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  3. let a be a diagonalizable n × n matrix and let

Let A be a diagonalizable n × n matrix and let P be an invertible n...

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Question

Advance Math

Let A be a diagonalizable n × nmatrix and let P be an invertible n × nmatrix 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 =

40−4
5−1−4
60−6

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