The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system. x₁ = 8x₁ + 3x₂ + 8x3, x'₂ = 3x₁ + 13x₂ + 3x3, x'3 = 8x₁ + 3x₂ + 8x3 What is the general solution in matrix form? x(t)
The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system. x₁ = 8x₁ + 3x₂ + 8x3, x'₂ = 3x₁ + 13x₂ + 3x3, x'3 = 8x₁ + 3x₂ + 8x3 What is the general solution in matrix form? x(t)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
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![**Finding the General Solution of a Linear System Using the Eigenvalue Method**
To determine the general solution to the differential equation system, you can inspect or factor the eigenvalues of the coefficient matrix. The system of differential equations is as follows:
\[ x_1' = 8x_1 + 3x_2 + 8x_3, \]
\[ x_2' = 3x_1 + 13x_2 + 3x_3, \]
\[ x_3' = 8x_1 + 3x_2 + 8x_3. \]
To find the general solution to this system, denoted in matrix form, we use the eigenvalue method.
The matrix form of the solution is:
\[ \mathbf{x}(t) = \boxed{ }
Explore the steps involved in finding eigenvalues and eigenvectors, and use them to formulate the solution to the system of differential equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06bbd155-c9d1-4bdc-8881-0cd893ac016a%2Ff3916c45-e196-4832-b139-7ddf2e98cbba%2F5g67uo1_processed.png&w=3840&q=75)
Transcribed Image Text:**Finding the General Solution of a Linear System Using the Eigenvalue Method**
To determine the general solution to the differential equation system, you can inspect or factor the eigenvalues of the coefficient matrix. The system of differential equations is as follows:
\[ x_1' = 8x_1 + 3x_2 + 8x_3, \]
\[ x_2' = 3x_1 + 13x_2 + 3x_3, \]
\[ x_3' = 8x_1 + 3x_2 + 8x_3. \]
To find the general solution to this system, denoted in matrix form, we use the eigenvalue method.
The matrix form of the solution is:
\[ \mathbf{x}(t) = \boxed{ }
Explore the steps involved in finding eigenvalues and eigenvectors, and use them to formulate the solution to the system of differential equations.
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