Find a general solution of the system = 4x1 + 2x2, x2 = — Зx1 — х2. The matrix form of the system in is х. The characteristic equation of the coefficient matrix is 4 - 2 = (4 – 1)(-1– 1) – 6 3 -1 - A = 12 – 31 – 10 = (1 + 2)(^ – 5) = 0, so we have the distinct real eigenvalues 21 = -2 and 12 = 5. For the coefficient matrix A in Eq. (12) the eigenvector equation (A – AI)v = 0 takes the form [* JD-C) :)-[{] 4 – 2 3 -1- 1 for the associated eigenvector v = [a b]°.
Find a general solution of the system = 4x1 + 2x2, x2 = — Зx1 — х2. The matrix form of the system in is х. The characteristic equation of the coefficient matrix is 4 - 2 = (4 – 1)(-1– 1) – 6 3 -1 - A = 12 – 31 – 10 = (1 + 2)(^ – 5) = 0, so we have the distinct real eigenvalues 21 = -2 and 12 = 5. For the coefficient matrix A in Eq. (12) the eigenvector equation (A – AI)v = 0 takes the form [* JD-C) :)-[{] 4 – 2 3 -1- 1 for the associated eigenvector v = [a b]°.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find a general solution of the system
![Find a general solution of the system
= 4x1 + 2x2,
x2 =
— Зx1 — х2.
The matrix form of the system in is
х.
The characteristic equation of the coefficient matrix is
4 - 2
= (4 – 1)(-1– 1) – 6
3
-1 - A
= 12 – 31 – 10 = (1 + 2)(^ – 5) = 0,
so we have the distinct real eigenvalues 21 = -2 and 12 = 5.
For the coefficient matrix A in Eq. (12) the eigenvector equation (A – AI)v = 0 takes
the form
[* JD-C)
:)-[{]
4 – 2
3
-1- 1
for the associated eigenvector v =
[a b]°.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5022ed2-dbbc-4611-8ce3-11705b138281%2F98c68b6b-8d84-4ec1-bcaa-33ad3bca2937%2Fb9ck1x7.png&w=3840&q=75)
Transcribed Image Text:Find a general solution of the system
= 4x1 + 2x2,
x2 =
— Зx1 — х2.
The matrix form of the system in is
х.
The characteristic equation of the coefficient matrix is
4 - 2
= (4 – 1)(-1– 1) – 6
3
-1 - A
= 12 – 31 – 10 = (1 + 2)(^ – 5) = 0,
so we have the distinct real eigenvalues 21 = -2 and 12 = 5.
For the coefficient matrix A in Eq. (12) the eigenvector equation (A – AI)v = 0 takes
the form
[* JD-C)
:)-[{]
4 – 2
3
-1- 1
for the associated eigenvector v =
[a b]°.
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