| Application of Cayley-Hamilton Theorem | |||
|---|---|---|---|
| 9 | -20 | 12 | |
| 4 | 61 | -168 | 108 |
| 5 | 529 | -1208 | 732 |
| 6 | 4741 | -10568 | 6348 |
| 7 | 42649 | -94808 | 56892 |
| 8 | 383821 | -852968 | 511788 |
| 9 | 3454369 | -7676408 | 4605852 |
| 10 | 31089301 | -69087368 | 41452428 |
| 11 | 279803689 | -621786008 | 373071612 |
| 12 | 2518233181 | -5596073768 | 3357644268 |
If the characteristic polynomial of the matrix A is p(x) = x3 - 9x2 + 20x - 12, then A5 = 529A2 - 1208A + 732I.
See also: Calculation
of An from an Annililating Polynomial