix.

$A = (\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix})$

02

Compute the matrices

The matrices are,

$A^{2} = (\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}) A^{3} = (\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}) A^{4} = (\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix})$

The series keeps on going.

But, $A^{m - 鈭�}$ does not exist.

Hence, the statement is true.

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Most popular questions from this chapter

Which of the functions f from R toR in Exercises 21 through 24 are invertible?22 $f (x) = 2^{x}$ .

TRUE OR FALSE?

If the linear system $A^{2} \overset{鈫�}{x} = \overset{鈫�}{b}$ is consistent, then the systemrole="math" localid="1659352762883" $A \overset{鈫�}{x} = \overset{鈫�}{b}$ must be consistent as well.

Question 8: Find the inverse of linear transformation

$y_{1} = x_{1} + 7 x_{2} y_{2} = 3 x_{1} + 20 x_{2}$

Is the product of two lower triangular matrices a lower triangular matrix as well? Explain your answer.

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