H2. Write the linear system d = 5x + 4y |tx (1): d dy(t) = x+2y as a matrix equation and find the eigenvalues and eigenvectors. Find a change of co-ordinates the system diagonalises in the new coordinates. Finally, solve the corresponding system and sketch the phase portrait in the new coordinates.

H2. Write the linear system d = 5x + 4y |tx (1): d dy(t) = x+2y as a matrix equation and find the eigenvalues and eigenvectors. Find a change of co-ordinates the system diagonalises in the new coordinates. Finally, solve the corresponding system and sketch the phase portrait in the new coordinates.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.7: The Inverse Of A Matrix

Problem 30E

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Question

can you provide explanations

H2. Write the linear system
d
|tx (1):
d
dy(t)
= 5x + 4y
= x + 2y
as a matrix equation and find the eigenvalues and eigenvectors. Find a change
of co-ordinates the system diagonalises in the new coordinates. Finally, solve the
corresponding system and sketch the phase portrait in the new coordinates.

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Step 1: Eigenvalues and eigenvectors of matrix

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