Program Explanation Given information: The differential equation shown below: x ′ 1 = 4 x 1 + x 2 + x 3 + 7 x 4 x ′ 2 = x 1 + 4 x 2 + 10 x 3 + x 4 x ′ 3 = x 1 + 10 x 2 + 4 x 3 + x 4 x ′ 4 = 7 x 1 + x 2 + x 3 + 4 x 4 The Eigen values of the coefficient matrix is − 3 , − 6 , − 10 , and 15 . The initial condition is shown below. x 1 ( 0 ) = 3 , x 2 ( 0 ) = x 3 ( 0 ) = 1 and x 4 ( 0 ) = 3 Explanation: Consider matrix form of the system of equation as A. A = [ 4 1 1 7 1 4 10 1 1 10 4 1 7 1 1 4 ] The Eigen vector of the coefficient matrix A is in the form as, [ 4 − λ 1 1 7 1 4 − λ 10 1 1 10 4 − λ 1 7 1 1 4 − λ ] [ a b c d ] = [ 0 0 0 0 ] The associated Eigen vector with the matrix Ais v = [ a b c d ] T . Substitute − 3 for λ in coefficient matrix, [ 4 + 3 1 1 7 1 4 + 3 10 1 1 10 4 + 3 1 7 1 1 4 + 3 ] [ a 1 b 1 c 1 d 1 ] = [ 0 0 0 0 ] [ 7 1 1 7 1 7 10 1 1 10 7 1 7 1 1 7 ] [ a 1 b 1 c 1 d 1 ] = [ 0 0 0 0 ] The scalar equation are shown below, 7 a 1 + b 1 + c 1 + 7 d 1 = 0 a 1 + 7 b 1 + 10 c 1 + d 1 = 0 a 1 + 10 b 1 + 7 c 1 + 7 d 1 = 0 7 a 1 + b 1 + c 1 + 7 d 1 = 0 After solving the equation the value of a 1 , b 1 , c 1 and d 1 can be obtained as, a 1 = 1 b 1 = 0 c 1 = 0 d 1 = − 1 Therefore, the associated Eigen vector is shown below. v 1 = [ 1 0 0 − 1 ] Substitute − 6 for λ in coefficient matrix, [ 4 + 6 1 1 7 1 4 + 6 10 1 1 10 4 + 6 1 7 1 1 4 + 6 ] [ a 2 b 2 c 2 d 2 ] = [ 0 0 0 0 ] [ 10 1 1 7 1 10 10 1 1 10 10 1 7 1 1 10 ] [ a 2 b 2 c 2 d 2 ] = [ 0 0 0 0 ] The scalar equation are shown below, 10 a 2 + b 2 + c 2 + 7 d 2 = 0 a 2 + 10 b 2 + 10 c 2 + d 2 = 0 a 2 + 10 b 2 + 10 c 2 + d 2 = 0 7 a 2 + b 2 + c 2 + 10 d 2 = 0 After solving the equation the value of a 2 , b 2 , c 2 and d 2 can be obtained as, a 2 = 0 b 2 = 1 c 2 = − 1 d 2 = 0 Therefore, the associated Eigen vector is shown below. v 2 = [ 0 1 − 1 0 ] Substitute 10 for λ in coefficient matrix, [ 4 − 10 1 1 7 1 4 − 10 10 1 1 10 4 − 10 1 7 1 1 4 − 10 ] [ a 3 b 3 c 3 d 3 ] = [ 0 0 0 0 ] [ − 6 1 1 7 1 − 6 10 1 1 10 − 6 1 7 1 1 − 6 ] [ a 3 b 3 c 3 d 3 ] = [ 0 0 0 0 ] The scalar equation are shown below, − 6 a 3 + b 3 + c 3 + 7 d 3 = 0 a 3 − 6 b 3 + 10 c 3 + d 4 = 0 a 3 + 10 b 3 − 6 c 3 + d 3 = 0 7 a 3 + b 3 + c 3 − 6 d 3 = 0 After solving the equation the value of a 3 , b 3 , c 3 and d 3 can be obtained as, a 3 = 2 b 3 = − 1 c 3 = − 1 d 3 = 2 Therefore, the associated Eigen vector is shown below

