# Homework Help: Find formulas for the entries of M^n

1. Apr 25, 2012

### icefall5

1. The problem statement, all variables and given/known data
Let $M = \begin {bmatrix} 8 & -1 \\ 2 & 11 \\ \end{bmatrix}$

Find formulas for the entries of $M^n$, where n is a positive integer.

2. Relevant equations
N/A

3. The attempt at a solution
I honestly have no clue where to start. We recently covered diagonalization, but I can't see how this relates.

2. Apr 26, 2012

### clamtrox

Let's suppose D is the transform that diagonalizes M, and denote $D M D^{-1} = \tilde{M}$. Then
$$M^n = M M M ... M = D^{-1} D M D^{-1} D M D^{-1} D M ... M D^{-1} D = D^{-1} \tilde{M}^n D.$$

3. Apr 26, 2012

### HallsofIvy

Also, The diagonal entries in $\tilde{M}$ are the eigenvalues of the matrix M and the columns of D are the corresponding eigenvectors of M.