Let A be a diagonalizable n x n matrix and let P be an invertible nx 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 the indicated power of A. A = [=¹16 AS A5= -11 -18 10 11 *

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Chapter2: Second-order Linear Odes
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Let A be a diagonalizable n x n matrix and let P be an invertible n x 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 the indicated power of A.
A = [-²6 1
AS
A5=
-11 -18
11
10
*
Transcribed Image Text:Let A be a diagonalizable n x n matrix and let P be an invertible n x 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 the indicated power of A. A = [-²6 1 AS A5= -11 -18 11 10 *
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