The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find general solution of the system. x'₁ = 4x₁ + 3x2+4x3, x'₂ = 3x₁ + 5x2 + 3x3, x'3 = 4×₁ + 3x2 + 4x3

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 30E
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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.
x'₁ = 4x₁ + 3x2+4x3, x'₂ = 3x₁ + 5x2 + 3x3, x'3 = 4×₁ + 3×2 + 4x3
What is the general solution in matrix form?
x(t)=
C₁ + 3C2e111 + C3e2t
-4c2e111-2c3e21
11t
-C₁-11c2e +
Transcribed Image Text: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. x'₁ = 4x₁ + 3x2+4x3, x'₂ = 3x₁ + 5x2 + 3x3, x'3 = 4×₁ + 3×2 + 4x3 What is the general solution in matrix form? x(t)= C₁ + 3C2e111 + C3e2t -4c2e111-2c3e21 11t -C₁-11c2e +
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