Calculator to do the suitable matrix exponentiation

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Reference no: EM13695875

Give the answer of given question and also give details.

Question: Every company makes particular restrictions for passwords, but employees of ABC have particularly strange restrictions. Their passwords may only consist of the lowercase letters a, b and c. Furthermore, for any a in a password, it must be followed by a b or c. For any b in a password, it must be followed by an a, and c may be followed by any of the three letters.

For examples, abaccba is a valid password of length 7. (Note that for both b's, a comes right after them.) Using a transition matrix, find the number of valid passwords of length 12.

You may either use a computer program or a calculator to do the suitable matrix exponentiation and multiplication.

Provide answer in detail: no word count.

Reference no: EM13695875

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