In the following problem apply the eigenvalue method to find a general solution of the given system. If initial values are given, find also the corresponding particular solution. use a computer system or graphingcalculator to construct a direction field and typical solutioncurves for the given system. x'1 = 5x1 - 9x2, x'2 = 2x1 - x2
In the following problem apply the eigenvalue method to find a general solution of the given system. If initial values are given, find also the corresponding particular solution. use a computer system or graphingcalculator to construct a direction field and typical solutioncurves for the given system. x'1 = 5x1 - 9x2, x'2 = 2x1 - x2
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 15EQ
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In the following problem apply the eigenvalue method to find a general solution of the given system. If initial values are given, find also the corresponding particular solution. use a computer system or graphingcalculator to construct a direction field and typical solutioncurves for the given system.
x'1 = 5x1 - 9x2, x'2 = 2x1 - x2
Expert Solution
Step 1
The given system is--
So,
In matrix form, the system can be written as-
Step 2
Let be the eigenvalues of the matrix A.
So,
The eigenvalues are and .
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