- #1

- 1,267

- 11

Let [tex]A = \left(\begin{array}{ccc}3&0&0\\0&1&2\\0&0&1\end{array}\right)[/tex]

Find a formula for A

This is a weird question, I asked a few tutors for help but none of them were able to help me. They said that this is a weird question.

Does anyone here know how to do that? My friends & I can’t figure it out. Therefore I decided to post it here to see if anyone can show us how this is done.

We haven’t studied eigenvalues & Eigenvectors or diagonalization etc… we have only studied basic Linear Algebra, just as a warning!

Let [tex]A = \left(\begin{array}{ccc}3&0&0\\0&1&2\\0&0&1\end{array}\right)[/tex]

Find a formula for A

^{n}## The Attempt at a Solution

This is a weird question, I asked a few tutors for help but none of them were able to help me. They said that this is a weird question.

Does anyone here know how to do that? My friends & I can’t figure it out. Therefore I decided to post it here to see if anyone can show us how this is done.

We haven’t studied eigenvalues & Eigenvectors or diagonalization etc… we have only studied basic Linear Algebra, just as a warning!

**I have three guesses;**

(I) [tex]A^n = \left(\begin{array}{ccc}3&0&0\\0&1&2\\0&0&1\end{array}\right)^n[/tex]

(II) [tex]A^n = \left(\begin{array}{ccc}3^n&0&0\\0&1^n&2^n\\0&0&1^n\end{array}\right)[/tex]

(III) [tex]A^n = \left(\begin{array}{ccc}3^n&0&0\\0&1^n&0\\0&0&1^n\end{array}\right)[/tex]+[tex]\left(\begin{array}{ccc}0&0&0\\0&0&2\\0&0&0\end{array}\right)[/tex]

**Is any of them close to the correct answer?**