5th Edition

ISBN: 9780135904206

Author: Edwards

Publisher: PEARSON

See similar textbooks

Concept explainers

Adjacency matrix representation

An adjacency matrix is a square matrix that represents a finite graph. The matrix denotes whether a particular pair of nodes in a graph is adjacent or not. In brief, an adjacency matrix is an array of size N x N, where N is the number of vertices in the …

Question

Chapter 5.2, Problem 41P

Program Plan Intro

Program Description:Purpose of problem is to obtain the particular solution of the coefficient matrix A.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.2, Problem 40P

Chapter 5.2, Problem 42P

Students have asked these similar questions

for the given rectangular coordinates, find two sets of polar coordinates for which 0≤θ<2π, one with r>0 and the other with r<0. (-2sqrt(3),9)

I circled the correct answer, could you show me how to do it using divergence and polar coordinates

The correct answer is D Could you explain and show the steps please

Chapter 5 Solutions

DIFFERENTIAL EQUATIONS+..-MYLAB ACCESS

Ch. 5.1 - Let A=[2347] and B=[3451]. Find (a) 2A+3B; (b)...Ch. 5.1 - Prob. 2P Ch. 5.1 - Find AB and BA given A=[203415] and B=[137032].Ch. 5.1 - Prob. 4P Ch. 5.1 - Prob. 5P Ch. 5.1 - Prob. 6P Ch. 5.1 - Prob. 7P Ch. 5.1 - Prob. 8P Ch. 5.1 - Prob. 9P Ch. 5.1 - Prob. 10P

