In: Advanced Math
Let A be a diagonalizable n × n matrix and let P be an invertible n × n matrix such that
B = P−1AP
is the diagonal form of A. Prove that
Ak = PBkP−1,
where k is a positive integer.
Use the result above to find A5
A =
|
4 | 0 | −4 |
|
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5 | −1 | −4 | ||||
6 | 0 | −6 |