Fibonacci Probem using Linear Algebra Methods

[Yossarian12]

Homework Statement

If a(0) = 2, a(1) = 3, and a(k+1) = 3a(k) - 2a(k-1), use methods of linear algebra to determine the formula for a(k).

Homework Equations

The Attempt at a Solution

I have found a matrix A such that A^k multiplied by the matrix [a(0)] = [a(k)]
[a(1)] [a(k+1)]
A = [ 0 1 ]
[ -2 3]

But I don't know what to do with this matrix A in order to solve for a(k).

Any help is appreciated. Thanks!

EDIT: The matrices are coming out weird. Matrix A is a 2x2 w/ row 1 being 0, 1...row 2 being -2, 3. The other 2 matrices are 2x1.. the first has a(0) as the first row and a(1) as the second. The other matrix has a(k) as the first row and a(k+1) as the second row.

 

[micromass]

So, actually you're interested in an easy calculation for A^k??
Diagonalizing the matrix will certainly help you there!