Ch. 5.1 - Prob. 11P Ch. 5.1 - Prob. 12P Ch. 5.1 - Prob. 13P Ch. 5.1 - Prob. 14P Ch. 5.1 - Prob. 15P Ch. 5.1 - Prob. 16P Ch. 5.1 - Prob. 17P Ch. 5.1 - Prob. 18P Ch. 5.1 - Prob. 19P Ch. 5.1 - Prob. 20P Ch. 5.1 - Prob. 21P Ch. 5.1 - Prob. 22P Ch. 5.1 - Prob. 23P Ch. 5.1 - Prob. 24P Ch. 5.1 - Prob. 25P Ch. 5.1 - Prob. 26P Ch. 5.1 - Prob. 27P Ch. 5.1 - Prob. 28P Ch. 5.1 - Prob. 29P Ch. 5.1 - Prob. 30P Ch. 5.1 - Prob. 31P Ch. 5.1 - Prob. 32P Ch. 5.1 - Prob. 33P Ch. 5.1 - Prob. 34P Ch. 5.1 - Prob. 35P Ch. 5.1 - Prob. 36P Ch. 5.1 - Prob. 37P Ch. 5.1 - Prob. 38P Ch. 5.1 - Prob. 39P Ch. 5.1 - Prob. 40P Ch. 5.1 - Prob. 41P Ch. 5.1 - Prob. 42P Ch. 5.1 - Prob. 43P Ch. 5.1 - Prob. 44P Ch. 5.1 - Prob. 45P Ch. 5.2 - Prob. 1P Ch. 5.2 - Prob. 2P Ch. 5.2 - Prob. 3P Ch. 5.2 - Prob. 4P Ch. 5.2 - Prob. 5P Ch. 5.2 - Prob. 6P Ch. 5.2 - Prob. 7P Ch. 5.2 - Prob. 8P Ch. 5.2 - Prob. 9P Ch. 5.2 - Prob. 10P Ch. 5.2 - Prob. 11P Ch. 5.2 - Prob. 12P Ch. 5.2 - Prob. 13P Ch. 5.2 - Prob. 14P Ch. 5.2 - Prob. 15P Ch. 5.2 - Prob. 16P Ch. 5.2 - Prob. 17P Ch. 5.2 - Prob. 18P Ch. 5.2 - Prob. 19P Ch. 5.2 - Prob. 20P Ch. 5.2 - Prob. 21P Ch. 5.2 - Prob. 22P Ch. 5.2 - Prob. 23P Ch. 5.2 - Prob. 24P Ch. 5.2 - Prob. 25P Ch. 5.2 - Prob. 26P Ch. 5.2 - Prob. 27P Ch. 5.2 - Prob. 28P Ch. 5.2 - Prob. 29P Ch. 5.2 - Prob. 30P Ch. 5.2 - Prob. 31P Ch. 5.2 - Prob. 32P Ch. 5.2 - Prob. 33P Ch. 5.2 - Prob. 34P Ch. 5.2 - Prob. 35P Ch. 5.2 - Prob. 36P Ch. 5.2 - Prob. 37P Ch. 5.2 - Prob. 38P Ch. 5.2 - Prob. 39P Ch. 5.2 - Prob. 40P Ch. 5.2 - Prob. 41P Ch. 5.2 - Prob. 42P Ch. 5.2 - Prob. 43P Ch. 5.2 - Prob. 44P Ch. 5.2 - Prob. 45P Ch. 5.2 - Prob. 46P Ch. 5.2 - Prob. 47P Ch. 5.2 - Prob. 48P Ch. 5.2 - Prob. 49P Ch. 5.2 - Prob. 50P Ch. 5.3 - Prob. 1P Ch. 5.3 - Prob. 2P Ch. 5.3 - Prob. 3P Ch. 5.3 - Prob. 4P Ch. 5.3 - Prob. 5P Ch. 5.3 - Prob. 6P Ch. 5.3 - Prob. 7P Ch. 5.3 - Prob. 8P Ch. 5.3 - Prob. 9P Ch. 5.3 - Prob. 10P Ch. 5.3 - Prob. 11P Ch. 5.3 - Prob. 12P Ch. 5.3 - Prob. 13P Ch. 5.3 - Prob. 14P Ch. 5.3 - Prob. 15P Ch. 5.3 - Prob. 16P Ch. 5.3 - Prob. 17P Ch. 5.3 - Prob. 18P Ch. 5.3 - Prob. 19P Ch. 5.3 - Prob. 20P Ch. 5.3 - Prob. 21P Ch. 5.3 - Prob. 22P Ch. 5.3 - Prob. 23P Ch. 5.3 - Prob. 24P Ch. 5.3 - Prob. 25P Ch. 5.3 - Prob. 26P Ch. 5.3 - Prob. 27P Ch. 5.3 - Prob. 28P Ch. 5.3 - Prob. 29P Ch. 5.3 - Prob. 30P Ch. 5.3 - Prob. 31P Ch. 5.3 - Prob. 32P Ch. 5.3 - Prob. 33P Ch. 5.3 - Verify Eq. (53) by substituting the expressions...Ch. 5.3 - Prob. 35P Ch. 5.3 - Prob. 36P Ch. 5.3 - Prob. 37P Ch. 5.3 - Prob. 38P Ch. 5.3 - Prob. 39P Ch. 5.3 - Prob. 40P Ch. 5.4 - Prob. 1P Ch. 5.4 - Prob. 2P Ch. 5.4 - Prob. 3P Ch. 5.4 - Prob. 4P Ch. 5.4 - Prob. 5P Ch. 5.4 - Prob. 6P Ch. 5.4 - Prob. 7P Ch. 5.4 - Prob. 8P Ch. 5.4 - Prob. 9P Ch. 5.4 - Prob. 10P Ch. 5.4 - Prob. 11P Ch. 5.4 - Prob. 12P Ch. 5.4 - Prob. 13P Ch. 5.4 - Prob. 14P Ch. 5.4 - Prob. 15P Ch. 5.4 - Prob. 16P Ch. 5.4 - Prob. 17P Ch. 5.4 - Prob. 18P Ch. 5.4 - Prob. 19P Ch. 5.4 - Prob. 20P Ch. 5.4 - Prob. 21P Ch. 5.4 - Prob. 22P Ch. 5.4 - Prob. 23P Ch. 5.4 - Prob. 24P Ch. 5.4 - Prob. 25P Ch. 5.4 - Prob. 26P Ch. 5.4 - Prob. 27P Ch. 5.4 - Prob. 28P Ch. 5.4 - Prob. 29P Ch. 5.5 - Prob. 1P Ch. 5.5 - Prob. 2P Ch. 5.5 - Prob. 3P Ch. 5.5 - Prob. 4P Ch. 5.5 - Prob. 5P Ch. 5.5 - Prob. 6P Ch. 5.5 - Prob. 7P Ch. 5.5 - Prob. 8P Ch. 5.5 - Prob. 9P Ch. 5.5 - Prob. 10P Ch. 5.5 - Prob. 11P Ch. 5.5 - Prob. 12P Ch. 5.5 - Prob. 13P Ch. 5.5 - Prob. 14P Ch. 5.5 - Prob. 15P Ch. 5.5 - Prob. 16P Ch. 5.5 - Prob. 17P Ch. 5.5 - Prob. 18P Ch. 5.5 - Prob. 19P Ch. 5.5 - Prob. 20P Ch. 5.5 - Prob. 21P Ch. 5.5 - Prob. 22P Ch. 5.5 - Prob. 23P Ch. 5.5 - Prob. 24P Ch. 5.5 - Prob. 25P Ch. 5.5 - Prob. 26P Ch. 5.5 - Prob. 27P Ch. 5.5 - Prob. 28P Ch. 5.5 - Prob. 29P Ch. 5.5 - Prob. 30P Ch. 5.5 - Prob. 31P Ch. 5.5 - Prob. 32P Ch. 5.5 - Prob. 33P Ch. 5.5 - Prob. 34P Ch. 5.5 - Prob. 35P Ch. 5.5 - Prob. 36P Ch. 5.6 - Prob. 1P Ch. 5.6 - Prob. 2P Ch. 5.6 - Prob. 3P Ch. 5.6 - Prob. 4P Ch. 5.6 - Prob. 5P Ch. 5.6 - Prob. 6P Ch. 5.6 - Prob. 7P Ch. 5.6 - Prob. 8P Ch. 5.6 - Prob. 9P Ch. 5.6 - Prob. 10P Ch. 5.6 - Prob. 11P Ch. 5.6 - Prob. 12P Ch. 5.6 - Prob. 13P Ch. 5.6 - Prob. 14P Ch. 5.6 - Prob. 15P Ch. 5.6 - Prob. 16P Ch. 5.6 - Prob. 17P Ch. 5.6 - Prob. 18P Ch. 5.6 - Prob. 19P Ch. 5.6 - Prob. 20P Ch. 5.6 - Prob. 21P Ch. 5.6 - Prob. 22P Ch. 5.6 - Prob. 23P Ch. 5.6 - Prob. 24P Ch. 5.6 - Prob. 25P Ch. 5.6 - Prob. 26P Ch. 5.6 - Prob. 27P Ch. 5.6 - Prob. 28P Ch. 5.6 - Prob. 29P Ch. 5.6 - Prob. 30P Ch. 5.6 - Prob. 31P Ch. 5.6 - Prob. 32P Ch. 5.6 - Prob. 33P Ch. 5.6 - Prob. 34P Ch. 5.6 - Prob. 35P Ch. 5.6 - Prob. 36P Ch. 5.6 - Prob. 37P Ch. 5.6 - Prob. 38P Ch. 5.6 - Prob. 39P Ch. 5.6 - Prob. 40P Ch. 5.7 - Prob. 1P Ch. 5.7 - Prob. 2P Ch. 5.7 - Prob. 3P Ch. 5.7 - Prob. 4P Ch. 5.7 - Prob. 5P Ch. 5.7 - Prob. 6P Ch. 5.7 - Prob. 7P Ch. 5.7 - Prob. 8P Ch. 5.7 - Prob. 9P Ch. 5.7 - Prob. 10P Ch. 5.7 - Prob. 11P Ch. 5.7 - Prob. 12P Ch. 5.7 - Prob. 13P Ch. 5.7 - Prob. 14P Ch. 5.7 - Prob. 15P Ch. 5.7 - Prob. 16P Ch. 5.7 - Prob. 17P Ch. 5.7 - Prob. 18P Ch. 5.7 - Prob. 19P Ch. 5.7 - Prob. 20P Ch. 5.7 - Prob. 21P Ch. 5.7 - Prob. 22P Ch. 5.7 - Prob. 23P Ch. 5.7 - Prob. 24P Ch. 5.7 - Prob. 25P Ch. 5.7 - Prob. 26P Ch. 5.7 - Prob. 27P Ch. 5.7 - Prob. 28P Ch. 5.7 - Prob. 29P Ch. 5.7 - Prob. 30P Ch. 5.7 - Prob. 31P Ch. 5.7 - Prob. 32P Ch. 5.7 - Prob. 33P Ch. 5.7 - Prob. 34P

Knowledge Booster

Learn more about

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

Program Description: Purpose of problem is to obtain the particular solution of the coefficient matrix A.

Solution Summary: The author explains that the problem is to obtain the particular solution of the coefficient matrix A.

Concept explainers

Program Description:Purpose of problem is to obtain the particular solution of the coefficient matrix A.

Want to see the full answer?

Chapter 5 Solutions