## Question

###### Present at least two methods for computing all arbitrary power of the following HOn-dliagonalizable matrix 12 25 and show that the results given by different methods are the same. Please exclude the naive method (multiplying the matrix many times without using its characteristic equation) . Discuss pros and cOnS The following formulas can be used without proof:mA"= (4 ;)" = (& Am ') 2A +1)A" mA"-1 0)" = ( ~mA"tI ~(m -IA" (9 2 )" = (-nx -4)A"

Present at least two methods for computing all arbitrary power of the following HOn-dliagonalizable matrix 12 25 and show that the results given by different methods are the same. Please exclude the naive method (multiplying the matrix many times without using its characteristic equation) . Discuss pros and cOnS The following formulas can be used without proof: mA"= (4 ;)" = (& Am ') 2A +1)A" mA"-1 0)" = ( ~mA"tI ~(m -IA" (9 2 )" = (-nx -4)A" ~mA"+! mA"-1 (m + 1)A"

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