Show that the 5 × 5 matrix
has an eigenvalue λ1 of multiplicity 5. Show that three linearly independent eigenvectors corresponding to λ1 can be found. Consider the 5 × 5 matrix given in Problem 33. Solve the system X′ = AX without the aid of matrix methods, but write the general solution using matrix notation. Use the general solution as a basis for a discussion of how the system can be solved using the matrix methods of this section. Carry out your ideas.
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Chapter 8 Solutions
FIRST COURSE IN DIFF.EQ.-WEBASSIGN
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
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