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Linear Algebra and its Applications
Found in: Page 1
Linear Algebra and its Applications

Linear Algebra and its Applications

Book edition 5th
Author(s) David C. Lay, Steven R. Lay and Judi J. McDonald
Pages 483 pages
ISBN 978-03219822384

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Short Answer

Consider a dynamical system x(t+1)=Ax(t) with two components. The accompanying sketch shows the initial state vector x0 and two eigen vectors υ1andυ2 of A (with eigen values λ1 and λ2 respectively). For the given values of λ1 and λ2 , draw a rough trajectory. Consider the future and the past of the system.


So, the required solution is Atx0=αυ1+0.9tβυ2.

See the step by step solution

Step by Step Solution

Step 1: Define the eigenvector

Eigenvector: An eigenvector ofA is a nonzero vector v in Rn such that Av=λv , for some scalar λ.

Step 2: Note the given data

It is given that:


Given graph is:

Step 3: Finding the required solution

We have:


For x0=αυ1+βυ2 ,We have:

role="math" localid="1668079897383" Ax0=A(αυ1+βυ2) =αAυ1+βAυ2 =αυ1+0.9βυ2

Therefore, Atx0=αυ1+0.9tβυ2.

Hence, the solutions is Atx0=αυ1+0.9tβυ2.


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