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

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CR: Review Exercises
Problem 15CR: For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of...
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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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