Let A be a diagonalizable nx n matrix and let P be an invertible n x n matrix such that B = P-AP is the diagonal form of A. Prove that A* = Pe*p-, where k is a positive integer. Use the result above to find the indicated power of A. 10 18 A = -6 -11 A =

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Chapter2: Second-order Linear Odes
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Let A be a diagonalizable nx n matrix and let P be an invertible n x n matrix such that B = P-AP is the diagonal form of A.
Prove that A = P8*p-, where k is a positive integer.
Use the result above to find the indicated power of A.
10
18
A =
-6 -11
A =
Transcribed Image Text:Let A be a diagonalizable nx n matrix and let P be an invertible n x n matrix such that B = P-AP is the diagonal form of A. Prove that A = P8*p-, where k is a positive integer. Use the result above to find the indicated power of A. 10 18 A = -6 -11 A =
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