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Exercise 101

Avg difficulty 2.5

Let A=[111111111]A = \left[ \begin{smallmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{smallmatrix}\right].

  1. What are the eigenvalues?
  2. What is/are the defect(s) of the eigenvalue(s)?
  3. Find the general solution of x⃗ ′=Ax⃗\vec{x}\,' = A\vec{x}.

Lebl, Notes on Diffy Qs, §3.7 Repeated eigenvalues, exercise 101

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Adapted from Notes on Diffy Qs © 2008–2026 Jiří Lebl. Licensed under CC BY-SA 4.0. Source: Notes on Diffy Qs: Differential Equations for Engineers. Imported at revision 658bcae.