Solve the system of differential equations - 12x + 8y y' = – 10x + 6y a (0) %3D — 10, у(0) — — 13 The lesser of the two eigenvalues is Its corresponding eigevector is (a, – 1). What is a? a The greater of the two eigenyalues is

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 35EQ
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Solve the system of differential equations
{3;
x'
12x + 8y
y'
10x + 6y
-
x(0)
– 10, y(0)
- 13
The lesser of the two eigenvalues is
Its corresponding eigevector is (a, – 1). What is a?
a =
The greater of the two eigenvalues is
Its corresponding eigevector is ( – 4, b). What is b?
b:
The solution to the system is
æ(t) =
y(t) =
Transcribed Image Text:Solve the system of differential equations {3; x' 12x + 8y y' 10x + 6y - x(0) – 10, y(0) - 13 The lesser of the two eigenvalues is Its corresponding eigevector is (a, – 1). What is a? a = The greater of the two eigenvalues is Its corresponding eigevector is ( – 4, b). What is b? b: The solution to the system is æ(t) = y(t) =
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