Answered: Find the general solution to the…

Find the general solution to the system: x' = A x + b, where A is the 2 X 2 matrix A = 3 -1 1 5 and b is the 2 X 1 vector b = 5 exp(2t) -3 exp(2t).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Find the general solution to the system:

x' = A x + b, where A is the 2 X 2 matrix

A = 3 -1

1 5

and b is the 2 X 1 vector

b = 5 exp(2t)

-3 exp(2t).

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