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Exercise 105

Avg difficulty 2.5

For any positive integer nn, find a formula (or a recipe) for AnA^n for the following matrices:

  1. [74−5−2]\begin{bmatrix} 7 & 4 \\ -5 & -2 \end{bmatrix}
  2. [−34−67]\begin{bmatrix} -3 & 4 \\ -6 & 7 \end{bmatrix}
  3. [0110]\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}

Lebl, Notes on Diffy Qs, §3.8 Matrix exponentials, exercise 105

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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.