Use the factorization A=PDP^{-1} to compute A^{k}.

ossidianaZ

ossidianaZ

Answered question

2021-05-27

Use the factorization A=PDP1 to compute Ak. where k represents an arbitrary integer.
[a11(ba)0b]=[11101][a00b][11101]
Ak=?

Answer & Explanation

Laaibah Pitt

Laaibah Pitt

Skilled2021-05-28Added 98 answers

Step 1
Given
[a11(ba)0b]=[11101][a00b][11101]
To find
Ak=?
Step 2
We know that,
Ak=PDkP1=[11101][ak00bk][11101]
=[ak11bk0bk][11101]
=[ak11ak+11bk0bk]
=[ak11bk11ak0bk]
Hence,
Ak=[ak11(bkak)0bk]

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