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Exercise 103

Avg difficulty 2.5
  1. Compute etAe^{tA} where A=[3−111]A=\left[ \begin{smallmatrix} 3 & -1 \\ 1 & 1 \end{smallmatrix}\right].
  2. Solve x⃗ ′=Ax⃗\vec{x}\,' = A \vec{x} for x⃗(0)=[12]\vec{x}(0) = \left[ \begin{smallmatrix} 1 \\ 2 \end{smallmatrix}\right].

Lebl, Notes on Diffy Qs, §3.8 Matrix exponentials, exercise 103

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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.