Explanation Given: The given system is, d y d t = 3 x − y d y d t = 9 x − 3 y Calculation: For the given system, the coefficient matrix is A = ( 3 − 1 9 − 3 ) . The characteristic equation is | ( A − λ I ) | = 0 where, I is the identity matrix. Substitute the values of matrix A and I in above equation. | 3 − λ − 1 9 − 3 − λ | = 0 ( λ 2 − 9 ) + 9 = 0 λ 2 = 0 Therefore, the eigenvalues of the above system is λ = 0 with multiplicity 2 . Obtain the eigenvector K 1 corresponding to the eigenvalue λ = 0 by solving the equation ( A − λ I ) K 1 = 0 where K 1 is given by ( x 1 y 1 ) . Substitute the values of A , λ and K 1 in the equation ( A − λ I ) K 1 = 0 , [ ( 3 − 1 9 − 3 ) − ( 0 0 0 0 ) ] ⋅ ( x 1 y 1 ) = ( 0 0 ) ( 3 − 1 9 − 3 ) ⋅ ( x 1 y 1 ) = ( 0 0 ) ( 3 x 1 − y 1 9 x 1 − 3 y 1 ) = ( 0 0 ) Solve above system of equations and obtain y 1 = 3 x 1 . Assume that x 1 = p 1 for some scalar p 1 which implies y 1 = 3 p 1 . Thus, the value of ( x 1 y 1 ) is, ( x 1 y 1 ) = ( p 1 3 p 1 ) = p 1 ( 1 3 ) Therefore, the eigenvector K 1 corresponding to λ = 0 is ( 1 3 ) . Obtain the second eigenvector K 2 by solving the equation ( A − λ I ) K 2 = K 1 where, K 2 is given by ( x 2 y 2 )

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

See similar textbooks

Videos

Question

Chapter 10.2, Problem 21E

To determine

To find: The general solution of the given system.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.2, Problem 20E

Chapter 10.2, Problem 22E

Students have asked these similar questions

1.3.1 Use elementary operations to solve the system of equations 3x + y = 3 x + 2y = 1.

1. Y = 5x + 2 2. 5y = 25x + 10 %3D 3. 5y = 10x + 10 4. 2y = 10x – 4 Which pair of equations forms a system that has infinitely many solutions? 2 and 4 2 and 3 O 1 and 2 O 1 and 4

_7. What term is eliminated the when the equations in the following system are subtracted? x² + y? = 36 x2 – y = 36 [A] x [B] x² [C] ¥ [D]y?

Chapter 10 Solutions

Advanced Engineering Mathematics

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.2 - Prob. 1E Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - Prob. 21E Ch. 10.2 - Prob. 22E Ch. 10.2 - Prob. 23E Ch. 10.2 - Prob. 24E Ch. 10.2 - Prob. 25E Ch. 10.2 - Prob. 26E Ch. 10.2 - Prob. 27E Ch. 10.2 - Prob. 28E Ch. 10.2 - Prob. 29E Ch. 10.2 - Prob. 30E Ch. 10.2 - Prob. 31E Ch. 10.2 - Prob. 32E Ch. 10.2 - Prob. 33E Ch. 10.2 - Prob. 34E Ch. 10.2 - Prob. 35E Ch. 10.2 - Prob. 36E Ch. 10.2 - Prob. 37E Ch. 10.2 - Prob. 38E Ch. 10.2 - Prob. 39E Ch. 10.2 - Prob. 40E Ch. 10.2 - Prob. 41E Ch. 10.2 - Prob. 42E Ch. 10.2 - Prob. 43E Ch. 10.2 - Prob. 44E Ch. 10.2 - Prob. 45E Ch. 10.2 - Prob. 46E Ch. 10.2 - Prob. 47E Ch. 10.2 - Prob. 48E Ch. 10.2 - Prob. 49E Ch. 10.2 - Prob. 50E Ch. 10.2 - Prob. 51E Ch. 10.2 - Prob. 52E Ch. 10.2 - Prob. 53E Ch. 10.2 - Prob. 55E Ch. 10.4 - Prob. 1E Ch. 10.4 - Prob. 2E Ch. 10.4 - Prob. 3E Ch. 10.4 - Prob. 4E Ch. 10.4 - Prob. 5E Ch. 10.4 - Prob. 6E Ch. 10.4 - Prob. 7E Ch. 10.4 - Prob. 8E Ch. 10.4 - Prob. 9E Ch. 10.4 - Prob. 10E Ch. 10.4 - Prob. 11E Ch. 10.4 - Prob. 12E Ch. 10.4 - Prob. 13E Ch. 10.4 - Prob. 14E Ch. 10.4 - Prob. 15E Ch. 10.4 - Prob. 16E Ch. 10.4 - Prob. 17E Ch. 10.4 - Prob. 18E Ch. 10.4 - Prob. 19E Ch. 10.4 - Prob. 20E Ch. 10.4 - Prob. 21E Ch. 10.4 - Prob. 22E Ch. 10.4 - Prob. 23E Ch. 10.4 - Prob. 24E Ch. 10.4 - Prob. 25E Ch. 10.4 - Prob. 26E Ch. 10.4 - Prob. 27E Ch. 10.4 - Prob. 28E Ch. 10.4 - Prob. 29E Ch. 10.4 - Prob. 30E Ch. 10.4 - Prob. 31E Ch. 10.4 - Prob. 32E Ch. 10.4 - Prob. 33E Ch. 10.4 - Prob. 34E Ch. 10.4 - Prob. 35E Ch. 10.5 - Prob. 1E Ch. 10.5 - Prob. 2E Ch. 10.5 - Prob. 3E Ch. 10.5 - Prob. 4E Ch. 10.5 - Prob. 5E Ch. 10.5 - Prob. 6E Ch. 10.5 - Prob. 7E Ch. 10.5 - Prob. 8E Ch. 10.5 - Prob. 13E Ch. 10.5 - Prob. 14E Ch. 10.5 - Prob. 15E Ch. 10.5 - Prob. 16E Ch. 10.5 - Prob. 17E Ch. 10.5 - Prob. 18E Ch. 10.5 - Prob. 25E Ch. 10.5 - Prob. 26E Ch. 10 - Prob. 1CR Ch. 10 - Prob. 2CR Ch. 10 - Prob. 3CR Ch. 10 - Prob. 4CR Ch. 10 - Prob. 5CR Ch. 10 - Prob. 6CR Ch. 10 - Prob. 7CR Ch. 10 - Prob. 8CR Ch. 10 - Prob. 9CR Ch. 10 - Prob. 10CR Ch. 10 - Prob. 11CR Ch. 10 - Prob. 12CR Ch. 10 - Prob. 13CR Ch. 10 - Prob. 14CR Ch. 10 - Prob. 15CR Ch. 10 - Prob. 16CR

Knowledge Booster

$Advanced Math$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

The general solution of the given system.

Solution Summary: The author explains how to find the general solution of the given system. The coefficient matrix is A=(cc3& -1 9&

Videos

To find: The general solution of the given system.

Want to see the full answer?

Chapter 10 Solutions