ODE question Putzer algorithm or any method, Thanks 23) Let A =Calculate etA. Can use Putzer algorithm or any other method

Given: A=21-14 Eigenvalues of A: Let λ be eigen value of A, therefore…

Answered: 3) Let A 1. Calculate et4. Can use…

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3) Let A 1. Calculate et4. Can use Putzer algorithm or any other method

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter87: An Introduction To G- And M-codes For Cnc Programming

Section: Chapter Questions

Problem 14A

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Question

ODE question Putzer algorithm or any method, Thanks

2
3) Let A =
Calculate etA. Can use Putzer algorithm or any other method

Expert Solution

Eigenvalues

Given:

$A = [\begin{matrix} 2 & 1 \\ - 1 & 4 \end{matrix}]$

Eigenvalues of $A$ :

Let $λ$ be eigen value of $A$ , therefore

$\begin{array}{rcl} |A - λ I| & = & 0 \\ |\begin{matrix} 2 - λ & 1 \\ - 1 & 4 - λ \end{matrix}| & = & 0 \\ λ^{2} - 6 λ + 9 & = & 0 \\ {(λ - 3)}^{2} & = & 0 \end{array}$

Therefore two eigenvalues are repeated and they are $λ_{1} = 3, λ_{2} = 3$ .

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