(b) We know that if D = C^-1AC, then A^k = CD^kC^-1. Use this result to compute the following power. bmatrix 1 & 3 \ 3 & 9 bmatrix^6 , (10%)

Ⅲ. The following song, Hero, is a famous song from Mariah Carey. If with this song in hand, how will you, a senior-high homeroom teacher who teaches English, use it as a teaching material for classroom management and what kind of activities will you develop in your English class? (20分)HeroThere's a heroIf you look inside your heartYou don't have to be afraidOf what you areThere's an answerIf you reach into your soulAnd the sorrow that you knowWill melt away *And then a hero comes alongWith the strength to carry onAnd you cast your fears asideAnd you know you can surviveSo when you feel like hope is goneLook inside you and be strongAnd you'll finally see the truthThat a hero lies in you It's a long roadWhen you face the world aloneNo one reaches out a handFor you to holdYou can find loveIf you search within yourselfAnd the emptiness you feltWill disappear(Repeat *) Oh ooohLord knowsDreams are hard to followBut don't let anyoneTear them away, hey yeahJust hold onThere will be tomorrowIn timeYou'll find the way(Repeat *) That a hero lies in youMhhhThat a hero lies in you

題組內容

(b) We know that if \( D = C^{-1}AC \), then \( A^k = CD^kC^{-1} \). Use this result to compute the following power. \[ \begin{bmatrix} 1 & 3 \\ 3 & 9 \end{bmatrix}^6 \] , (10%)

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